in this video we're going to focus on just some basic topics in math this is for those of you who really want to boost your math skills so we're going to talk about how to add subtract especially when there's negative numbers um how to multiply do mental math in your head we're going to go over the multiplication tables uh the ones that you got to know we're also going to talk about how to divide and how to uh convert fractions into decimals how to add subtract fractions multiply divide how to convert them to mixed numbers we're going to talk about how to do percentages in your head and how to simplify fractions like mentally we're also going to go over like exponents and uh even exponential fractions order of operations we're going to talk about square roots how to simplify radicals cube roots um we're going to go into scientific notation how to convert it into decimal or standard form and vice versa how to multiply divide two numbers in scientific notation even how to take a square root of a scientific notation number now we're also going to talk about how to solve equations both linear equations equations with decimals fractions equations involving radicals cube roots and also how to factor and use the quadratic equation and then after that we're going to talk about how to graph linear and quadratic equations and we'll go over some general parent functions and how to do some transformations so just some some of the common topics that you'll see in algebra but the beginning part of this video focus more mostly on arithmetic and then for those of you who are looking to do well in algebra the rest of the video might be of use to you so um let's begin so let's start with some basic addition problems if you want to add 5 plus four what is the answer now for those of you who know you know it's uh nine but let's say if you don't know the answer to that problem what you could do is imagine a number line over here you have 0 on the left side negative 1 negative 2 negative 3 and so forth on the right you have 1 2 3 4 and five but now let's start from five let's say zero is over here and this is five starting from five you want to add four if you wish to add you need to go to the right if you want to subtract you need to move to the left side so since you want to add 4 we're going to add we're going to go four units from the right so 1 2 3 4 and we're going to stop here so this is going to be six seven eight nine therefore five plus four is nine let's try some other examples so what is seven minus three seven minus three is four but let's prove it with the number line so let's say this is zero and seven is somewhere over here if we start from seven and we wish to subtract it by three we need to go three spaces to the left so one two three so this is going to be six five four therefore seven minus three is four so what about this one five minus eight what's the answer to that particular problem now five minus eight is negative three so we're going to start um at five and because we're subtracting we're going to go eight spaces to left so one two three four this would be five six seven eight so this is four three two one zero negative one negative two negative three what's negative four plus five negative four plus five is positive one so if you start from negative four and since we're adding we're adding five to four we're gonna go five units to the right so one two three four five negative three negative two negative one zero one now you can also add it the other way too negative four plus five is the same as uh five minus four you can reverse the numbers this will also give you one so if you started at five and went four units to the left one two three four you would end up at the same location which is one so try this one negative eight plus three by the way for these problems feel free to pause the video try it yourself and see if you can get the answer negative eight plus three is negative five so starting at negative eight we're adding three so we're going to go three spaces to the right one two three so negative seven negative six negative five and there it is now what about negative nine minus four what's the answer to that problem so negative 9 minus 4 is negative 13. so if we start at negative 9 we're going to subtract 4 to it so we need to go four units to the left so one two three four this is going to be negative 10 negative 11 negative 12 negative 13. now what if there's like three negative signs like negative 10 minus negative four sometimes you might see this in parentheses but it's the same as if it's written like this too now whenever you see two negative signs right next to each other with no number in between them you can change that into a positive so this is the same as negative ten plus four a negative times a negative is a positive um a negative times a positive is a negative and a positive times a positive is just a positive number so we have is negative 10 plus four so starting from negative 10 we're gonna add four units or go four units to the right so one two three four negative nine negative eight negative seven