Transcript for:
Pharmacy Math Concepts Overview

hi my name's Amanda and I'm a pharmacist this is my full video presentation series a pharmacy technician math calculations to help prepare for the ptcb pharmacy technician certification exam it includes 10 lectures combined into one video for your convenience and as always if you find this video useful please like share and subscribe and if you'd like to support this Channel with a donation press the heart thanks button to give me a super thanks thanks I really appreciate it the pharmacy technician math calculation lectures in this video include basic math skills ratios and proportions conversions day supply concentrations dilutions allegations IV flow rates temperature conversions and weight-based dosage calculations hope it's helpful hi my name's Amanda and I'm a pharmacist today I'll be talking about basic math skills for pharmacy technicians we'll be covering fractions decimals and percentages and if you find this video useful please press the like button subscribe to my channel and share it with others who may find it helpful too thanks I really appreciate it so basic math skills are the building blocks for solving a variety of Pharmacy calculations this includes fractions decimals and percentages so we'll begin with fractions so what is a fraction a fraction is a portion of a whole indicated by division of the whole into equal parts so for example one-fourth it can be written as one over four or one slash four and sometimes that will be said one per four or as I said one over four so one-fourth means one of four equal parts so you can see I have a pi shape here and we have one of the parts shaded it's divided into four equal parts and we have one part shaded so one of the four equal parts that would be one-fourth so the top number of a fraction that is the portion of the whole and it's called the numerator the bottom number of a fraction that is the whole and it is called the denominator so for our example of 1 4 1 on the top is the numerator and that is the portion and 4 on the bottom that's the denominator and that's the whole so here's another pie to look at so what fraction of this pie is shaded and the answer is two-fourths so two of the four equal parts is what's shaded so two-fourths means that there are two equal parts which are worth one-fourth each so now we'll talk about equivalent fractions I'm a fraction can be changed to an equivalent fraction by multiplying or dividing the numerator and denominator by the same number so for our PI that we just had the example of two-fourths if we divide the numerator and the denominator each by 2 2 divided by 2 equals one four divided by 2 equals two so that equals one-half so 2 4 is equal to one-half and you can see that with our PI it's all it's two-fourths but also if you're looking at it as a as halves um there is one half of it shaded so now we'll talk about when a fraction has an equal numerator and denominator so we have our PI again in the four pieces each piece is worth one-fourth so if we add our fourths we have 1 4 plus 1 4 plus 1 4 plus 1 4 that equals four fourths so we have an equal numerator and denominator and when we have that that is always going to equal one so four fourths equals one so we have four out of the four pieces that's going to be one whole pie and you can see the numerator and denominator are equal now we'll talk about improper fractions so when the numerator and denominator equal the fraction equals one which we just saw in our last slide for like four over four equals one now when the numerator is greater than the denominator the fraction is going to be greater than one and this is known as an improper fraction for example 5 4 5 over 4 . it is equal to 1 and 1 4. and you can see if we have 5 4 here we're going to have one whole Pi which is four fourths plus a fourth of another Pi so that's five fourths it's it's an improper fraction we can convert it to its whole number and the fraction that's remaining which will be 1 and 1 4. so now we're going to talk more about the definition of a fraction look a little closer at that so a fraction is a portion of a whole indicated by division of the whole into equal parts so the line separating the portion and the whole of a fraction it means to divide so per means to divide remember I said one of the ways to say like a fraction like one-fourth is one per four or one over four but per means to divide so for example of one-fourth one over four one fourth equals one divided by four and if we solve that with a calculator or working out the division problem that equals 0.25 so 0.25 is what 1 4 is in decimal form and we'll talk a little more about that when we get to our decimal section so we'll look now at some fraction and decimal equivalents these are common ones that that you may see three-fourths equals 0.75 one-half is 0.5 one-third is 0.33 1 4 is 0.25 1 8 is 0.125 now it's not necessary to memorize this because they can easily calc easily be calculated by dividing but these are helpful to know especially if you aren't familiar with fraction and decimal equivalents now we'll look at a whole number when it's written as a fraction so since a fraction means to divide to write a whole number as a fraction we just simply put it over one so for example the number four written as a fraction would be four over one and you can see that that makes sense because 4 divided by one is four and we know that the fraction line means to divide so 4 equals four over one and this is a very important concept to know for pharmacy conversion calculations and you'll see that in some of the other math videos I've done about how we we put a number over one to set up a conversion now we'll look at multiplying fractions so fractions are often multiplied in Pharmacy conversion calculations so to multiply fractions first we're going to multiply the numerators across remember that's the top number and then we're going to multiply the denominators across that's on the bottom and then we're going to reduce the new fraction to its simplest form so for example if we have 3 4 times 2 3 we're going to multiply the top across the numerators 3 times 2 is 6 and then we'll multiply the denominators across 4 times 3 is 12. and so we get 6 12 well that's not in its simplest form because we know that both of those numbers can be divided by the same number and the highest number that they can be divided by is six so six divided by 6 is 1 and 12 divided by 6 is 2. so that equals one-half in its simplest form okay so that's finishes fractions now we're going to look at decimals so a decimal is a way of writing a fraction expressed as a base of 10 and the word decimal actually means based on 10. so decimals they contain a decimal point on the left side of the decimal point is a whole number and on the right side is the fraction part so I have a little chart here you can see I'm the decimal there I'm on the left you have the whole number this will be the hundreds tens and ones places and then on the right of the decimal that's the fraction portion so that would be tenths hundredths thousandths ten thousandths and it keeps going so for example 0.1 that would be one tenth 2.25 that is 2 and 25 hundredths okay so now we'll just look a little more at the number place values with decimals so you have the decimal point um think of that being in the middle and then on the left side we have the whole numbers which are going to be numbers greater than one and then on the right side we have the numbers that would be less than one these would be the fractions so on the right side we have tenths hundredths thousandths ten thousandths one hundred thousands than millionths and it just keeps going on that way so as it goes to the right it gets smaller and then for their whole numbers as it goes to the left it's going to get larger so from the decimal point to the left we have the ones tens hundreds thousands ten thousands hundred thousands and millions places so that just hopefully explains that a little better so now we'll talk about naming decimals so decimals are named by their lowest place value and it's important to know how to name decimals when we get to some of our calculations so 0.2 we can say 0.2 but that would be 2 10 is the way that that is said by its official name 0.02 is two hundredths and 0.002 would be two thousandths so when a decimal also contains a whole number on the way that you say that you're going to read the whole number first followed by point or and so common way to say it would be 3.125 that that is actually 3 and 125 thousandths okay now we'll look at adding and subtracting decimals so when adding and subtracting decimals be sure that the decimal point is lined up so for example 0.25 plus 0.55 um our decimal points are already lined up so there's nothing we need to do but just make sure they're in a line when we add so 5 plus 5 is 0 carrier one um five plus two plus one would be eight and then our zero plus zero is zero and our decimal point just stays lined up so the answer is 0.80 but since the 0 is the last number of the decimal that can be removed and the value Remains the Same so 0.80 is 0.8 okay now here's another example with subtracting a decimal so 3.25 minus 1.2 in this case we need to add a 0 onto the end of the decimal so that our decimal points line up remember a zero is the last number of a decimal and it could be added or removed and the value will remain the same so we would do 3.25 minus 1.20 and then do the math so 5 minus 0 is 5 2 minus 2 0 and then 3 minus 1 is 2. so we get 2.05 so now we'll talk about how to convert a decimal to a fraction so this is why knowing how to read decimals is important so for example what is 0.1 as a fraction so 0.1 is read as 1 10. well 1 10 as a fraction is 1 over 10. so 0.1 equals 1 over 10 or 1 10. and now another example what is 0.35 as a fraction 0.35 is red as 35 hundredths so 35 hundredths as a fraction would be 35 over 100. so that would be in its fraction form but now we need to reduce it to the simplest form so both of these numbers are divisible by five so we'll do that to reduce it to the simplest form so we'll divide our numerator and our denominator both by five so 35 divided by 5 is 7. 100 divided by 5 is 20. so 0.35 equals seven twentieths okay so here's our chart again of our common fraction decimal equivalence and as I said it's not necessary to memorize this because they can be easily converted to one another but it is helpful to know especially if you aren't familiar with fraction and decimal equivalents so 3 4 is 0.75 one-half is 0.5 1 3 is 0.33 1 4 is 0.25 and 1 8 is 0.125 okay now we're going to look at percentages so a percentage is a number expressed as a fraction of 100 and percent actually means per 100. so percentages contain a percent sign and just to give you an idea about what percentages mean um 100 percent would equal the full amount so you could think of this as the whole pie when we were looking at fractions one percent will be one part out of one hundred so drug strengths are sometimes expressed as percentages and may need to be converted to fractions or decimal amounts so that's what we're going to be focusing on with percentages so I have our chart once again with the common fraction and decimals and I've added the percentage equivalents on here as well so we'll just go over those quickly again 3 4 equals 0.75 which is 75 percent one-half equals 0.5 which is 50 percent one-third is 0.33 which is 33 percent 1 4 is 0.25 which is 25 percent and 1 8 is 0.125 which is 12.5 percent so you can see the similarity between the decimal and percentage equivalents so and you can see that's easily converted so determine a percentage equivalent of a decimal all you have to do is move the decimal point two places to the right so for example just 0.05 that is 5 percent 0.44 we just move the decimal two places to the right and that's 44 percent so now we'll look at converting percentages to fractions so first you're going to write the percentage as a fraction by putting the number over 100. remember percent means per 100 and then we'll reduce the fraction to its simplest form so for example five percent to write that as a fraction would be 5 over 100. okay that's not in its simplest form because both numbers are divisible by five so we'll divide five by five and that equals one and then 100 divided by 5 equals twenty so five percent as a fraction would be one twentieth now if we go the other way and convert a fraction to a percentage what we do is multiply the fraction by 100 over 1. and then reduce the fraction to its simplest form in this case it's usually going to be dividing so our example was 5 8 times 100 over 1. so 5 times 100 is 500 8 times 1 is 8 and then if we do the math and divide 500 by 8 to get it to its simplest form that equals 62.5 percent so 5 8 as a fraction it equals 62.5 percent as a percentage okay now we'll look a little more converting decimals to percentages I briefly touched on that with our chart but we'll just look at a little more detail here so for converting a decimal to percentage we're going to move the decimal point two places to the right so basically what we're doing here is we're multiplying the decimal by 100. and then we'll add a percent symbol so for example 0.65 would be 65 percent 0.2 would be 0.20 remember I I've mentioned before that a 0 is the last number of a decimal can be added and the value Remains the Same which in this case we need to do that to make it a percentage so and then we add our percent sign so that would be 20 percent 0.45 move our decimal two places to the right and then add the percent sign it's 45 percent and the number one if we move our decimal two places we can you know put our zeros on there 1.00 that's the same as one so one equals one hundred percent okay now we'll look at the other way converting percentages to decimals so first we're going to remove the percent symbol and then we'll move the decimal point two places to the left so here we're dividing by one hundred so 99 percent would be 0.99 30 percent would be 0.30 but then since we have the 0 on the end of the decimal we can drop that so it's 0.3 and 82.5 percent would be 0.825 okay now we'll look at a summary of our fractions decimals and percentages there's some key points here so a fraction is a portion of a whole indicated by division of the whole into equal parts and remember we had our examples of the pie where you can see you divided in four equal parts one of the parts is shaded that would be one-fourth if we have two of the parts shaded that would be two-fourths and so a fraction can be changed to an equivalent fraction by multiplying or dividing the numerator remember that's the top number and the denominator which is the bottom number by the same number so for example um two fourths it equals one-half when both would be divided by two and the line separating the portion and the hole of a fraction means to divide remember per means to divide and this is how to convert a fraction to a decimal so for example one-fourth that's one divided by 4 that equals 0.25 when the