Transcript for:
GED Math Fractions

need to master GED math fractions for the GED test then you're in the right place hi this is Parker from Description pians teaching you how to pass the GED fast and get started by clicking subscribe down below in this video on fraction basics first we're going to start by talking about what a fraction actually is we're going to look at the new minor in the denominator of the fraction will then discuss the three types of fractions proper improper and mixed numbers we'll also look at how to convert an improper fraction to a mixed number and vice versa and we'll also look at fraction and decimal equivalents so let's get started so first what is a fraction a fraction uses two numbers to show a part of a whole again a fraction uses two numbers to show a part of a whole so in this example here we see the fraction seven eighths seven over eight so there are two numbers in this fraction the top number is what we call the numerator the top number here is seven so the numerator in this fraction is seven and the bottom number in the fraction is what we call the denominator so in this example eight is our denominator again the denominator is the lower number in the fraction so one way to remember that is to look at the letter D here so think of the word downstairs both downstairs in denominators start with the letter D so the denominator you can think of that as being downstairs again denominator downstairs the denominator is the lower number and the fraction so what is the denominator and what is the numerator and what do they mean well the denominator tells you how many equal parts there are in the whole and the numerator tells you how many parts of the whole you're working with so for example let's look at this pizza here so if you count these up you'll see that there are eight slices in this pizza so let's assume that these slices are all equal in size here so again there are eight slices here in this pizza so the whole pizza has eight parts to it so to write this as a fraction we would want to put eight in the denominator because again the denominator tells you how many equal parts there are on the whole and we see that the whole pizza has eight parts to it and we're assuming that these parts are equal in size and so now if we look at this pizza here we see that this one slice here has been cut out of our pizza so I'm gonna highlight or trace this pizza slice here and so let's say that you eat the slice of the pizza so you've eaten this slice of the pizza and you see that there are seven parts left so if we wanted to write the fraction of pizza slices that are left we would write seven over eight and again that's if we assume that we take out this one slice of pizza that I've traced here we're left with seven slices of pizza so there are seven parts left here so we'd write the 7 in the numerator and there are 8 parts in that hole so that's why we have the 8 here so again the denominator tells you how many equal parts there are on the whole since there's 8 equal pieces here in the hole we put the 8 in the denominator and the numerator tells you how many parts of that hole you're working with so if we eat this pizza slice and we're left with 7 slices here we are working with 7 slices so the numerator is 7 for the GED test there are three types of fractions that you have to know proper fraction improper fractions in mixed numbers so here we have an example of all three types so the first example here is 2/3 2 over 3 so 2/3 is a proper fraction so what is a proper fraction well in a proper fraction the top number of the fraction is smaller than the bottom number of the fraction in other words in a proper fraction the numerator is smaller than the denominator so 2 is the numerator here and we see that 2 is smaller than 3 which 3 is our denominator so the other thing about a proper fraction to note is that it's always equal to a number that it's less than 1 so that's what this symbol here means less than 1 so for example if you ever want to convert a fraction into a decimal all you have to do is just put the top number to your calculator hit division and then hit the lower number in the fraction and then hit equals so for example you would do in the calculator to divide it by 3 and that's going to give you point six six six six six six six repeating and so let's round that 2.67 so in your calculator if you do 2/3 you're going to get 0.67 if you round it all right and so we see that 0.67 is a number that is less than 1 so now let's look at the improper fraction here so the improper fraction is the reverse of the proper fraction in that in an improper fraction the top number is greater than the bottom number so in other words in an improper fraction the numerator of the fraction is greater than the denominator of the fraction so for example here if we've got 3 over 2 we see that the bigger number is 3 3 is in our numerator the smaller number 2 is in the denominator so we know that this is an improper fraction and so with an improper fraction the value of that fraction is equal to a number that's greater than or equal to 1 so with an improper fraction the fraction is always equal to a number that's greater than or equal to 1 so to convert this fraction to a decimal take your calculator you would hit 3/2 hit equals and it's going to give you 1 point 5 so 3 over 2 is equal to one point five one point five is greater than or equal to one so now let's look at our last example here let's look at our mixed numbers so the mixed number here is four and three-fifths