negative six therefore negative ten plus four is equal to negative six so what about eight minus negative three how would you do that one so we can change the two negative signs into a plus so this is a plus three which we know is eleven if we start from eight and go three units to the right we would end at eleven so now let's take a quiz try these problems eight plus seven five plus nine six plus seven and five plus twelve so try these four problems first you can use the number line technique and then i'm going to pause the video to take a minute to do that and i'll just give you the answers so 8 plus 7 is 15. so if you go if you start from 8 and you go seven units to the right you should end at fifteen six plus seven is thirteen five plus nine is fourteen and five plus twelve is seventeen try these let's say if you have nine minus four and uh 12 minus 5 and 14 minus 6 and one more that's similar to this type of problem 22 minus 13. so in these four problems notice that the positive number is larger than a negative number when that happens usually uh your result is going to be positive so nine minus four is equal to positive five using a number line if you start at nine and go four units to the left since you're subtracting by four this is going to be eight seven six five so fourteen minus six if you don't see that correctly it looks like this 14 minus 6 is positive 8 and 12 minus 5 that's positive 7 and 22 minus 13 is positive 9. so you can use the number line to check your answers or if you have a calculator you can use that too but it's always good to do mental math try these four problems seven minus nine four minus twelve five minus sixteen and eight minus nineteen so notice that the negative number is larger this time so therefore the result should be negative seven minus nine is negative two so if you start from seven and if you travel nine units to the left this will be six five what else let's count it one two three four five six seven eight nine so this would be six five four three two one zero negative 1 negative 2 so we get that answer 5 minus negative 16 you should get negative 11 4 minus 12 is negative 8 and 8 minus 19 is negative 11 as well so let's use the number line for one more example now let's use it for four minus twelve but counting twelve spaces backwards that might seem like a long task you could do it though but we can also write it as negative 12 plus 4 that's the same as 4 minus 12. so if we start at negative 12 and if we go 4 units to the right it's it's going to be a 1 2 3 4. so this is negative 11 negative 10 negative 9 negative 8. but if you want to do it the long way you could start with 4 and go 12 spaces backwards 1 2 3 4 5 6 7 8 9 10 11 12. and as you can see you're going to reach negative 8. try these examples negative six plus nine negative 5 plus 14 negative 8 plus 12 and negative 9 plus seventeen so we have a positive and a negative number notice that the positive number is larger so when we add these two values we should get a positive value at the end so negative six plus nine is positive three using a number line if we start with negative six and if we go nine spaces to the right one two three four five six seven eight nine this will be negative five negative four negative three negative two negative one zero one two three negative eight plus twelve that's going to equal positive four negative five plus fourteen that's nine and uh negative nine plus seventeen will give you eight so here's the next round of questions negative 5 plus 2 negative 12 plus 5 negative 16 plus 7 and negative 14 minus five so try those so starting with negative five we're going to add two units so one two we're gonna go two units to the right this will be negative four and negative three so negative five plus two is negative three so notice that the first number the negative one is larger so therefore um the result will be negative negative 12 plus five is equal to negative seven negative 16 plus seven um you should get negative nine and negative fourteen minus five is negative nineteen try these what if so let's say if we have two negative signs negative three minus five what do you think the answer will be to that particular problem so negative three minus five is negative eight so if we make the number line starting at negative three we're going to subtract it by five so we need to go five units to the left one two three four five so this will be negative four negative five negative six negative seven and negative eight so when you have two number like two negative numbers written in the way that we have it in this video um what you could do is just add three plus five which is eight and then make a negative so negative eight minus four is the same as eight plus 4 with a negative on the outside so what you could do is say a plus 4 is 12 and add the negative sign to confirm it we're going to start at negative 8 which is over here and we're going to subtract it by four or go four units to the left one two three four so this is negative nine negative ten negative eleven negative twelve so negative seven minus