numerator equals the denominator the fraction equals one so our examples four over four equals one eight over eight equals one three over three that equals one when the numerator is greater than the denominator the fraction is going to be greater than one so for example five over four or three over two that's going to be greater than one to write a whole number as a fraction put it over one so four written as a fraction would be four over one and to multiply fractions multiply the numerators across multiply the denominators across and then reduce the new fraction to its simplest form so for example two-thirds times one-fourth if we multiply across the top and across the bottom we get 2 12 that can be reduced if we divide the numerator and the denominator both by two that would equal 1 6 so a decimal that's a way of writing a fraction expressed as a base of 10 remember decimal actually means based on 10. and on the left side of the decimal point is a whole number and on the right side is the fraction and decimals are named by their lowest place value remember going from the decimal point to the right we have tenths hundredths thousandths ten thousandths and knowing how to read decimal place value is important for converting decimals to fractions for example 0.1 that's 1 10 and that so that's what it equals is a fraction one-tenth one over ten remember a percentage is a number expressed as a fraction of 100 percent actually means per 100. and percentages can be converted to fractions and decimals so to convert a percentage to a fraction put the percentage over 100 and then reduce it to its simplest form to convert a fraction to a percentage multiply by one hundred over one and then reduce it to its simplest form to convert a percentage to a decimal drop the percent symbol and move the decimal two places to the left so basically you're dividing by 100. and to convert a decimal to a percentage move the decimal two places to the right so here you're multiplying by 100 and then add the percent symbol and here's our chart um that we looked at with the common fraction fraction decimal and percentage equivalence 3 4 is 0.75 which is 75 percent one-half is 0.5 which is 50 percent one-third is 0.33 which is 33 percent 1 4 is 0.25 which is 25 percent 1 8 is 0.125 which is 12.5 percent and you can see an example here with our 1 4 it's drawn as the pi we have one part out of the four equal parts shaded and that would be equal to 0.25 and that equals 25 percent just to give you a little more visual there thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name's Amanda and I'm a pharmacist today I'll be talking about ratios and proportions and if you find this video useful please press the like button and subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so first we'll begin with what is a ratio a ratio is a comparison of numbers that indicates their sizes in relation to each other there are two ways to write a ratio as a fraction or with a colon and I'll just give you an example just to show you more what I mean here um if we have five grams of dextrose in 100 milliliters of water this is known as D5W and the ratio of dextrose to water could be expressed as 5 over 100 as a fraction and you would say that 5 per 100 or 5 with a colon 100 and you would say that five to one hundred and most ratios in Pharmacy are stated as a fraction so now we'll look at proportions so what is a proportion proportions Express the relationship between two equal ratios you can think of these as equivalent fractions and I'll just give you an example to show you what I mean here if there are five grams of dextrose in 100 milliliters of water remember this is D5W there will be 10 grams of dextrose in 200 milliliters of water so you can see both the dextrose and the water double and so written as a proportion where you can think of this as equivalent fractions or equal ratios 5 over 100 equals 10 over 200. now we'll talk about ratio and proportion calculations many types of Pharmacy calculations can be solved using ratio and proportion calculations this includes conversions day supply concentrations I'm just to name a few and there are others as well proportions are useful because if three out of the four numbers are known the fourth number can be calculated I'm an unknown number of math is called a variable it's represented by a letter X is commonly used if you know anything about algebra you'll be familiar with this but if not don't worry this you'll still understand how to do this math um the basic steps for solving a proportion calculation you set up equivalent fractions cross multiply then divide and we'll go through some examples here so example number one how many grams of dextrose are in 25 milliliters of a solution containing 5 grams of dextrose in 100 milliliters of water so first we'll set up equivalent ratios what we know is 5 grams of dextrose so 5 grams over 100 milliliters and we'll set that equal to X grams remember X is a variable representing the number we're looking for over 25 milliliters so we have three of the numbers we're going to solve for the for the fourth number to get the answer so we set up the equivalent ratios now we're going to cross multiply this just means to multiply in an x pattern when you have equivalent rate equivalent ratio set up here so we can do 5 times 25 equals 100 times x and if we just simplify that we get 125 equals 100x and then we just have to divide to get our answer to divide to solve for x so we have 125 divided by 100 that will give us x what our answer is we're looking for and that is if we do the math it's 1.25 grams okay now another example of example number two how many grams of sodium chloride are in 50 milliliters of a solution containing 9 grams of sodium chloride in one liter of water and just a note here 9 grams per one liter of sodium chloride solution this is a product called normal saline just something something else to throw in there for you to know so first our steps for our ratio and proportion calculations number one we set up equivalent ratios so what we know is we knew 9 grams of sodium chloride in one liter of water which if you'll remember from our conversion equivalence we know that one liter equals one thousand milliliters an important Point here to know is that the units must match so we have grams and milliliters we want to we want to have grams and milliliters in both of the ratios so 9 grams per 1000 milliliters equals x grams or that's our unknown over 50 milliliters so next we'll cross multiply 9 times 50 equals 1000 times x we simplify that that's 450 equals 1000 X now we'll divide to solve for x so 450 divided by 1000 gives us our answer which is 0.45 grams so just a summary here to review a ratio is a comparison of numbers that indicates their sizes in relation to each other you can think of this usually in Pharmacy as a fraction it's going to be set up proportions Express the relationship between two equal ratios so you can think of proportions as just equivalent fractions and proportions are useful because if three out of the four numbers are known the fourth number can be calculated and the basic steps for solving a proportion calculation number one we're going to set up equivalent fractions two cross multiply and three divide to get our answer thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name's Amanda and I'm a pharmacist today I'll be talking about a type of Pharmacy calculation called conversions and if you find this video useful please press the like button and subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so we'll begin with what are conversions conversions are the changing from one unit of measure to a different unit of measure for example going from ounces to milliliters or grams to milligrams the most common conversions in Pharmacy are for measures of weight and volume and sometimes length so we'll cover those as well the key to conversion calculations is memorization of the commonly used conversion equivalents now we'll look at the different systems of measurement there's the U.S customary system and the metric system these are two systems of measurements that are commonly seen the United States customary system is derived from English units with no pattern of relationship between one another this is the one most of us are familiar with one yard equals three feet equals 36 inches there's not really a pattern of numbers for equivalents the metric system however is based on multiples and fractions of 10 which make converting between larger and smaller units easy so both systems are used in the medical field and many of the common conversions are for changing measurements from one system to the other now we'll look more at the metric system It Centers on a base unit that increases or decreases by multiples and fractions of 10. and there's a prefix that indicates its relationship to the base unit and that's the main thing to look at with this chart is to know the relationship between the prefix and the base units so if you look in the middle of the chart where it says base unit the base units are gram liter and meter and moving up the chart first we see the prefix deci so a decigram would be one tenth of a gram then a centigram would be one hundredth of a gram a milligram would be one thousandth of a gram and a microgram would be one ten thousandth of a gram and then if we come back to the base unit and then going the other way first we have decagram so 10 grams would equal one decagram hectogram 100 grams would equal one hectogram and kilogram one thousand grams would equal one kilogram and I've put in bold here the ones that are the most commonly seen in pharmacy so microgram which is abbreviated with the lowercase Greek letter mu or MC with a G the microgram milligram which is mg or milliliter ml centimeter cm and then kilogram or kg now we'll look at the weight conversions weight conversions are used to determine solid medication dosages and quantities and for Waste bait dosage calculations so this chart are the common weight conversion equivalents that should be committed to memory with gram one gram equals one one thousand milligrams a milligram one milligram equals one thousand micrograms a kilogram one kilogram equals one thousand grams and that also equals 2.2 pounds grain which is gr and one grain equals 64.8 milligrams and I just put a note here gr is the abbreviation for grain that does not equal gram the G or GM is gram so be sure you know the difference between those pound which is lb one pound equals 454 grams now we'll look at the volume conversions and the volume conversions are used to determine liquid medication quantities and doses and here this chart shows the common volume conversion equivalence in pharmacy a teaspoon tsp one teaspoon equals five milliliters a tablespoon which is tbsp one tablespoon equals 15 milliliters which also equals three teaspoons later which is l 1 liter equals one thousand milliliters milliliter or ml one milliliter equals 20 drops and if you remember drops is often abbreviated gtts and that also equals one cc which stands for cubic centimeter for ounce that it's o z or it's also seen as a fluid ounce one ounce equals 30 milliliters and gallon or gal one gallon equals four quarts which equals eight pints and a pint which is PT one pint equals 473 milliliters and the last two on there I have I didn't bold those because those aren't as common but they still are ones you need to know now we'll look at the length conversions as I said length conversions aren't used much in Pharmacy but they're good to know for tests so some common length conversion equivalents inch which is abbreviated in one inch equals 2.54 centimeters meter which is m one meter equals 100 centimeters and feet which is Ft one foot equals 12 inches and now we'll look at how we solve conversion calculations and there are two methods we'll we'll look at today and I just thought the best way to explain this is just to have an example of something that we need to convert and then we'll look at how to solve it so the example here is how many ounces are in 300 milliliters so what we know I said we need to memorize these conversions that were on the tables um one ounce equals 30 milliliters so knowing that with method one what we'll do is set up fractions that cancel like units of measurement and then we'll multiply the fractions to get the answer so there's one ounce per 30 milliliters and you can just think of you know per means to divide so you can set that as a fraction one ounce over 30 milliliters and then that will be times 300 milliliters over one remember to make a whole number into a fraction you just put it over one and then for like units to cancel we have to have one on the top one on the bottom so you see we have a milliliter on the top and the in the second fraction and there's a milliliter on the bottom from the first fraction so we can just Mark those out those cancel and then that leaves us with ounces which is what we are looking for how many ounces and so if we just do the math here we have 300 ounces divided by 30 because our milliliters were canceled out so we're left with is ounces and that equals 10 ounces so just something to remember with this method is the unit that you're looking for must be on the top after your units cancel you want to make sure that the one that you're looking for is left on the top so that that will give you the correct answer now method number two the same problem how many ounces are in 300 milliliters as I said what we know from our memorization one ounce equals 30 milliliters so with this method too we're going to set up equivalent fractions cross multiply and then divide so there's one ounce per 30 milliliters and we're gonna see if that is equal to X ounces where X here is a variable representing the answer we're looking for per 300 milliliters so we've set up this this is sort of an algebra way to do it and the first thing we'll do is cross multiply so we have 1 times 300 mil 300 and that gives us 300. and then we'll divide by the other side to solve for x so so 300 divided by 30 equals 10 ounces and now we'll just look at a summary kind of a review of the conversions video conversions are the changing of one unit of measure to a different unit of measure and memorization is key you have to know the the equivalence to be able to even even begin a conversion calculation and I'll just review the common conversion equivalence once more here one gram equals one thousand milligrams one milligram equals one thousand micrograms one kilogram equals one thousand grams which also equals 2.2 pounds one grain remember this is gr is the abbreviation is 64.8 milligrams one pound equals 454 grams one inch equals 2.54 centimeters so one meter equals 100 centimeters one teaspoon equals five milliliters one tablespoon equals 15 milliliters which also equals three teaspoons one liter equals one thousand milliliters one milliliter equals 20 drops remember drops is abbreviated gtts sometimes which also equals one cc which is a cubic centimeter one ounce equals 30 milliliters one gallon equals