so mixed numbers have two parts they've got your whole numbers so this number out front here which is 4 is the whole number then they've also got the fraction so the fraction is just 3/5 or you could say it 3 over 5 however you want to say it so again mixed numbers have a whole number and a fraction here and so also about mixed numbers what you want to know is that a mixed number is always going to be greater than 1 and so that should be pretty easy to remember because it's gonna have a whole number out front here so 4 and 3/5 so to convert this fraction into or the mixed number into a decimal you would just do 3/5 in your calculator so 3/5 gives you point 6 and then you keep the 4 out there so you would have 4.6 here so that would be the value of this mixed number so later in the video we're going to look more closely at converting fractions into decimals but just know for now that you can always convert a fraction into a decimal just using your calculator very simply and so what I want you to see here is the difference between a proper fraction an improper fraction and a mixed number and so a very key point here that's very important for your test is that when you have an improper fraction can change it into a mixed number and you can take a mixed number and change it into an improper fraction so one skill that we're going to work on here in a minute but it's a skill that you want to master for the test is taking an improper fraction and turning that into a mixed number and taking mixed numbers and turning them into improper fractions and you want to have that skill bound so you can do it very quickly on your tests so to make sure that you have this down let's look at a few examples here so I'm going to show you examples of one of the three types of fractions that I want you to tell me if each example is a proper fraction an improper fraction or a mixed number so let me show you the first example here so the first example is two and one-third so is two and one thirds a proper fraction an improper fraction or a mixed number pause the video and try to figure this out okay let's go over this so two and one thirds is a mixed number in the way that you can tell that is because the mixed number has a whole number and a fraction so the whole number here is the two and the fraction is one-third so a mixed number is a mix between that whole number and the fraction so two and one thirds is a mixed number so let me show you another example now so the example is 3/5 so is 3/5 a an example of a proper fraction an improper fraction or a mixed number pause the video and try to figure this out okay so let's go over this so whenever you see a fraction where the top number is smaller than the bottom number it's a proper fraction so this is a proper fraction so another way to say that is that the numerator is smaller than our denominator so therefore it's a proper fraction so 3/5 is a proper fraction okay and so the only one that we haven't shown an example of yet is the improper fraction so since that's the last one standing here let me just show you an example of that right now so any number again that's going to have the top number that's bigger than the bottom number is an improper fraction so an example would be say 20 over 9 and so you would do that 20 over 9 is that improper fraction because the numerator is bigger than the denominator so hopefully you got these down so now let's look at how to convert a mixed number to an improper fraction in vice-versa so first let's start with a mixed number here so let me give you a mixed number let's do 3 3 and 1/2 and so this is our make number so three and a half is a mixed number and we want to convert that to an improper fraction so the way that we do it is we take the denominator of our fraction and we multiply it by the whole number and then we're going to add the numerator so that's the first step here so let's do that so again we're going to take the denominator and multiply it by the whole number then we're going to add the numerator so the denominator is two the whole number is three so we multiply the denominator by the whole number so we do 2 times 3 and that's equal to 6 and so what comes next so again the first step you multiply the denominator by that whole number which we did here 2 times 3 equals 6 then the next step is to add the numerator so we'll take that 6 and we'll add the numerator and so that gives us 7 and so the last thing that we do here is we take that 7 and we write it over the original denominator so the original denominator and our mixed number was 2 so we take that 7 and we write it over 2 so 3 and 1/2 is equal to 7 over 2 as a mixed number so let me show you another example how to do this let's let me clear this out of the road here so here's one that you can try on your own here so let's say that we've got 2 & 5 sixth sixth so pause the video and try to convert this mixed number into an improper fraction using the method I just showed you okay let's go over how to do this so we've got a mixed number mixed number here which is 2 and 5/6 and we want to convert that into an improper fraction so what we do again the strategy is we take our denominator we multiply it by the whole number we then add the numerator and then we take that and then we put write that over the denominator in our mixed number all right so let me write this out for you here and show you how you do it so again the steps you take that denominator and multiply it by the whole number so let's do that so we take our denominator we're going to