six is the same as 7 plus 6 with a negative on the outside 7 plus 6 is 13 so this is negative 13. and this is going to be negative and then 9 plus 8. so 9 plus 8 is 17 so this is going to be negative 17. try these negative 8 minus negative 3 negative nine minus negative fifteen negative twelve minus negative four and negative fourteen minus negative sixteen so whenever you see two negative signs like right next to each other you can make that into a positive number so this is the same as negative eight plus three so using the number line if we start at negative eight we're going to add three units to the right one two three so this is going to be negative seven negative six and negative five so negative nine minus negative fifteen is the same as negative nine plus 15. and negative 9 plus 15 is the same as 15 minus 9 so you're gonna get positive six so you can reverse it if you want so negative 12 minus negative four is the same i mean minus negative four is the same as plus four and negative twelve plus four is the same as four minus twelve and that should give you negative eight here we have negative 14 minus negative 16 so that's negative 14 plus 16 and negative 14 plus 16 is the same as 16 minus 14 which equals 2. so keep that in mind you can always reverse the order if you have negative 3 plus 8 you can switch it the 8 is positive the 3 is negative so this is the same as positive 8 minus 3 which is just 8 minus 3 and that's equal to 5. so if you have like negative 10 plus 7 you can reverse and say you know what that's seven minus ten and the negative number is larger so when i subtract them i get three but since the sign of the larger one is negative this is going to be negative here the sign of the larger is positive so this is positive so that covers some basic addition but let's say if you want to add larger numbers let's say if you want to add a 26 plus 74 what would you do without a calculator well you can write it like this 6 plus 4 is 10 so we're going to put the 0 here but the 1 we're going to put it in the next column and then we add one plus two plus seven one plus two is three three plus seven is ten so uh 26 plus seventy four is therefore one hundred try this one add 35 and 62. so 35 plus 62 5 plus 2 is 7 3 plus 6 is 9 so this equals 97. now what about 47 plus 65 so 47 plus 65 5 plus 7 is 12. you gotta carry over the one and then one plus four is five five plus six is eleven so this gives you one twelfth now what about subtraction so let's say if we wish to subtract 87 minus 23 so let's write it like this 87 minus 23 so 7 minus 3 is 4 and then 8 minus two is six so this is equal to 64. not bad right so you can see it here eight minus two six and then the seven minus three is four so you get 64. what about this one 64 minus 39 so if we subtract 4 minus 9 we're going to get a negative number so we don't want that actually let me put some space between these two numbers now what you could do is borrow a 1 from the 6 so the 6 turns into a 5. and we're going to put the 1 here so 14 minus 9 is 5 and then you could subtract 5 and 3 that gives you 2. so therefore 64 minus 39 is 25. let's try another one like that so 76 minus 48 so 6 minus 8 that's going to give us a negative number so let's take away or borrow a one from the seven so that turns into a six so instead of having six we now have uh sixteen so sixteen minus eight is eight and six minus four is 2 so we get 28. now what about 125 minus 69 what is that equal to so let's uh borrow a one from two so now we have fifteen fifteen minus nine is six and so this is nine one and so now what we have here is 11 minus six is five so therefore 125 minus 69 is equal to 56. try this one 42 minus 68 notice that 68 is a bigger number than 42 so therefore the overall result was negative now you don't want to subtract it the way it's written what you could do is if you're subtracting by a larger negative value reverse it 68 minus 42 so 8 minus 2 that's going to be six and six minus four is two since you reverse it add the negative sign so therefore 42 minus 68 is equal to negative 26. let's try another example twenty five minus seventy four so we're subtracting twenty five by a larger negative number so let's reverse it so four minus five we can't do that we need to borrow a one so the seven will turn into a six and the four will become fourteen so fourteen minus 5 is 9 and 6 minus 2 is 4 so we get 49 but we're going to add a negative sign so this is negative 49. so now let's go over multiplication um the first thing we're going to do is construct a simple multiplication table so let's begin now if you can construct a table yourself it's going to help you to like know your multiplication numbers which i would highly recommend you do so as well because you'll see a pattern so for example what's like what's five times four now some of you may know the answer but if you if you're not sure what that is um it might help for you to uh get a calculator or construct a multiplication tables and you want to know your multiplication numbers up to 12. it's going to help you with a lot of arithmetic