four quarts which equals eight pints and one pint is equal to 473 milliliters thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thanks hi my name is Amanda and I'm a pharmacist today I'll be talking about day supply calculations and if you find this video useful please press the like button and subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so first we'll just have an overview of day supply day supply is basically just how many days the quantity of a prescribed medication will last like for example seven days 30 days Etc and this video will cover day supply calculations for solid dosage forms this includes tablets and capsules oral liquids such as suspensions and solutions inhalers and nasal sprays eye and ear drops and injectables will be focusing on insulin so first we'll look at some basic information about the day's Supply calculations days supply for a prescription may be given or it may need to be calculated if the date Supply is given the amount of medication to dispense must be calculated this is done by taking the amount of medication used in one day and multiplying it by the number of days to use the medication so for example the prescription is for taking two tablets per day is for 30 days that will be 2 times 30 which would be to dispense 60 tablets if the day supply needs to be calculated you take the total amount of the medication dispensed and divide that by the amount of medication used in one day and in order to for this to work you these have to be in the same units and this is where the conversion calculations may be needed so for example if you have 60 tablets is going to be the total amount of medication dispensed and the amount of medication used in one day was two tablets you would just divide 60 by two and I would give you 30 days so let's look more closely at the different types of prescriptions for the day supply first we'll start with the solid dosage forms and this includes tablets capsules suppositories or anything that's in a unit dose and I thought the best way to do this is to actually give prescription examples with a question so this first one is for metformin 500 milligram tablets one bid that's one twice a day dispense a one month supply refill times three so how many tablets should be dispensed for this prescription so we'll take our number of tablets used in one day multiply by the number of days that will give us the answer so 1bid that would that's twice a day so that would be a total of two tablets in a day and times one month one month a good number to use for that is just 30 days because that's a good round number so 2 times 30 will be 60 tablets we'll look at another example of solid solid dosage form day supply um this one is Amoxicillin 500 milligram capsules one tid uat means one three times a day until all are taken number 21 to be dispensed and no refills so here we have the quantity and we're going to need to calculate the day supply so what is the day supply for this prescription so we're going to take the total amount of medication dispensed divided by the amount of medication used in one day that'll give us the answer so the total is 21 capsules to dispense and one tid that's one three times a day so that will be a total of three capsules in a day so 21 divided by 3 gives us seven so it's a seven day supply now we'll look at the oral liquids day supply oral liquids this includes suspension Solutions and syrups and this may involve the volume conversion calculations so I thought this would be a good place to review those the common volume conversion equivalents include one teaspoon equals five milliliters one tablespoon equals 15 milliliters which equals three teaspoons one milliliter equals 20 drops which equals one cc one ounce equals 30 milliliters and one liter equals one thousand milliliters so our first prescription we have here is for Amoxicillin 250 milligram per 5 ml suspension and the directions are one teaspoon bid times 10d that's one teaspoonful twice a day for 10 days dispense quantity sufficient Qs and with no refills so how much Amoxicillin suspension should be dispensed for this prescription from our conversion equivalents we know that one teaspoon equals five milliliters so this is for five milliliters one teaspoon bid which is twice a day so that would give us a total of 10 milliliters per day so now we're going to take the amount used in one day and multiply it by the number of days so that's 10 milliliters times 10 those 10 days gives us a total of 100 milliliters is well how much we need to dispense and we'll look at one more example now for the oral liquid State Supply so we have Robitussin AC cough syrup one teaspoon poq4 to 6h PRN cough that's one teaspoonful by mouth every four to six hours as needed for cough a dispense four ounces with no refills so what is the day's supply for this prescription okay from our conversion equivalence we know that one teaspoon equals five milliliters so that's going to be five milliliters six times a day we get the six times a day because the maximum that could be taken would be it could be taken every four hours so there are 24 hours in a day so we would divide 24 by 4 which gives us six times a day so five milliliters times six times a day five times six gives us 30 milliliters that could be taken in one day and now we need to convert our amount dispensed also to milliliters because remember this has to be they have to be in the same units so we have 30 milliliters in one ounce and we're doing four ounces here so be 30 milliliters over one ounce times four ounces over one and our ounces cancel if you remember from our conversion calculations and so we have 30 times 4 gives us 120 milliliters so now we'll just take our total amount of medication dispensed and divide it by the amount of medication used in one day so 120 divided by 30 gives us a four day supply now we'll look at the inhalers and nasal sprays day supply so inhalers and nasal sprays have a specified number of metered doses per container the number of doses per inhaler or bottle of nasal spray is is product specific and can be found by reading the label on the product and the number of doses may be on the product label as metered inhalations this is usually for inhalers or metered sprays this will be for the nasal sprays or it may just say metered doses and we'll look at our first example here albuterol inhaler 90 micrograms one to two Puffs q6h PRN wheezing the spins one inhaler refill times three so that's we know from our albuterol package that it comes the one inhaler has 200 meter doses so if we calculate the maximum amount of medication for one day the max will be two Puffs and it'll be four times a day two six hours you have 24 hours in a day divided by six hours will give us four times a day it could be used so two times four would give us eight a maximum of eight doses per day and we know from our package that it's 200 meter doses so now we'll just do our calculation of the total amount of medication dispensed divided by the amount of medication used in one day so we have 200 divided by 8 and that gives us a 25 day supply and one more example now with a nasal spray we have Flonase nasal spray two sprays QD into each nostril dispense one bottle refill times two so QD is once a day so two sprays once a day and we know from our Flonase bottle it has a 120 metered sprays in it so the amount of medication in one day two sprays into each nostril so you have two nostrils so be two times two that will be four and it's just once a day so it's a total of four sprays a day um so now we're going to take the total amount of medication dispensed divided by the amount of medication used in one day so one bottle we know from the package it has 120 sprays we divide that by four sprays a day and that gives us a total of 30 day supply okay now we'll look at the eye and ear drops they Supply day supply calculations for iron ear drops they typically require a conversion calculation first and it's just the 1ml or milliliter equals 20 drops remember drops can be be abbreviated gtts so iron ear drops come in different size bottles for example we can have a 2.5 milliliter five milliliter or 10 milliliter bottle it's the same product but they just come in different sizes and sometimes a calculation is required to determine the correct bottle size to dispense to the patient with eye and ear drops so we'll look at that an example that as well so our first Iron ear drop example we have a prescription for xalatan 0.005 percent ophthalmic solution and the directions are one gttou qpm that's one drop into each eye every evening dispense 2.5 milliliters with no refills so the question here is what is the day supply for this prescription so the directions are one drop into each eye every evening so that's just one drop and you have two eyes so that will be two drops and once a day so be two times one that gives us a total of two drops per day and we know from our conversion equivalent that one milliliter equals 20 drops so we simply take 2.5 milliliters and multiply it by 20 to find out how many drops are in the 2.5 milliliter package that gives us a total of 50 drops so now we're going to take our total amount of medication dispensed divide it by the amount of medication used in one day so 50 drops is how much is to be dispensed divided by two drops 50 divided by 2 gives us a 25 day supply and one more example in the eye and ear drops and we have prednisolone one percent ophthalmic suspension 2 gtts OS tid times 7D so that's two drops into the left eye three times a day times seven days dispense one bottle with no refills so what size bottle should be dispensed for this prescription and 2.55 or 10 mL sizes are available so those are our choices so this is for two drops three times a day just into one eye so it would be two times three that gives us a total of six drops per day and then we're going to do that for seven days so six drops a day times seven days six times seven is forty two drops total now we know from our conversion equivalence that 20 drops equals one milliliter so what we need to find out now is how many milliliters does 42 drops equal so we simply set up our conversion calculation 1 ml per 20 drops times 42 drops over one our drops cancel out we're left with milliliters and so we have 42 divided by 20. that gives us 2.1 milliliters so the size that would be closest to that would be the 2.5 milliliter bottle now we'll look at the injectable State Supply we're really going to focus on insulin here because that's the most common day supply calculation for injectables on the doses for insulin are specified in number of units to inject and something to know about injectables is they may have a short expiration date after opening and this must be taken into consideration when determining the day supply for these products insulins expire 28 days after opening that's something you you'll want to know the number of units per milliliter in a valve insulin also depends on the specific insulin product a little more details about that u100 insulin is the most common concentration but there are others and with u100 insulin that equals 100 units per milliliter and I've listed here some common u100 insulin products um NovoLog or insulin aspart Humalog which is insulin list Pro Lantus or basiclar which is insulin guard Gene lavamir which is insulin detomir and tresiba which which is insulin degladec so the the common insulins that are in the top 200 drugs are actually u100 insulins but I have a note here that the traceva and the Humalog are also available in u200 so it's just something to watch for the concentration which is the units per mL of insulin is on the package if there are ever any questions you can just look at the package and see what the units per ml is on that and something that's helpful to know a 10 milliliter valve of u100 insulin equals 1000 units so that's something you'll want to memorize so we'll look at a couple examples here Lantus 100 units per milliliter um 5u SQ qhs that's five units subcutaneously which is Under the Skin every night at bedtime dispense a 10 milliliter valve refill times three so what is the day's supply for this prescription so the amount for one day is five units because it's just five units once at bedtime and then a 10 mL a vowel of u100 insulin that's what we're dispensing here equals one thousand units that's that little helpful thing I said to memorize so we'll take the total amount of medication dispensed divide it by the amount of medication used in one day so we have a thousand units divided by five units so that equals a 200-day supply but insulin expires 28 days after opening so the day supply for this prescription would be 28 days one more example here for insulin we have Humalog quick pen u100 20u SQ t-i-d-a-c that's 20 units subcutaneously Under the Skin three times a day before meals um dispense five three milliliter pins and refill times two so what is the day supply for this prescription 20 units three times a day would be a total of 60 units for one day 20 times three and then to find out how much is in the the five pins we have three five three milliliter pins so that'll be a total of 15 milliliters so we know this is u100 insulin so that means 100 units per 1 ml and we'll multiply that by 15 milliliters our milliliters cancel out we're left with our units on the top so that equals 100 times 15 equals 1500 units will be dispensed so now we're going to take our total amount of medication dispensed and divide it by the amount of medication used in one day so we have 1500 divided by 60. and that gives us a 25 day supply and we know insulin is good for 28 days so that day supply we can leave it as is so now we'll just look at a little summary of our day supply calculations day supply is how many days the quantity of prescribed medication will last if day supply is given the amount of medication to dispense has to be calculated and this is done by taking the amount of medication used in one day and multiplying it by the multiplying it by the number of days to use the medication and if day supply needs to be calculated we take the total amount of medication dispensed and divide it by the amount of medication used in one day and remember these must be in the same units for this to work and um conversion calculations may be needed to obtain the same units before the day supply can be calculated so thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more my drug information videos thank you hi my name is Amanda and I'm a pharmacist today I'll be talking about a type of Pharmacy calculation called concentrations and if you find this video useful please press the like button subscribe to my channel and share it with others who may find it helpful too thanks I really appreciate it so we'll start with a definition so what are concentrations um concentrations are the strengths of liquid and topical products and more specifically a concentration is the amount of active ingredient per the total weight or volume of the product so a formula for determining concentration is concentration equals the