multiply it by our whole number and then the next step will be to add 5 to that so let me just do that right now we'll put 5 to that and so let's let's do the math here so 6 times 2 is 12 12 plus 5 is 17 so the answer here to this part would be 17 so now what's the last step here so after we've taken the denominator and we multiplied it by the mixed number or by the whole number and then we added five to that we end up with a 17 the last step is to write that 17 over the denominator in our original mixed number which is 6 so we have 17 over 6 and so that's our mixed number so let me show you one more example here and you can try this at home so now it's let's do 1 and 3/5 so pause the video and try to write this mixed number as an improper fraction ok let's go over how to do this one now let's go over it a little bit quicker now since you guys are really smart and you guys are starting to get this so what we do is we take the mixed number we take the denominator in the mixed number which is 5 we multiply that by the whole number so the whole number is 1 and then what we're going to do is we're going to add our numerator so the numerator is the 3 so we do 5 times 1 which is just 5 plus 3 is 8 and so then the last step is we take this number which is 8 and we're going to write that over the denominator in the original mixed number so the denominator and the original mixed number again is the 5 here so that's all we did well all we do is we take that again to recap we take the denominator in the fraction which is 5 we multiply it by the whole number which is 1 then we add the numerator which the numerator was there 3 and that's how we got our 8 and so then the last step is we just go back to the mixed number we look at what the denominator was the denominator is 5 so we write that 8 over 5 and that's how you do a mixed number to an improper fraction so that's how you go from a mixed number to an improper fraction but how do you go from an improper fraction to a mixed number so here's what we're gonna do I'm going to show you an example here and don't worry about these words so some of you might be reading all these words on the screen and freaking out don't worry about it we're gonna go through it step by step it's really not that hard it might look harder than it is right now but pretty soon you're gonna see how easy it actually is so we've got an improper fraction here as your example 7 over 2 is an improper fraction and again it's an improper fraction because the numerator is bigger than our denominator so that's how we know it's an improper fraction so we want to take this improper fraction and we want to convert it into a mixed number so what do the mixed number in the improper Frank have in common so they both have a denominator they share the same denominator so I'm just gonna write t nom to abbreviate for a denominator or you know what I'll write it out here so we've got denominator so the mixed number in the improper fraction they both have the same what they both have the same denominator so the seven over two is our improper fraction and we want to convert it into a mixed number right off the bat we know that the mixed number is going to have a denominator of two because our improper fraction as a denominator of two so again what is a mixed number so here's an example of a mixed number again because this is really important that we understand this so the mixed number has a whole number and it's got a fraction so and any mixed number there were three different numbers it's got a whole number it's got a numerator and it's got a denominator so now let me get rid of that little example here let's focus on the first example which was seven over two so seven over two is an improper fraction and we want to convert it to a mixed number mixed numbers have a whole number a numerator and a denominator but we already know what the denominator of the mixed number is going to be so since our improper fraction has a denominator of two the mixed number that we get is going to also have a denominator of two and that's because again the mixed number and the improper fraction have the same denominator so the mixed number it's got that whole number that denominator and it's got a numerator so how do we get the whole number well here's how we do it so on the screen here it says to get the whole number you multiply the denominator by a number that gives you a product this should say product close to the numerator but less than the numerators this should say product it gives you a product close to the numerator but less than that numerator so let's get the whole number here so we've got seven over two so how do we do it well we want to take our denominator so the denominator is two and we want to multiply it by a number that's going to give us a product that is close to the numerator but it has to be less than the numerator so what is our numerator again so the numerator is seven here and the denominator is two so we want to take our two and we want to multiply it by something that it's going to give us a product that's close to seven but it's got to be less than seven so let's just look at some two times tables here so two times two is four and two times three is six and two times four is eight so these are just some time staples here and so why did I stop at two times sports anybody know why do you know why I stopped after two times four well the reason is because remember we're looking to take this denominator and we want to multiply it by a number so that we get a product that is close