calculations that we're going to do from here on so don't skip this step now i may not go up to 12 in this particular example but i want you to i want to give you an idea of how to construct a table so what we're going to do is put numbers in the first row this is going to be 1 2 3 4 5 6 7 8 9. and here we're gonna have one two three four five six seven i guess we'll go up to eight here and maybe we can go up to ten so one times one is one one times two is two and then these numbers will increase by one now two times one is uh two two times two is four two times three is six and these numbers will continue to increase by twos so notice the pattern and so now for the threes three times one is three three times two is six three times three is nine three times four is twelve three times five is fifteen three times six is eighteen three times seven is twenty one three times eight is twenty four three times nine is twenty seven three times ten is thirty so notice we're just adding threes now four times one is four four times two is eight four times three is twelve four times four is sixteen four times five is twenty four times six is twenty four four times 7 is 28 4 times 8 is 32 4 times 9 is 36 and 40 and 4 times 10 is 40. now 5 and 1 is 5. 5 times 2 is 10 and then these numbers will continue to increase by 5. so five times five is twenty five five times eight is forty and five times ten is fifty so these numbers will continue to add by six six times four is twenty-four six times seven is forty-two and so forth seven times one is seven seven times three is twenty one seven times six is forty two seven times eight fifty-six and now for the eights so this will keep increasing by eight so let's say if you wish to multiply uh six times eight so you would look for you would go on the sixth row and stop once you reach the eight column so six times eight is forty eight so now let's say if you want to multiply um seven times nine so here's seven here's nine so from the seventh row go towards the ninth column and you get sixty three so therefore seven times nine is sixty-three so let's say if we wish to multiply uh four times six so fourth row six column four times 6 is 24. so that's how you would use it so um feel free to take a moment and study the table and even get to a point where you can construct the table um yourself go up to 12. you want to know your multiplication numbers um from 1 to 12. and then i'll quiz you on it so let's say if you want to multiply 5 times 6 this can be written like this or it can be written as five times six five times six is thirty now if you ever forget the table what you could do is um you can add five six times because that's what multiplication is five times six means you're adding five six times and this will give you thirty so for example four times three is equal to twelve four times three means that you're adding four three times and that's equal to twelve it can also mean that you're adding three four times which will also be equivalent to twelve so five times three according to the table is fifteen um but if you wanna turn it into addition five times three is five plus five plus five three times or it's adding three five times and that gives you in both cases fifteen so what's six times four six times four is twenty four if you add six four times you get twenty four okay so at this point make sure you have the multiplication table memorized and then once you do try this quiz 8 times 7 just make sure you know it is 56 9 times 9 is 81 7 times 6 is 42 10 times 5 is 50. okay try these feel free to pause the video so twelve times twelve eight times six four times nine and three times twelve so twelve times twelve is one forty four eight times six is forty eight four times nine is thirty six and three times twelve is also thirty six so 12 times 5 that is equal to 60 7 times 9 is 63 8 times 12 is 96 and 11 times 11 is 121. okay let's try a few more problems so what's 12 times 9 5 times 8 five times eleven seven times twelve twelve times eleven and finally nine times eight so twelve times nine is 108 5 times 8 is 40 5 times 11 is 55 7 times 12 is 84 12 times 11 is 132 9 times 8 is 72 so make sure you're able to perform such multiplication now let's say if you have larger numbers let's say if you wish to multiply 15 times 8 how would you do that well you could do it the old-fashioned way 15 times 8. eight times five we know it's forty so we're going to put the zero and move the four to the top and then you're gonna multiply eight times one eight times one is eight but we need to add the four so this is equivalent to one twenty now if you have a calculator with you or you can go online and type in online calculating google you can punch in this number in your calculator 15 times 8 is 120. now another way you can do this is you can break up the 15 um into 10 plus 5. 10 plus 5 is 15 and then multiply by 8. 