amount of active ingredient per which means divided by the total weight or volume of the product and there are a few different ways that a product's concentration can be expressed it can be expressed as a drug strength this would be something like amoxicillin suspension 250 milligram per five milliliters that's the concentration as a percentage this will be something like five percent dextrose IV solution five percent is the concentration of that solution or it can also be expressed as a ratio and this will be something like epinephrine one two one thousand injection the drug strength and percentage are the more common ways that a product's concentration is generally expressed a ratio is not as common but we're going to talk specifically about each of these now so first we'll look at concentration as a drug strength concentration is a drug strength is the amount of active drug per a given amount of drug product and remember we're talking here about liquid and topical products so for drug strengths there are many different units of measure it's generally something per something so it can be milligrams per milliliters micrograms per milliliters units per gram grams per milliliters and and so on there are many different units of measure um here are some different types of drug strength concentrations there are amount of drug per dosage unit an example this will be something like albuterol nebulizer solution unit Doses and these come in 2.5 milligrams per three milliliter for each vowel there's also amount of drug per quantity of liquid example of this would be amoxicillin suspension 250 milligrams per five milliliters or there are amount of drug per quantity of a topical product this will be something like Nystatin cream 100 000 units per gram now we'll look at some drug strength concentrations questions question number one how many milligrams of prednisolone are in 100 milliliters of prednisolone 15 milligram per 5 ml solution the way we're going to solve this is we're going to set up equivalent fractions cross multiply and then divide if you've seen any of my other Pharmacy calculation videos you know that this is a very common method for solving Pharmacy math problems so we know the concentration of our prednisolone solution is 15 milligrams per 5 milliliters so that'll be our first fraction 15 milligrams per 5 MLS equals x milligrams that's what we're looking for is how many milligrams per 100 milliliters so another other fraction is X milligrams per 100 milliliters and X here is the variable representing the answer we're looking for next we're going to cross multiply so 15 milligrams times 100 milliliters equals 1500 then we're going to divide to solve for x so 1500 divided by 5 equals 300. so that's 300 milligrams are in 100 milliliters of prednisolone solute 15 milligram per 5 ml solution and also note here that our numerators which is the top number of the fractions they have to be the same units and the denominators have to be the same units which are the bottom numbers of the fractions so and it it is that way the 15 milligrams and then we have X milligrams we have five milliliters and 100 milliliters that always has to be set up for these equivalent fraction this equivalent fraction method to work okay drug strength concentrations question number two how many milligrams of amoxicillin are in 50 milliliters of amoxicillin 400 milligram per 5 ml suspension we're going to solve this one the same way we're going to set up equivalent fractions cross multiply and then divide so we have our concentration of the amoxicillin suspension is 400 milligrams per 5 MLS that'll be our first fraction we'll set that equal to X milligrams that's what we're looking for per 50 milliliters we'll cross multiply so 400 times 50 equals 20 000. and then we'll divide to solve for x so 20 000 divided by 5 equals four thousand so that's our answer there are four thousand milligrams of amoxicillin and 50 milliliters of an amoxicillin 400 per five suspension now we'll look at drug strength concentrations question number three if there are 800 milligrams of acetaminophen in 25 milliliters of Tylenol suspension how many milligrams of acetaminophen are in each teaspoonful so we're going to solve this one the same way we're going to set up equivalent fractions cross multiply then divide so we know the concentration 800 milligrams of acetaminophen per 25 milliliters of Tylenol so our first fraction is 800 milligrams per 25 milliliters and we'll set this equal to X milligrams that's what we're solving for as the milligrams per five milliliters it says in each teaspoon full but one teaspoonful equals five milliliters remember us that our units have to match so we have milligrams and milligrams on the top for the fractions milliliters and milliliters on the bottom of the fractions so next we'll cross multiply so 800 times 5 equals four thousand then we'll divide to solve for x 4 000 divided by 25 equals 160 milligrams so in each teaspoon full of Tylenol suspension there's a 160 milligrams of acetaminophen now we'll look at concentration as a percentage so percent means per 100 or you can think of it as divided by 100. and there are three formulas for concentrations as percentages there's weight per weight or sometimes you may hear this as weight in weight this means grams of drug per 100 grams of product so those are both weight units of measure there's weight per volume or weight in volume and I have a star here beside it because it is the most common one you'll probably see and this means grams of drug per 100 milliliters of product so it's a weight unit on the top and a volume unit on the on the bottom and then there's volume per volume or volume in volume and this is milliliters of drug per 100 milliliters of product so both are milliliters are volume units of measure so you can think of the formula for concentration as a percentage as grams or milliliters of drug per 100 grams or 100 milliliters of the total product and I'll give you an example here if we have five percent dextrose solution this means there are five grams of dextrose per 100 milliliters of solution so 5 grams per 100 ml that is equal you say five per 100 which remember percent means per 100 so 5 per 100 equals 5 percent and here are some common IV product abbreviations and concentrations you'll want to memorize these and what they mean because these are these are common abbreviations in Pharmacy especially in a hospital setting so there's D5W this means dextrose five percent and this means that there are five grams of dextrose and 100 milliliters of sterile water in s that stands for normal saline and that is 0.9 percent NaCl which is sodium chloride and this means a concentration of 0.9 grams of sodium chloride and 100 milliliters of sterile water then there's half in s which is half normal saline this is 0.45 percent NaCl which is sodium chloride and and the concentration of this would be 0.45 grams of sodium chloride in 100 milliliters of sterile water so now we'll look at some percentage concentration questions and we'll start question number one how many grams of dextrose are in 250 MLS of D5W so first we have an abbreviation here of our product so we need to determine the concentration of the product D5W that means dextrose 5 percent so that that means five grams of dextrose per 100 milliliters so next we're going to set up equivalent fractions cross multiply and then divide so our first fraction is going to be our 5 grams per 100 milliliters and we'll set this equal to X grams that's what we're solving for is through the grams per 250 milliliters next we'll cross multiply so we'll take 5 times 250 that equals one thousand two hundred and fifty and then we'll divide to solve for x so then we'll divide by 100 and that equals 12.5 grams so there are 12.5 grams of dextrose and 250 MLS of D5W now we'll look at percentage concentration question number two how many grams of NaCl are in one liter of NS so this again is an abbreviation for a for a product NS is normal saline so we have to we first we have to determine the concentration so NS is normal saline and that's equal to 0.9 percent NaCl and that means 0.9 grams of NaCl per 100 milliliters so now we can set up equivalent fractions cross multiply then divide so we have 0.9 grams per 100 milliliters that's the concentration of the normal saline we're going to set that equal to X grams that's what we're looking for how many grams per 1000 milliliters notice in the question it's one liter is what we're looking for but remember our units have to match the numerator units and the denominator units of the fractions have to match so since we have milliliters in our first fraction has to be milliliters in our second fraction and if you've memorized your conversions you know that one liter equals one thousand milliliters so now that we have that set up we'll cross multiply so we have 0.9 grams times or 0.9 times 1000 and that equals 900 then we'll do then we will divide to solve for x so 900 divided by 100 equals 9 grams so there are 9 grams of NaCl in one liter of normal saline okay we'll look at one more percentage concentration question question number three how many milligrams of hydrocortisone are in one gram of 2.5 percent hydrocortisone cream so this one we're going to set up equivalent fractions cross multiply then divide we don't have to figure out our percentage because it's already given and we just need to know what that percentage means so 2.5 percent that means 2.5 grams per 100 grams so where that's going to be our first fraction and we're going to set that equal to X over 1 gram because we're looking for how much in one gram and our unit for X is going to be grams remember our fractions units have to match what's on the top of one fraction has to be what's on the top of the other fraction and the bottom units have to match as well so first we're going to solve for x and grams and then we'll convert it to milligrams for our final answer here so we have our equivalent fractions set up so now we'll cross multiply 2.5 times 1 that equals 2.5 then now we'll divide to solve for x so 2.5 divided by 100 equals 0.025 grams now we need to convert to our correct units so we need to convert from grams to milligrams and to do this there are 100 milligrams per 1 gram and we're going to multiply that by 0.025 grams over 1. our grams cancel out because there's a gram on the top a gram on the bottom and we're left with milligrams for the top unit so that's that's what we want we want this in milligrams so now we'll just do the math and multiply 1000 times 0.025 and that gives us 25 milligrams so there are 25 milligrams of hydrocortisone in one gram of the height the 2.5 percent hydrocortisone cream now we'll look at concentration as a ratio ratio strength describes a drug concentration in terms of a ratio you can think of a ratio as a fraction with a colon so like 1 to 200 would equal like one per 200. a ratio strength is generally one two something so for example one to one thousand one to two thousand one to ten thousand the formula for ratio strength the concentration is grams to milliliters so for example a ratio strength of 1 to 1000 would mean there's one gram and one thousand milliliters of solution ratio strengths are used to express concentrations of weak Solutions when the percentage strength is very low for example a ratio strength of one to ten thousand is equal to 0.01 percent so you can see how it can be a more convenient way of expressing a low concentration however ratio strengths are not very common anymore because they've been linked to medication errors and in 2016 their FDA required removal of ratio strengths from labels of single ingredient products and they will still still see those on Multi ingredient products and this was to help prevent medication errors labels were changed to express drug strength instead of a ratio so one of those products that was affected was epinephrine injection so it comes in a one to one thousand strength and it also comes in a one to ten thousand strength so you can see how those are very similar just you know one zero is all that makes a difference and it's a they're very different concentrations but because they look similar that could increase the risk for medication errors so these aren't as common the ratio strengths but you know they they still are used somewhat so we'll look at a couple questions with those ratio concentrations question number one how many milligrams of epinephrine are in 10 milliliters of epinephrine one to two hundred solution so we're going to do these very similar to the other concentration problems and we'll set up equivalent fractions cross multiply and then divide so a ratio concentration of 1 to 200 would be equal to one gram per 200 milliliters so that's our first fraction one gram per 200 milliliters and this will set equal to X grams per 10 milliliters remember we are solving for milligrams here but we have to set it for grams because our top numbers of the fractions have to match I mean our top units of the fractions have to match and our bottom units of the fractions have to match so we'll first solve for the X in grams and then we'll convert it to milligrams so now that our equivalent fractions are set up we'll cross multiply 1 times 10 equals ten then we'll divide to solve for x 10 divided by 200 equals 0.05 grams now we'll convert to the correct unit we're going from grams to milligrams so we'll do 1000 milligrams per one gram that's how many milligrams are in a gram times 0.05 grams per over one just to put it over something because the number over one is equal to itself so now our grams cancel out because we have a gram on the top of a fraction and one on the bottom so those cancel we're left with the unit of milligrams now we'll do the math multiply 1000 times 0.05 and that equals 50 milligrams so there are 50 milligrams of epinephrine and 10 milliliters of an epinephrine 1 to 200 solution you can also do the conversions of grams to milligrams by moving the decimal place and if you know how to do that that's that's great but I like to set it up this way just so that you're sure that you're getting the correct going the correct way moving the decimal place and that this is a good way to check because your the unit that you're looking for is always going to be left on top and your other units will cancel out okay ratio concentrations question number two if an epinephrine product has a strength of one milligram per milliliter what is the concentration expressed as a ratio so first we need to convert to correct units for equivalent fractions remember the ratio units is or grams two milliliters so first we'll convert milligrams to grams remember one gram equals one thousand milligrams so we have one gram per 1000 milligrams times one milligram over one and that is will our milligrams cancel because there's one on the top one on the bottom we're left with the unit of grams and that is equal to 0.01 grams so now we'll set up our equivalent fractions cross multiply and then divide so our first equivalent fraction would be 0.01 grams per