to seven but it has to be something less than seven so when we did two times four we got eight and so eight is a number that's it's close to seven but it's bigger than seven so this is we want to get rid of this here this is not correct so two times four the whole number can't be four because we're looking for a number that is going to multiply with the denominator to give a product that is close to the numerator but it has to be less than the numerator so eight is greater than seven so we now have two times three which is six so when we multiply the denominator which is 2 times three the product that we get is six here so six is close to the numerator which is seven but it's less than seven so this is going to work here so the whole number is going to be three so we have as our whole number are three and we already know that the denominator and our mixed number is two and so we know that that the nominator is two again because we just look at our improper fraction in the denominator in the improper fraction is two since the mixed number and the improper fraction have the same denominator when we write our mixed number over here the denominator is also going to be two in that mixed number so what goes in the numerator right here well all we do is we just do two times three which is six and so then we take our numerator which was seven and we just subtract that 6 and that gives us one and so our mixed number is three and a half so what we did here was we took this seven over two which was their improper fraction and we converted this improper fraction to a mixed number and we got three and a half so let's look at another example of how to do this now so this time let's go with let's do eight over three so the improper fraction is 8 over 3 so convert that into a mixed number so pause the video and try to take this improper fraction turn it into a mixed number so hopefully you just had a chance to try that so eight over three so what we want to do here is we want to focus on the denominator so the denominator is three so we want to multiply three by some number and we want to get a product that is close to eat but it's got to be less than eight so let's try a few different things here so let's try so three times one is just going to be three we already know that so we've got three times to here and three times two gives us six and so what about 3 times 3 3 times 3 gives us 9 okay and so we know that 9 is greater than 8 so 3 is not going to work so the whole number is not going to be 3 because if you do 3 times 3 you get 9 and that's bigger than 8 so the whole number is going to be 2 so and the reason is because when you do 3 times 2 you get 6 so 6 is a number that's close to 8 but it's less than 8 whereas only did 3 times through we got nine 9's too big so the whole number is r2 and what about our denominator well the denominator is just 3 here and remember when we look at our improper fraction we see that the denominator is 3 so if we go over here to our mixed number we know that the denominator is also going to be 3 because the denominator over the mixed number in the improper fraction they're both the same so here we've got one more number to figure out so we need to know what this numerator is so what we do is we look at our numerator here in the improper fraction so the numerator the improper fraction is 8 so let me write that now write that here let me write it right here so we've got our 8 right here and so now what we want to do is subtract so we do 3 times 2 which gives us 6 so we do 8 minus 6 which gives us which is equal to 2 so 8 minus 6 is equal to 2 so the answer is 2 and 2/3 so let me do one more example here of how to convert an improper fraction to a mixed number so let's do let's try 11 over 13 now so take or we want to go the other way around so let's do 13 over 11 13 over 11 now so take 13 over 11 which is an improper fraction and convert that into a mixed number so pause the video and try to do that now okay let's go over this so we've got thirteen over eleven which is an improper fraction so what we want to do here is if we consider our eleven times tables we see that eleven times one is eleven and eleven times two gives us 22 so eleven times two gives us 22 22 is greater than thirteen so right off the bat here we know that two cannot be the whole number in the mixed number and the reason is because when you do 11 times two you're going to get a number that is greater than 13 so this is out here so the whole number is just one in this case so our whole number is one and what is our denominator so the denominator is 11 and so how do we know that well we just look here at our improper fraction with the improper fraction as a denominator of 11 since the mixed number in the improper fraction have the same denominator we know that in the mixed number the denominator will be 11 so we've got the whole number and we've got our denominator we just need to get the numerators so what we do is we go back to our improper fraction we see that 13 is in the numerator so then we look at our mixed number and we do 11 times 1 which is just 11 so we do 13 minus 11 which gives us 2 and so that is the number that we put in here for our numerator which is just 2 so 1 + 2 / 11 so you know let's let's look at one more example here because I want to really make sure that you guys are getting this down so here's one more example here so this time let's do 17 over 3 so this is a good one so you've got an improper fraction of 17 over 3 pause the video and try to convert that into