8 times 10 is 80 and five times eight is forty now eight plus four is twelve if you add the zero you get one twenty so eighty plus forty is one twenty let's try another problem so what's 20 times 14 how would you multiply those two numbers so 4 times zero is zero and then four times two is eight now we're gonna add a zero so one times zero is zero and one times two is two so if we add these numbers zero plus zero is zero zero and eight that's eight and drop down the two we get two eighty so another way to multiply twenty by fourteen is picture in your mind if you have fourteen twenty dollar bills what's the value of fourteen twenty dollar bills you know five twenty dollar bills is a hundred so another five of another five twenty dollar bills is another hundred and then you have four leftover twenty dollar bills four twenties is eighty so if you add this up you have two hundred eighty dollars and as you can see you have fourteen twenties on this side five plus five plus four is fourteen um when it comes to money it's very easy to do math everyone understands it now another way you could have done this is you could separate the 14 into 10 plus 4 and 20 times 10 is 200 if you have 10 20 dollar bills that's 200 and 20 times 4 well 2 times 4 is 8 so if you add the 0 you get 80 and then so this adds to 280. so let's say if you want to multiply um point 25 by 15 what would you get so 5 times 5 is 25 so we're gonna put the five here and add the two to the top five times two is ten plus two that's twelve then we need to add a zero five times one is five and five times two i mean one times two that's uh two so if we add this we get five seven and three now notice that we have two spaces um after the decimal so we need two spaces here after the decimal so this is three point seven five so that's how you can multiply a number in the decimal another way to multiply 15 by 25 is we know 0.25 is 25 cents imagine if you have 15 quarters 15 quarters has a value of 375 for every four quarters you have as a dollar so four times 25 cents that's one dollar another four quarters is a dollar and another set of four quarters is dollar so that's 12 quarters that we have so far and then 15 quarters we need three more so the remaining three quarters is 25 cents i mean 75 cents so you have and seventy-five cents yeah if you add these numbers if you have these you have a total of fifteen quarters four plus four plus four plus three is fifteen so let's say if you want to multiply 8 times 17. so try this problem but using both techniques so let's do it this way 17 times 8 so 8 times 7 that's 56 we're going to move the 5 here and uh 8 times 1 is 8 plus 5 that's 13. so now let's use the other technique let's replace 17 with 10 plus 7. so eight times ten is eighty and eight times seven is fifty six if you add these two numbers eighty and fifty six six plus zero is six eight plus five is thirteen you get the same answer 136 so there's many techniques that you can use to do mental math or even just math on paper without the use of a calculator but now let's go over some other concepts let's say if you want to multiply ten times ten now by instinct you probably know that this is a hundred but the way you should do this is in your mind you should multiply one times one which gives you one and then add the two zeros so for example ten times a hundred well if we multiply one and one we get one and then add the three zeros that we see we have one two three zeros so one that means zero zero zero so that's a thousand so a hundred times a hundred so one times one is one and then add the four zeros so we get ten thousand so what do you think a hundred times ten thousand is well here we have a total of six zeros so this is one million okay so now let's try that let's try um this principle to other harder problems let's say if you want to multiply 50 times 100 so basically if you have 50 100 dollar bills how much money do you have so if we multiply the numbers on the outside five and one five times one is five and then add the three zeros this is five thousand if you want to multiply 40 by 200 what you do first is multiply four times two and that's going to give you uh eight and then add the three zeros so therefore forty times two hundred is eight thousand so what's thirty times six hundred well three times six is eighteen and if we add the three zeros that's eighteen thousand so what about seventy times eight hundred seven times eight is 56 out of three zeros that's 56 000. okay so let's try a quiz so try these problems so these large calculations you can do without the use of a calculator so 40 times 900 seems like you're multiplying very very huge numbers but remember all you need to do is multiply the numbers on the outside 4 times 9 is 36 and then add the three zeros so therefore 40 times 900 is 36 000. so what's 500 times 700 so 5 times seven is 35 and then we have four zeros to add so this is going to be 350 000. 60 times 40. so 6 times 4 is four add the zeros this is twenty four hundred what's eight times five eight times five is forty then add the six remaining zeros so this is equal to 40 million now what's 12 000 times 70 000 now this is why you want to know your multiplication tables up to 12. 