one milliliter that that's what we took from our ratio remember it's grams per milliliter so that's our ratio and we'll set that equal to one gram per X milliliters this one's a little different we know that a ratio concentration is one two something so our one gram is at the top and we're solving for the X milliliters on the bottom so we'll cross multiply and divide to get our answer one times one equals one then we'll divide by 0.001 and that gives us one thousand milliliters but that's not our answer because we're looking for a ratio so our answer is if an epinephrine product has a strength of one milligram per milliliter what's the concentration expressed as a ratio it's one to one thousand so it's that that the entire second fraction one gram to one thousand milliliters or one to one thousand okay now we'll just look at a summary and some key points to remember about concentrations concentrations are the strengths of liquids and topical products remember as a formula this would be the amount of drug per the total weight or volume of the product um there are drug strength concentrations remember these come in many units of measure milligrams per milliliter grams per milliliter micrograms per milliliter units per gram many different units of measure percentage concentrations percent means per 100 and the units for a percentage concentration are grams or milliliters per 100 grams or 100 milliliters so we have to be in grams and milliliters with percentages and then there are ratio concentrations ratio generally means one two something and the units for ratio concentrations are grams to milliliters and the steps for solving concentration questions first we're going to set up equivalent fractions with correct units remember our top numbers of the fractions have to match units and the bottom numbers of the fractions have to match units we're going to cross multiply and then divide to solve for x and then we'll convert our answer to the correct unit what was asking the question if needed that isn't always necessary thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name's Amanda and I'm a pharmacist today I'm going to be talking about a type of Pharmacy calculation called dilutions and if you find this video useful please press the like button subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so first we'll begin with a definition what are dilutions dilutions are drug products with increased volume which causes a decrease in concentration when a product is diluted the quantity of active ingredient actually Remains the Same but the concentration of the product decreases because of the increased volume so I have an illustration here you can see the small circle with the five dark blue circles inside it and we'll say that's five grams per 100 milliliters is its concentration which is five percent so dilution which is adding more volume we'll say we add 100 milliliters to this that's going to give us a concentration now of 5 grams per 200 milliliters which would be 2.5 percent so you can see our drugs drug amount the active ingredient actually Remains the Same Same in both cases it's five grams but the amount of volume is what is increased so that's what dilutions are about um there's there are a couple different types of dilutions we're going to talk about there are liquid dilutions these are weight per volume usually in the units of gram per milliliter and these are solutions solid dilutions these are weight per weight generally you see these in gram per gram and this includes creams and ointments and Pharmacy dilution problems typically involve determining how to make a weaker product from a more concentrated stock product and this is our formula for solving dilution problems q1 times C1 equals Q2 times C2 and you'll want to memorize this q1 is quantity one and we're going to multiply that by concentration 1 and that will equal quantity 2 times concentration 2. and when we know 3 out of the four variables will be able to solve for the one the the one that we need and something to remember about this the quantity units must match so if it's a quantity of grams both quantities have to be in grams q1 and Q2 and the concentration units must match so if the concentration is in a percentage they might both must be a percentage C1 and C2 both have to be a percentage or if they're in a strength like milligrams and they would both have to be milligrams and the answers are going to be what units are used so if we're solving for we have a percent in in C1 and we're solving for C2 percent will be what the answer units are now we'll look at some example questions about dilutions we'll begin with question number one and this is part a how many milliliters of a five percent stock solution are required to make one liter of a 0.5 percent solution so first we're going to determine the known variables of the dilution formula and our dilution formula is q1 times C1 equals Q2 times C2 so for quantity one that's what we're going to be looking for because it's how many milliliters the concentration of this is five percent it's how many milliliters of a five percent stock solution so q1 times 5 percent equals and for part two of the equation we're going to it's one liter of a 0.5 percent solution so our Q2 is going to be one liter but since we're going to asking for how many milliliters we'll put in one thousand milliliters since one liter equals one thousand milliliters because remember our quantities must match in units and so be a thousand milliliters times 0.5 percent now we're going to solve for our unknown variable in this case it was q1 quantity one so q1 times 5 equals one thousand times 0.5 1000 times 0.5 is 500 and then to solve for Quant for q1 we're going to divide both sides by 5. so 500 divided by 5 equals one hundred so q1 equals 100 milliliters so 100 is how many milliliters of the five percent stock solution are required to make one liter of the 0.5 percent solution now we'll look at Part B of question one how much sterile water should be added to make the final product so if you look at our question you know we need a total of one liter which is one thousand milliliters for the final product we know from part A solving part A that 100 milliliters will be the five percent stock solution so now we need to determine the volume to add and we'll do this by taking the total volume needed and subtract the stock solution needed and that will give us the volume to add so 1 000 milliliters minus 100 milliliters equals 900 milliliters so we need 100 milliliters of the five percent stock solution and then we'll need 900 milliliters of the sterile water and that will make a total of one liter or a thousand milliliters of the 0.5 percent solution question number two how many grams of five percent hydrocortisone ointment and ointment base must be combined to obtain 100 grams of one percent hydrocortisone ointment so first we're going to determine the known variables of the dilution formula so q1 again that's what we're looking for in this question as well because it's how many grams and the concentration is five percent that goes with part one so be q1 times 5 percent and that equals Q2 which will be 100 grams of concentration 2 which is one percent so 100 grams times one percent so now we need to solve for our unknown variable which in this case is q1 so q1 times 5 equals 100 times 1. 100 times 1 is 100 then we'll divide by five for both sides to solve for q1 and 100 divided by 5 equals twenty so q1 will be 20 grams of five percent hydrocortisone ointment is what's needed for this so now the other part of the question it asks for how much hydrocortisone the five percent hydrocortisone ointment and also how much of the ointment base so if we know we need 20 grams of 5 hydrocortisone we're making a product that's a total of 100 grams so we will take 100 grams minus our 20 grams and that gives us 80 grams of the ointment base will be needed so to prepare this we will add 20 grams of the 5 hydrocortisone ointment 80 grams of the ointment base and that will give us a total of 100 grams of one percent hydrocortisone ointment question number three if you combine 30 grams of 5 lidocaine ointment with 15 grams of ointment base what is the new percent strength so this is a solid dilutions problem so we're going to do it the same way we're going to determine the known variables of the dilution formula so q1 times C1 equals Q2 times C2 so q1 in this case is 30 grams and our C1 is 5 so 30 grams times 5 percent and then Q2 that's going to be our total of our product which we know we're putting 30 grams plus 15 grams so our Q2 is going to be 45 grams here so be 45 grams times C2 so now we're going to solve for our unknown variable in this case it's C2 so 30 times 5 equals 45 times C2 30 times 5 is 150 then we divide both sides by 45 to give us what C2 equals so 150 divided by 45 equals 3.3 percent that will be our new percent strength of our final product of concentration two and you can see the reason that's percent is because that was it was percent um for C2 or C1 was percent so C2 also has to be percent just as we had q1 was grams Q2 also was grams so we always always make sure your units match for quantities and then the units match for concentrations and your answer will be in whatever those units are whether you're solving for concentration or quantity okay now we'll look at a summary and just some key points to remember about dilutions dilutions are drug products with increased volume and when we have this increased volume this is going to decrease the concentration but the active drug ingredient Remains the Same some types of dilutions include liquid and solid liquid ones are generally in grams per milliliter this includes Solutions solid dilutions are generally in grams per gram this includes creams and ointments and our formula for solving dilution problems is q1 times C1 equals Q2 times C2 where Q stands for quantity and C stands for concentration and remember our quantity units must match and our concentration units must match and the answers are going to be in what units are used and our steps for solving concentration questions first we'll determine the known variables of the dilution formula and then we'll solve for the unknown variable thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name is Amanda and I'm a pharmacist today I'm going to be talking about a type of Pharmacy calculation called allegation if you find this video helpful please press the like button subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so we'll begin with what is allegation allegation is a method for calculating the amounts of two concentrations of the same drug needed to make a different concentration from what is available so allegation can be used for various products including liquids and creams and it's useful in compounding and I'm going to give you an example just so you can see what I'm talking about a prescription requires 100 milliliters of a 20 solution you have 50 and 10 percent of that solution in stock how much of each solution should be mixed to make 100 milliliters of 20 solution so we'll solve this in a few minutes but I just want to give you an example just so you can see exactly what I'm talking about you have two concentrations of the same drug and you're going to make a different concentration using those two that you have so one concentration is stronger and one is weaker than is the desired concentration in all allegation problems so part of the difficulty in solving allegation calculations is being able to recognize them to recognize an allegation calculation number one there will be two concentrations available so two different strengths will be specified that are available and number two a different concentration is required to be made from those two concentrations that you have so there are two methods for solving allegation calculations I'll be covering both of these and use the one that's easiest for you there's the ratio method and the tic-tac-toe method so first we'll look at the allegation ratio method step one what we're going to do is identify the high concentration which I'll refer to as HC the low concentration or LC and the desired concentration which I call DC step two we'll subtract to obtain the ratio of HC to LC so the desired concentration minus the low concentration will give us the high concentration ratio value then the high concentration minus the desired concentration will give us the low concentration ratio value so we'll just put those in the HC to LC those numbers and step three we'll add the HC ratio value and the LC ratio value to determine the total number of parts so that will give us the total number when we add those together and step four we're going to set up fractions and multiply by quantity needed I guess this will be given in the problem to obtain how much of each concentration is needed so that's just an overview of the steps to do the ratio method and now we'll look at the example that I gave you at the beginning and we'll solve that using the ratio method so the example was a prescription requires 100 milliliters of a 20 solution you have fifty percent and ten percent of that solution in stock how much of each solution should be mixed to make 100 milliliters of 20 solution so step one we're going to identify the high concentration the low concentration and the desired concentration so HC is 50 LC is 10 and DC is 20. now we're going to subtract to obtain the ratio of HC to LC so the DC minus LC will be 20 minus 10. that will give us 10. and then the HC minus the DC will give us the LC ratio value that will be 50 minus 20 so that equals 30. so our HC to LC are high concentration to low concentration ratio will be 10 to 30 or you can reduce that to one to three but you don't have to reduce it you could go with the 10 to 30 but I just reduced it to keep the numbers more simple okay now in step three we're going to add the HC ratio value and the LC ratio value to determine the total number of parts so our ratio is one to three so one part of high concentration to three parts of low concentration is what that ratio means and so we'll add one plus three and that gives us the total it gives us a total of four parts now in step four we're going to set up a fraction and multiply by quantity needed which will be given in the problem in our problem you can see it's a hundred milliliters of how much of the final solution we need and this will help us to obtain how much of each concentration is needed okay so for our HC our high concentration the ratio value for it is one so our fraction will be one fourth because there are four Total Parts so one over four and then times 100 milliliters because that is our quantity to be made and if we do the math there we do one times a hundred then divided by 4 will give us 25 milliliters of the high concentration which is the 50 solution then for the low concentration our ratio value is three so three out of 4 3 4 because 4 is the total Parts times 100 milliliters so 3 times 100 is 300 then divided by 4 that gives us 75 milliliters of the low