a mixed number then we'll go over it okay so here's a great problem here so we've got 17 over 3 and so again what we want to do is we want to find the whole number in the mixed number first so right off the bat let's think of some some numbers that we could possibly multiply 3 by here so let's try something bigger like let's try maybe 3 times 7 so 3 times 7 is 21 so that's going to be a little bit too high because 21 is greater than 17 so we want to get we want to get a product that is less than 17 years so 7 is going to be a little bit too high so let's just go down 1 so let's do 3 times 6 so 3 times 6 is 18 so 6 won't be the whole number 6 is a little bit too big here because when you 3 times 6 you get 18 18 is greater than 17 which is and what we want we want a number that is lower than 17 it's got to be close to 17 but lower than 17 so we try it 7 we tried 6 so let's bump this down by 1 so let's do 5 so 3 times 5 equals 15 and so look what we've got here so 15 is a number that's close to 17 but it's less than 17 so 5 is perfect so 5 is going to be the whole number so in our mixed number here the whole number is going to be 5 so what is the denominator so the denominator is going to be 3 so the reason is because the improper fraction has a denominator of 3 and so therefore the mixed number will also have a denominator of 3 because the mixed number and the improper fraction show the same denominator so now how do we figure out what the numerator is well what we do is we go back and we look at the numerator and improper fraction which is 17 and so we want to take that 17 and so then we do 3 times 5 which is 15 so 17 minus 15 gives us 2 and so that is our numerator so the impress so the mixed number would be 5 in two-thirds so earlier on the video I was talking about how to convert a fraction into a decimal using a calculator and so that is always going to work so that's the fast way to do it and that's the best way to do it so if you have a fraction and you can't remember what it is equal to as a decimal you just use that calculator so for example let's say 1/5 so if you want to convert 1/5 as a fraction into the decimal you would just do 1/5 in your calculator so you take the calculator put in 1 hit the division sign hit 5 hit equals and it's gonna spit out the answer which is point 2 so that's always how you're gonna want to do it however if you don't have a calculator you're gonna have to just know some of these values by memory because there's not really a good way to do it by hand or to do it in your head so to convert a fraction to a decimal you have to either use your calculator or you just have to understand certain patterns or at least memorize these numbers here so I've given you a chart here and the numbers in this chart or a good values to have memorize so for example 1/2 that is equal to 0.5 and so that's just something that you definitely want to know so the most important one in this whole entire chart is definitely the fact that 1/2 equals 0.5 so 1/2 equals 2.5 so definitely definitely definitely if nothing else if you take nothing else away from this part of the video know that 1/2 is equal to point 5 all right so also you do need to know and you should know that 1/4 is equal to 0.25 3/4 is equal to point 75 and so the fourths are usually easier to remember for students because they can just think about quarters so let's say you see 4 here so how many quarters are there in $1 well 1 dollar is equal to 4 quarters so what about 1 so we see 1/4 so let's say you've got 1/4 well that's equal to 25 cents or 0.25 what about 3/4 so we see 4 here and right away we should think well for 4 quarters are in $1 so what if I've got 3 quarters how many quarters is that or how much money is that so three quarters is equal to 0.25 so whenever you see those fourths just think about quarters so one-fifth is equal to point two and that's just something that's good to memorize then you'll have two thirds which is equal to 0.666 and a bunch of repeating sixes here one-third is equal to point 3 3 3 3 3 and a bunch of repeating threes as we see here now here's another nice pattern here to just pot here so 1/10 is equal to point one two tenths is equal to point two three tenths or 3 over 10 is equal to point 3 and so if we keep going here right so if we do 4/10 and 4/10 would be equal to 0.4 okay so what about 5 over 10 any guesses as to what 5 divided by 10 is equal to so if one tenth is point one two tenths is point two three tenths is 0.3 4 tenths is equal to 0.4 then logically if the pattern continues which it does then five tenths is equal to point five and so on and so forth with 6 7 8 & 9 all right and so these are some fraction decimal equivalents that I really recommend you memorize so add these in your notes and you can either you can use flashcards or you can just put them down somewhere and then come back and review them every couple days just read over the list again again but you definitely want to at least know that 1/2 is equal to 0.5 you should know these quarter values what I call the quarters the 1 4 3 or 3 fourths you should I know these ones and definitely no no the rest of them - they're all good - they're all good to remember the first three are definitely the ones that are gonna come up most often on your test in my next video in my GED math fraction series we're going to take a look at how to simplify fractions I'm going to give you some tricks to use to simplify fractions to get more questions right on the GED test so make sure you subscribe for that video