concentration which is the 10 percent and you can see that the 25 milliliters and the 75 milliliters add up to 100 milliliters so that will give us 100 milliliters of 20 solution if we mix 25 milliliters of 50 solution and 75 milliliters of the 10 solution okay so now we're going to look at the allegation tic-tac-toe method so step one with it we're going to identify the high concentration low concentration and desired concentration and we're going to place them at the correct location in a tic-tac-toe grid so you can see where it gets its name and the high concentration is going to go in the top left the desired concentration will go in the very center and the low concentration goes in the bottom left now for step two we're going to find the differences diagonally so we're going to find the difference between the high concentration and the desired concentration and we're going to write that in the bottom right grid then we're going to find the difference in the low concentration and the desired concentration and we'll write that in the top right grid next we're going to add the differences vertically so we'll add the difference between the low and the desired concentration with the difference between the high concentration and the desired concentration and this will give us the total parts next we're going to determine the fraction of each needed so for the high concentration and this will be at the top we have the difference between the LC and DC number that we have there that will be our HC part and then we will put that over the total part so that will be our high concentration fraction and then we'll do the same thing for the low concentration we'll take the number we have there in the bottom right box that's the difference between the high concentration and desired concentration that's our low concentration part and we'll put that over the total part so that will give us our low concentration fraction now we're going to multiply each fraction by the quantity needed remember this is given in the problem and this will allow us to obtain how much of each concentration is needed so we'll take our high concentration fraction which is our high concentration part over our total concentration part multiply that by the quantity needed that will give us our amount of high concentration solution needed then we'll take for our low concentration fraction it's the low concentration part over the total part we'll multiply that by the quantity needed that will give us the amount of low concentration needed so now we'll go through this with an example the tic-tac-toe method so we'll use the same example a prescription requires 100 milliliters of a 20 solution you have 50 and 10 percent in stock how much of each solution should be mixed to make a hundred milliliters of 20 solution so first we're going to identify our high concentration desired concentration and low concentration and we'll place them in the correct location in your tic-tac-toe grid so remember the high concentration goes in the top left corner the desired concentration goes in the center and then the low concentration goes in the bottom left now we're going to find the differences diagonally so with the high concentration the difference between 50 and 20 will give us 30 and we'll put that in the bottom right and then diagonally for the low concentration the difference between 10 and 20 that gives us 10 and we'll put that in the top right next we're going to find the total parts and we'll do this by adding the differences vertically so we have 10 plus 30 and that gives us 40. so 40 is our total parts now we're going to determine the fraction of each needed so for the high concentration um it's a it's 10 Parts out of the out of 40 is our total parts so our high concentration fraction is 10 out of 40. and for the low concentration we have 30 parts out of the total 40 parts so it's 30 out of 40. now we're going to multiply each fraction by the quantity needed that's given in our problem which is 100 milliliters in this problem and this will allow us to obtain how much of each concentration is needed so our high concentration fraction was 10 out of 40 so times 100 milliliters so you can do that 10 times 100 which is a thousand divided by 40 equals 25 milliliters of the 50 solution that's our high concentration and then the low concentration fraction was 30 out of 40. so 30 times 100 that gives us 3 000 divided by 40. that equals 75 milliliters so that will need 75 milliliters of the low concentration solution which is the 10 solution and you can see we got the same exact answer just a little bit different methods of doing it but you can see it you add the 25 milliliters and the 75 milliliters and that gives us a hundred milliliters total and now of 25 milliliters of the 50 solution plus 75 milliliters of the 10 solution that will give us 100 milliliters of 20 solution so now we'll just go over a summary and some key points to remember remember allegation is a method for calculating the amounts of two concentrations from the same drugs needed to make a different concentration from what's available one concentration is stronger or higher I refer to this as HC and one is weaker or lower this will be LC low concentration and then the desired concentration which is DC and allegation problems can be solved using the ratio method or the tic-tac-toe method I use the one that makes the most sense for you and both allegation methods are ways to determine the amounts of the high concentration low concentration needed to make the desired concentration just a summary of the ratio method steps you're going to identify the high concentration low concentration and desired concentration from the problem subtract to obtain the high concentration to low concentration ratio and to get this you'll take the DC minus the LC that will give you the HC ratio value then you'll take the HC minus the DC and that will give you the LC ratio value next you'll add the HC and LC ratio values to obtain the total parts and then set up fractions and multiply by the quantity needed so you'll set up a fraction with the low concentration ratio value over the total parts and multiply that by the quantity needed that will give you your low concentration quantity amount and then for the high concentration ratio value over the total Parts times the quantity needed that will give you your high concentration quantity amount and then a summary for the tic-tac-toe method first you'll identify the high concentration low concentration and desired concentration and place them in the correct location in the tic-tac-toe grid remember the high concentration goes in the top left the desired concentration goes in the center and the low concentration goes in the bottom left then you're going to find the differences diagonally write those numbers in the grid then add the different parts add the differences vertically to get the total parts and then you'll determine the fraction of the high concentration which will be across the top and the low concentration which will be on the bottom and you'll just put the high concentration amount over the total parts and the low concentration amount over the total parts that will give you those fractions and then multiply each fraction by the quantity needed which like I said before it's it's specified in the problem thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name is Amanda and I'm a pharmacist today I'll be talking about a type of Pharmacy calculation called IV flow rates and if you find this video useful please press the like button and subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so we'll begin with what are flow rates a flow rate is the volume per time that a medication is delivered by intravenous or IV route to a patient it's also known as a drip rate or infusion rate so you can see flow rate equals volume per time so volume this is for liquid measurements it can be liters milliliters or drops time this is a Time measurement such as hours or minutes and just to show you some examples of some common flow rate units there could be milliliters per hour or drops per minute and there you see it's a volume per time so now we'll talk a little bit about Avi Administration sets IV Administration sets or IV sets deliver IV solution to the patient by connecting to the IV bag Ivy sets work by either a gravitational drip chamber you can see this in photo one or an electronic infusion pump and this is an example in photo 2. electronic pumps they can be set at various flow rates but with a gravitational drip chamber IV set they have different drop factors that are used in flow rate calculations now we'll talk a little more about that a drop factor or also known as a drip factor is the number of drops it takes to have a volume of one milliliter so the drop Factor units are drops per ml or if you remember in our abbreviations drops is abbreviated gtts so gtts per ml there are different IV sets that have different drop factors there's what's known as macro sets and macro means large so you can think of these as having a large amount with each drop for example 10 drops per milliliter it would only take 10 drops to make one milliliter and then there are micro sets and micro means small so you can think of these as having a small amount with each drop so an example would be 60 drops per milliliter the drops are small so it's going to take more drops for one milliliter in this case 60 drops now we'll talk about solving flow rate calculations and flow rate calculations can be solved by using conversions and ratio and proportion calculations and it's important that you know the common conversions conversions that are often seen in flow rate calculations include volume time and dosage ones and here I have a table that shows some of the common conversions for flow rate calculations liters to milliliters so one liter equals one thousand milliliters hours and minutes um one hour equals 60 minutes grams with Mill milligrams I'm one gram equals one thousand milligrams and milligrams with micrograms one milligram equals one thousand micrograms now we'll look at the steps for solving flow rate calculations first you want to identify the unit or units the problem is asking for this could be just a single unit such as milliliters or hours or it could be multiple units such as milliliters per hour next you want to use the other information in the problem to get the units needed and there are two methods for this and if you've seen any of my other Pharmacy calculations videos you'll recognize these methods are from my conversions video so it's the same exact methods method number one you can set up fractions that cancel like units leaving the desired units only then multiply the fact fractions so for example if we're trying to convert five hours into minutes here we know there are 60 minutes per one hour times five hours over one we have an hour on the top an hour on the bottom so those units cancel we're left with minutes and then we just multiply the fractions so 60 times 5 is 300 then divided by 1 times 1 which is one that gives us 300 minutes or we can use method two set up equivalent fractions cross multiply then divide to solve for x so for this example um we'll we'll use the same example as the five hours converting it to minutes so there are 60 minutes per one hour and we'll set that equal to X minutes per five hours and notice with these you have to have the same units on the top and the same units on the bottom so we have minutes on the top hours on the bottom so 60 times five it's our cross multiplication is 300 then we'll divide by one that gives us 300 and that is that solves for X so X here is 300 minutes and you can use whichever method makes the most sense for you or whichever method makes the most sense for the problem that you're solving okay now we'll look at some examples of flow rate calculations and this is example one and I'm going to work through both methods with all of our examples so you can see multiple ways to do these calculations so this is with method number one so our order is for 1200 milliliters of NS and NS stands for normal saline and this is 0.9 percent sodium chloride solution so 1200 milliliters of normal saline to be infused over eight hours how many milliliters will be infused every hour so first we're going to identify our units the problem's asking for and here it's milliliters so with method one we'll set up our fractions that cancel like units then multiply the fractions so we can know there's 1200 milliliters per eight hours milliliters is the unit that we're wanting and then times one hour we want to know how many milliliters for every hour so be one hour over one we have an hour on the top an hour on the bottom so the hours cancel we're left with milliliters and if we do the math 1200 times 1 is 1200 divided by 8 times 1 which is eight that gives us 150 milliliters and if you're using method one um if there's only one unit that you're trying to solve for make sure it's on top and I will make sure that you get the correct answer and just remember there for units to cancel you must have it one unit on the top and one on the bottom that's how they'll cancel and to make a fraction that has only one unit you can you just put a one with it that could be either on the top or the bottom in this case it was on the bottom okay now we'll look at the same example with method number two so example number one with method number two so our order was for 1200 milliliters of normal saline to be infused over eight hours how many milliliters will be infused every hour so here we're looking for milliliters and with method two we're going to set up equivalent fractions cross multiply then divide to solve for x so we know there's 1200 milliliters per 8 hours and we'll set that equal to X milliliters per one hour and where X here it's the variable representing the answer we're looking for and our unit of the top fractions which those are numerators they have to match and they do they're both milliliters and the unit of the bottom fractions which are denominators those must match and they do they're both hours so now we'll just cross cross multiply then divide to solve for x so so 1200 times 1 equals 1200 and then we'll divide by 8 to solve for x so 1200 divided by 8 equals 150 milliliters okay now we'll look at example number two with method number one so it's very similar problem here we have 1200 milliliters of normal saline to be infused over eight hours how many milliliters will be infused every 10 minutes so we're looking again for milliliters but we're instead of for every hour we're going to find for every 10 minutes so with method one we'll set up our fractions that cancel like units then multiply the fractions to get the answer so we have 1200 milliliters per eight hours times one hour per 60 minutes and we have an hour on the top an hour on the bottom so those cancel and then we have I'm going to multiply that by 10 minutes over one so now we our minutes will cancel we have a minute on the top a minute's on the bottom those cancel and we are left with what we want milliliters so now we'll just do the math 1200 times 1 times 10 equals twelve thousand and then divided by 8 times 60 which is 480. so 12 000 divided by 480 equals 25 milliliters okay now we'll look at the same example with method number two so 1200 milliliters of normal saline to be infused over eight hours how many milliliters will be infused every 10 minutes so we are looking for milliliters here and with method two we'll set up equivalent fractions cross multiply then divide to solve for x so we know 1200 milliliters and we're going to set that over 480 minutes and in the rectangular box here I have how I converted the eight hours into 480 minutes so one hour equals 60 minutes and then there are eight hours here so eight hours times 60 that equals 480 minutes so that's why we have 1200 milliliters over 480 minutes and we'll set set that equal to X milliliters over 10 minutes so 1200 times 10 it's our cross multiplying equals 12 000 and then we'll divide by 480 to get X and that equals 25 milliliters okay now we'll look at example number three with method number one our order is for 500 milliliters of D5W and D5W that means dextrose five percent in water solution so 500 milliliters of D5W to be infused over six hours what is the flow rate in drops per minute and drip rate equals 60 drops per milliliter so if we identify our units the problem's asking for it's drops per minute so with method one we know there are our drip rate is 60 drops per milliliter we'll multiply that by 500 milliliters per six hours so we have a milliliter on the top and a milliliter on the bottom and those cancel and then we know there's one hour per 60 minutes so we'll multiply that by one hour over 60 minutes so we have an hour on the top an hour on the bottom and those cancel and we're now left with our drops on the top and minutes on the bottom so that will give us the correct answer once we do the math so 60 times 500 times 1 that equals thirty thousand divided by 6 times 60 that's 360. and that gives us 83.3 and we'll round that to 83 so it's 83 drops per minute okay now we'll look at example number three with method number two um our order is 500 milliliters of D5W to be infused over six hours what is the flow rate in drops per minute and our drip rate is 60 drops per milliliter so if we identify our units we're looking for drops per minute and with method two we'll set up equivalent fractions cross multiply then divide to solve for x so we have 60 drops per one milliliter that's our drip rate and we'll set that equal to X drops per 500 milliliters so this will give us the the first unit our drops with this one so 60 times 500 equals 30 000 and then divided by 1 that gives us thirty thousand so it's 30 000 drops now we need to look at the time part of this we know one hour equals 60 minutes and this is for six hours so six hours times sixty would be 360 minutes so we'll take thirty thousand drops divided by 360 minutes and that gives us 83 drops per minute okay now we'll look at example number four using method one so our order is for one liter of D5W to be infused over six hours if using a 10 drop per milliliter IV set how many drops per minute will be delivered to the patient so identify our units the problems asking for and this is drops per minute and with method one we'll set up our fractions that cancel like units then multiply the fractions so we know one liter equals one thousand milliliters so we'll we'll start with that one thousand milliliters per one times ten drops per one milliliter times one hour per 60 minutes times one over six hours and this cancels milliliters cancel we have a milliliter on the top milliliter on the bottom we have an hour on the top an hour on the bottom and that leaves us with our units we want drops per minute drops on the top minutes on the bottom so we'll do the math 1000 times 10 times 1 times 1 would be ten thousand and then we'll divide that by one times one times sixty times six which would be 360. and that gives us 27.8 drops per minute and we'll round that to the nearest number which would be 28 drops per minute okay now we'll look at the same example example four with method number two so our order is for one liter of D5W to be infused over six hours if using a 10 drop per milliliter IV set how many drops per minute will be will be delivered to the patient so we're looking for drops per minute and with method two we'll set up our equivalent fractions cross multiply then divide to solve for x so 10 drops per one milliliter equals x drops per 1000 milliliters because we know that one liter equals a thousand milliliters we can go ahead and do that so if we cross multiply and divide we have 10 times 1000 equals ten thousand divided by one that gives us ten thousand drops so that's the the top part of our unit now we have to find the the other part the minutes so one hour equals 60 minutes and there are six hours here so six hours times sixty that's 360 minutes so now we take ten thousand drops divided by 360 minutes and that equals 27.8 drops per minute and we'll round that to 28 drops per minute okay we'll look at one more example here um example five with method number one our order is for Vancomycin 1.5 grams per 500 milliliters at 10 milligram per minute rate how long would it take to deliver the medication at the correct rate so I have a note about the IV Vancomycin here it is a medication that must be administered slowly at a rate no faster than one gram per hour or 10 milligrams per minute to prevent an adverse reaction called Vancomycin Vancomycin flushing syndrome or VFS so this causes redness in the in the face and the upper body so it has to be administered slowly that's something important to know about Vancomycin I just thought I'd put that in there since we had an example about Vancomycin so back to our problem we want to identify the units the problem's asking for um here we don't have a specific unit it's just how long so it's time so it's either going to be minutes or hours so with method one we can set up fractions that cancel like units then we'll multiply the fractions so our rate is it's 10 milligrams per minute well we want time so we're going to put minutes on the top so we're going to say one minute per 10 milligrams and that will be times 1 000 milligrams per 1 gram because our dose is given in grams but we want our we have to have milligrams for it to be able to cancel and then times 1.5 grams over one so that leaves us with minutes on the top we have a milligram on the top and a milligram on the bottom and those cancel and then we have a gram on the top and a gram on the bottom and those cancel and that equals 150 minutes when we do the math one times a thousand times 1.5 and divide that by 10 times 1 times 1 that gives us 150 minutes when we know there are 60 Minutes in one hour so if we take 150 and divide it by 60 that will give us how many hours so it'd be 2.5 hours okay now we'll look at example number five with method number two so we have Vancomycin 1.5 grams per 500 milliliters at 10 milligram per minute rate how long would it take to deliver the medication at the correct rate so identify our units it's asking how long so this is going to be time either minutes or hours and with method two we'll set up equivalent fractions cross multiply and then divide to solve for x so we'll get our milligrams first um so 100 1000 milligrams per one gram equals x milligrams per 1.5 grams and if we cross multiply and divide we get 1000 times 1.5 divided by one that gives us 1500 milligrams so now we can set that up with our rate to solve for our time so 1500 milligrams per X minutes that's what we're solving for equals 10 milligrams per one minute so if we have 1500 times ones 1500 divided by 10 that gives us 150 minutes or when we divide by 60 that gives us 2.5 hours so now we'll look at the summary key points about IV flow rates so flow rate is the volume per time that a medication is delivered by IV route to a patient it's also known as a drip rate or infusion rate there are IV sets that have different drop factors these are in drops per milliliter that can be used in flow rate calculations and flow rate calculations can be solved with conversions and ratio and proportion calculations and there are two methods method one and we set up fractions that cancel like units and then multiply to get our answer method two you can set up equivalent fractions cross multiply and then divide to solve for x thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name is Amanda and I'm a pharmacist today I'll be talking about a type of Pharmacy calculation called temperature conversions and if you find this video useful please press the like button subscribe to my channel and share with others who may find it helpful too thanks I really appreciate it so first we'll begin just talking about temperature measurements there are two temperature scales the Fahrenheit and Celsius scale and both are measured in degrees so you have degrees Fahrenheit or degrees Celsius and Fahrenheit is used in the United States as the standard temperature measure Celsius is the metric system measurement of temperature it's used in science because its scale is shaped around when a reaction will take place so for example zero degrees Celsius equals the temperature the water freezes and Fahrenheit this is 32 degrees and 100 degrees Celsius is the temperature the water boils in Fahrenheit this is 212 degrees so you can see that those are easy numbers to remember because that's when reactions occur now we'll talk a little bit about Fahrenheit versus Celsius Fahrenheit temperatures are typically much higher than equivalent Celsius temperatures but differences get smaller the lower you go in temperature and I have a chart here that shows the common fahrenheit in celsius equivalence and these are good to know just so you have an idea of the differences between the Fahrenheit and Celsius temperatures the boiling point of water is 212 degrees Fahrenheit it's 100 degrees Celsius normal body temperature is 98.6 degrees Fahrenheit it's 37 degrees Celsius controlled room temperature it's 68 to 77 degrees Fahrenheit or 20 to 25 degrees Celsius many times drugs are specified to be stored at controlled root temperature freezing point of water is 32 degrees Fahrenheit or zero degrees Celsius and parity this is the point at which the two temperature units are equal parity for Fahrenheit and Celsius is negative 40. so this means negative 40 degrees Fahrenheit equals negative 40 degrees celsius that's the point at which they are equal now we'll talk about the temperature conversion formulas so Fahrenheit and Celsius units are not proportionate so conversions require a formula you can't just do a ratio calculation with these it's because their units are not proportionate so there are two formula types there are plug-in formulas or an algebra formula and the best thing to do is just to choose the formula that's easiest for you because these formulas have to be memorized so the plug-in formulas for Fahrenheit and Celsius conversions there are two of them Celsius times 1.8 and that's in parentheses so it means you do that part first plus 32 that will give you the degrees Fahrenheit and then to calculate the degrees Celsius let me take the Fahrenheit temperature minus 32 and that's in parentheses that means you do that first then divided by 1.8 so that will give you the degrees Celsius then the algebra formula for Fahrenheit to Celsius it's a little simpler to remember as long as you know how to do the algebra part of the math 5f equals 9C Plus 160. and it's those can be a little difficult to remember so I have a some memorization tips I'm just depending on which ones you you choose to memorize but like I said these formulas have to be memorized and choose what's easiest for you so for the plug-in formulas if you memorize one the other is backward and opposite so if we look at these here again the degrees Fahrenheit is going to equal Celsius times 1.8 Plus 32. so then we look at the one for finding Celsius it equals Fahrenheit minus 32 so you can see that's backward and opposite then divided by 1.8 once again it's you know backward and opposite and if you choose to do the algebra formula you can remember it a little easier by remembering that 5 starts with f so it's FF at the beginning 5f equals 9C Plus 160. now we'll look at some examples and so you can see how to work these problems so the first example is convert 100 degrees Celsius to degrees Fahrenheit so if we use the plug-in formula we're going to take the degrees Celsius times 1.8 plus 32 that will give us the degrees Fahrenheit that's our formula so we have 100 times 1.8 and that's in parentheses we do that part first that equals 180 then plus 32 180 plus 32 is 212 so that equals our degrees Fahrenheit so 100 degrees Celsius equals 212 degrees Fahrenheit now we'll look at the same example but using the algebra formula so convert 100 degrees Celsius to degrees Fahrenheit we have 5f equals 9C plus 160 is our formula so we'll just plug in our Celsius temperature here so we have 5f equals 9 times 100 plus 160. so we do what's in parentheses first 9 times 100 that will be 900 then plus 160 that gives us 1060. so 5f equals 1060. and then in algebra what we do to one side we have to do to the other so we want to get our F by itself so in order to do that we're going to divide by 5. so because 5 divided by 5 equals one and one F we can just simplify that and say f so 5f divided by 5 that will give us F what we do to one side we have to do to the other so we have 1060 divided by 5 and that equals 212. so F our degrees Fahrenheit will be 212. 100 degrees Celsius equals 212 degrees Fahrenheit now we have example number two convert 12 degrees Celsius to degrees Fahrenheit and first we'll look at our plug-in formula and we're using the same one on this because we're finding Fahrenheit again so degrees Celsius times 1.8 plus 32. that will give us our degrees Fahrenheit so we just plug in the 12 for the degree celsius so 12 times 1.8 and we keep that in parentheses means we do that first plus 32 equals our Fahrenheit degrees so 12 times 1.8 equals 21.6 plus 32 and that equals 53.6 and that will round up to 54 degrees so 12 degrees Celsius equals 54 degrees Fahrenheit now we'll look at the same problem with the algebra formula so convert 12 degrees Celsius to degrees Fahrenheit and our algebra formula is 5f equals 9C Plus 160. so 5f equals 9 times 12 then Plus 160. so 9 times 12 is 108 and then plus 160 is 268. so now we have it to 5f equals 268. we have to get F by itself so we're going to divide by 5. remember what we do in algebra well we do to one side we do to the other so 5f divided by 5 will leave us with f and then 268 divided by 5 will give us 53.6 so the fahrenheit degrees is 53.6 round that to 54 degrees so 12 degrees Celsius equals 54 degrees Fahrenheit now we'll look at example number three convert 86 degrees Fahrenheit to degrees Celsius so here we need our other plug-in formula because we're converting to degrees Celsius so it's degrees Fahrenheit minus 32 remember that's in parentheses divided by 1.8 so we'll just plug in our Fahrenheit number 86 minus 32 equals 54. then divided by 1.8 gives us 30. so that's our degrees Celsius so 86 degrees Fahrenheit equals 30 degrees Celsius and now we'll look at the same example with our algebra formula convert 86 degrees Fahrenheit to degrees Celsius so our algebra formula is 5f equals 9C Plus 160. so 5 times 86 equals 9C Plus 160. so we're plugging in for our Fahrenheit there so 5 times 86 is 430. and then we have 430 equals 9C plus 160. remember in algebra what we do to one side we have to do to the other so we're trying to get our C by itself so first thing we're going to do is we have to subtract 160 off of each side so if we take 160 off 430 minus 160 equals 270 equals 9C so now we've got the 160 off so now we have to get the 9 off Celsius and in order to do that we're going to divide by 9 on both sides so 9 Celsius the 9C divided by 9 will be 1C so we can just write C and then 270 divided by 9 is 30. so our degrees Celsius is 30. so 86 degrees Fahrenheit equals 30 degrees Celsius and we'll do one more example example number four convert 110 degrees Fahrenheit to degrees Celsius so with our plug-in formula we have degrees Fahrenheit minus 32 that's in parentheses divided by 1.8 that will give us our degrees Celsius so we plug in our Fahrenheit number we have 110 minus 32 that equals 78 then divided by 1.8 equals 43.3 that's our degrees Celsius so 110 degrees Fahrenheit equals 43 degrees Celsius and now we'll look at that same example with our algebra formula so convert 110 degrees Fahrenheit to degrees Celsius so our algebra formula is 5f equals 9C Plus 160. so we just plug in our number here we have our degrees Fahrenheit and we're going to be solving for C our degrees Celsius so 5 times 110 equals 9C Plus 160. 5 times 110 is 550 and that leaves us with 550 equals 9C Plus 160. so now we're going to subtract 160 off each side and that will leave us with 550 minus 160 which is 390. equals 9C divide both sides by 9 to get our C by itself 390 divided by 9 is 43.3 and that equals c so that's our Celsius so 110 degrees Fahrenheit equals 43 degrees Celsius now we'll just look at a summary and some key points about temperature conversions Fahrenheit and Celsius degrees are not proportionate so conversions require a formula remember this isn't just a simple ratio calculation and there the plug-in formulas or the algebra formula and just do this the method that's easiest for you and remember this these formulas have to be memorized so choose the method that's easiest to memorize that formula so the plug-in formulas for conversion are degrees Celsius times 1.8 in parentheses plus 32 equals degrees Fahrenheit and degrees Fahrenheit minus 32 in parentheses divided by 1.8 equals degrees Celsius and remember any when it's in parentheses that just means you do that part first and a way to remember these is that they are exactly backward and opposite each other and the algebra formula for conversions remember our is 5f equals 9C Plus 160. and you just solve for the variable that you need and when you can remember that by remembering 5f it's FF 5 starts with f and that goes with the f so thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my drug information videos thank you hi my name is Amanda and I'm a pharmacist today I'll be talking about weight-based dosage calculations and if you find this video useful please press the like button subscribe to my channel and share it with others who may find it helpful too and if you'd like to support this Channel with a donation press the heart thanks button to give me a super thanks thanks I really appreciate it so for some medications the amount of drug to be given to a patient depends on the patient's weight most medications for children are dose based on weight due to the extreme differences in patient size and this makes sense typically a small the smaller the patient's size the smaller the dose will be needed the greater the patient size the greater the dose will be needed there are also some adult medications that are dose based on weight due to characteristics of a particular drug being given some characteristics of drugs that require weight-based dosages for adult medications include drug distribution this is how a drug is transferred to the tissues of the Body for example if a drug is fat soluble the greater the patient weight the higher the dose is typically needed for fat soluble drugs to reach appropriate concentrations in the body and another characteristic is the therapeutic index this is the ratio between the toxic dose and the effective dose with a narrow therapeutic index drug or an NTI drug a small change in dose equals a large change in effect now we'll talk about how to solve weight-based dosage calculations so first weight-based dosages are typically specified in milligrams per kilogram or milligrams per kilogram per day so to solve weight-based dosage calculations first you want to determine the patient's weight in kilograms and our conversion equivalent for this is one pound equals 2.2 kilograms so basically what we're going to do on this we'll divide the pound weight by 2.2 that will give us the weight in kilograms next we'll determine the patient's dose this is done by multiplying their kilogram weight by the milligram per kilogram dose and then we'll determine the amount per dose if it's in milligrams per kilogram per day and to do this we'll divide the total daily dose by the number of doses per day and now we'll look at each of these steps in more detail so first we'll look at how to convert a patient's weight from pounds to kilograms so many weight-based dosages are specified in milligrams per kilogram or milligrams per kilogram per day of the medication so when a patient's weight is given in pounds it must be converted to kilograms and our weight conversion equivalent is one kilogram equals 2.2 pounds so in order to convert a patient's weight from pounds to kilograms and we can divide it by 2.2 you can memorize it just that and do it that way or if you just want to memorize the conversion equivalent you can also set up a set up fractions that cancel like units and multiply to get your answer so I have an example of that here if we have a 150 pound patient there's one kilogram per 2.2 pounds times 150 pounds over one so you have a pound on the top pounds on the bottom those cancel you're left with kilograms then you just do the math 1 times 150 is 150 then divided by 2.2 times 1 that it gives us 68.2 or as I said if you just take 150 divided by 2.2 68.2 kilograms so once the weight has been converted to kilograms the amount of drug to be given can be obtained as I said weight-based dosages are usually specified in milligrams per kilogram or milligrams per kilogram per day so to obtain the dose you can simply just multiply the weight in kilograms by the milligram per kilogram dose so if you have a 68.2 kilogram patient and a dose of 5 milligrams per kilogram we can just multiply 68.2 times 5 that will give us our milligram dose or if you want to set up the fractions that cancel like units you can do it that way too just so you can see well how the units cancel and two it's a good double check on yourself so 68.2 kilograms over 1 times 5 milligrams per kilogram you have a kilogram on the top kilogram on the bottom those cancel you're left with milligrams so then you just do the math 68.2 times 5 divided by one that would equals 341 milligrams so if the dosage is specified in milligrams per kilogram per day and the directions are not QD that's once a day then the amount per dose may also need to be calculated so to calculate the amount per dose divide the total daily dose by the number of doses per day so we'll continue with our example we have five milligram per kilogram per day and that equaled 341 milligrams per day and we'll say that's given q6 hours q6h is q6 hours so q6h we have 24 hours in a day divided by six hours that would be four doses per day so if we take 341 and divide it by 4 that equals 85.25 milligrams so the patient would receive 85 milligrams q6h so 85 milligrams would be the amount per dose so sometimes the dosage is specified in milligrams per kilogram and the frequency is stated with the dose so the amount per dose is already determined so for example we have our 68.2 kilogram patient to be given 5 milligrams per kilogram q6 hours um if you just do the math the five milligrams per one kilogram times 68.2 kilograms over one we cancel a kilogram on the top 50 kilogram on the bottom we're left with milligrams 5 times 68.2 is 341 and that's 341 milligrams q6h because our our amount is already determined our dose is already determined the 5 milligrams per kilogram is every six hours so now we're going to look at some examples so example one 176 pound patient is to be given Lovenox 1.5 milligram per kilogram sqqd what is the patient's total daily dose so the medication we're working with here is Lovenox its generic name is enoxaparin and it's a low molecular weight Heparin blood thinner to treat or prevent blood clots so we're giving in 1.5 milligrams per kilogram sqqd SQ stands for subcutaneously that means Under the Skin and QD is once every day so we're wanting the patient's total daily dose so since it's once a day we just figure out our milligram per kilogram dose and that will be the amount given for the day so one kilogram equals 2.2 pounds so there's one kilogram per 2.2 pounds times 176 pounds over one our pounds cancel ones on the top ones on the bottom so they cancel we're left with kilograms so 176 divided by 2.2 equals 80 kilograms and then we're given the dose of 1.5 milligram per kilogram times 80 kilograms over one kilogram on the top a kilogram on the bottom those cancel we're left with milligrams that gives us a total of 120 milligrams so that is our total daily dose since it's administered once a day now example number two a 148 pound patient is to receive Vancomycin 10 milligram per kilogram IV q12h what is the amount to be given for each dose so our medication here is Vancomycin it's a glycopeptide antibiotic that's used to treat a variety of serious infections it's given IV and it's one that is dose-based according to weight and also other factors such as a patient's renal function so we're given Vancomycin 10 milligram per kilogram IV q12h so that's every 12 hours and we're wanting to know what the total amount is to be given for each dose so we have one kilogram equals 2.2 pounds so we have to figure out the how the much the patient weighs in kilograms first so one kilogram per 2.2 pounds times 148 pounds over one so 1 times 148 is 148 divided by 2.2 is 67 kilograms so that's the patient's weight in kilograms and then our dose is 10 milligrams per kilogram times 67 kilograms we're left with milligrams a kilogram on the top kilogram on the bottom those cancel so 10 times 67 is 670 milligrams for each dose so since it says it's 10 milligram per kilogram every 12 hours that is the amount for each dose it's already we don't have to determine how many doses in the day it's an example number three a child is prescribed cephalexin 75 milligrams per kilogram per day given qid the child weighs 30 pounds what amount of cephalexin will be given per dose so cephalexin this is an antibiotic that's a cephalosporin and so we have 75 milligram per kilogram per day qid qid is four times a day so first we have to convert the child's weight into kilograms so one kilogram per 2.2 pounds times 30 pounds 30 divided by 2.2 is 13.6 kilograms so now we have a dose of 75 milligrams per kilogram and that's going to be per day so 75 milligram per kilogram times 13.6 kilograms we're left with milligrams on the top kilogram on the top a kilogram on the bottom those cancel 75 times 13.6 is 1020 milligrams so that is the total dose per day so this is given qid so four times a day so we're going to divide that by 4 to get the amount per dose so 1020 divided by 4 equals 255 milligrams per dose okay now we'll look at our last example example number four and it has three parts so a child is to receive amoxicillin at a dose of 50 milligram per kilogram per day what is the total daily dose if the patient weighs 21 pounds then the dose of amoxicillin is to be given q12h how many milligrams should be given per dose and then part C if amoxicillin 400 milligram per 5 ml is dispensed how many milliliters should we give them per dose so we'll look at part a first so a child is to receive amoxicillin at a dose of 50 milligram per kilogram per day what is the total daily dose of the patient weighs 21 pounds so amoxicillin that's an antibiotic in the penicillin class um we're dealing with it at a dose of 50 milligram per kilogram per day so we're looking for the total daily dose if the patient weighs 21 pounds so one kilogram equals 2.2 pounds so 21 Pounds divided by 2.2 that equals 9.5 kilograms then we have a dose of 50 milligram per kilogram so 50 times 9.5 equals 477 milligrams so that is our total daily dose 477 milligrams and Part B the dose of amoxicillin is to be given q12h how many milligrams should be given per dose so q12h means every 12 hours so 24 hours divided by 12 hours so that would be two doses so the total daily dose was 477 milligrams if we divide 477 by 2 that equals 239 milligrams per dose so now we'll look at part C if amoxicillin 400 milligram per 5 milliliters is dispensed how many milliliters should be given per dose so this one we know we need 239 milligrams per dose so the way we'll do this is we're going to set up equivalent fractions cross multiply and then divide so if there are 400 milligrams per 5 milliliters set that equal to 239 milligrams per X milliliters so we're solving for x so if we take 5 times 239 that equals 1195. then divide to solve for x divided by 400 equals 2.99 we'll round that to three so be three milliliters would give us 239 milligrams and that would be the amount that the patient should take per dose okay so now we'll just look at a summary and some key points to remember so weight-based dosages are typically specified in milligram per kilogram or milligram per kilogram per day to solve weight-based dosage calculations first determine the patient's weight in kilograms remember one pound equals 2.2 kilograms and a shortcut to do this you can just divide the pound weight by 2.2 or if you want to set up the fractions that cancel like units you can do that as well just so you can see exactly what's going on next you determine the patient's dose so we'll we can do this by multiplying the kilogram weight by the milligram per kilogram dose and then determine the amount per dose if the milligram per kilogram if it's in a milligram per kilogram per day and to do this we'll divide the total daily dose by the number of doses per day thanks for watching please like and share this video with others who may find it helpful and please subscribe to see more of my Pharmacy learning videos and if you would like to support this Channel with a donation press the heart thanks button to give me a super thanks thanks I really appreciate it foreign