12 times 7 is 84 and we have three zeros on this side and four zeros here so we have a total of seven zeroes so let me make sure i put the comma in the right place so i need a comma here and here so this twelve thousand times seventy thousand is eight hundred forty million so regardless of how big these numbers get as long as you follow the basic principles you can pretty much do math up to any limit by the way the video that you're currently watching is a one hour trailer version of a longer four hour paid video so i'm gonna post a link here in case if you uh want to watch the remaining three hours of this video um if you find it useful and you can check that out if you have any questions feel free to post it in the comment section below so now let's go over uh division let's say if you wanted to divide 56 by seven what is the answer now this can be written as 56 over 7 as a fraction in both cases it represents division now division is the reverse of multiplication so you need to ask yourself 7 times what number is equal to 56 again you need to know your multiplication tables 7 times 8 is 56 therefore 56 divided by 7 is 8. so let's try another example what is 24 divided by 6 so 6 times what number is equal to 24. so hopefully you have your multiplication tables memorized at this point but take a minute see if you can figure this out without the use of a calculator you can check your answer with the calculator though 24 divided by 6 is 4 because 6 times 4 is 24. okay let's try one more example so what is 42 divided by six or six times what number is forty two since six times seven is forty two forty two divided by six is seven so now it's your turn feel free to try the following problems so 20 divided by four 36 divided by six 72 divided by 8 and 144 divided by 12. so go ahead take a minute and see if you can find the answers to those questions so 20 divided by 4 is 5 because 4 times 5 is 20. since 6 times 6 is 36 36 divided by 6 is 6. now 8 times 9 is 72 so 72 divided by 8 is 9 and since 12 times 12 is 144 144 divided by 12 is 12. try these 30 divided by five eighteen divided by two forty eight divided by six and fifty four divided by nine so 30 divided by 5 is 6. 18 divided by 2 is 9 since 9 times 2 is 18 and 48 divided by 6 is 8 and 9 times 6 is 54 so fifty four divided by nine is six try this example four hundred divided by five now you might think this is outside of your range but you can view it this way 400 is 40 times 10 divided by 5. now what you could do is divide 10 by 5. 10 divided by 5 is 2 because 5 times 2 is 10 and we still have the 40. so 40 times 2 is 80. another way you could have seen this is you could focus on the 40 right here 40 divided by 5 is 8 and then simply add the zero you can get 80. so try this one 3 500 divided by seven so let's divide 35 by seven first 35 divided by seven is five and then add the two zeros so thirty five hundred divided by seven is five 500. so what about this one what's 18 000 divided by 30 18 divided by 3 is six now we can cancel a zero so we have two zeros left over we're going to carry it over so eighteen thousand divided by thirty is six hundred now what about 4500 divided by 900 well we can cancel the zeros so this is basically 45 divided by f nine and since nine times five is forty five then forty five over nine is five so forty five hundred over nine hundred that's just five now what about six hundred thousand divided by twelve hundred so let's cancel the zeros we can cancel two zeros and if we divide sixty by twelve we get five since five times twelve is sixty now there's two zeros remaining that we didn't account for so we're going to add those two zeros here so therefore six hundred thousand divided by twelve hundred is five hundred now let's try this example sixty three thousand divided by seventy well we can cancel zero 63 divided by seven is nine and we're going to add these two zeros so therefore sixty three thousand over seventy is nine hundred so now let's say if you have a number that doesn't go into it let's say like 39 over 6 6 and 39 that's not in the multiplication tables so what can you do in a situation like this since 39 is not a multiple of 6 you can use long division to get the answer so basically we're converting a fraction into a decimal the 39 is going to go inside the long division symbol now you have to ask yourself how many times does 6 go into 39 well if you write out all the multiples of 6 is 6 12 18 24 30 36 42 is too much so we're gonna get rid of that you need to add six six times to get to 36 since 6 times 6 is 36 and then you need to um they need to subtract these numbers 39 minus 36 is 3. now 6 doesn't go into 3 so we're going to add a 0. so we're going to add a decimal point and we're going to treat this as if it's 30. so 6 goes into 30 five times because we have to add six five times skip to 30. so this shouldn't have been a zero here i should have just put just a decimal point but we're still going to bring down the zero so 6 times 5 is 30 and we have a remainder of 0. so the answer therefore is 6.5 so that's a simple way in which you can convert a fraction into a decimal but let's try another example let's try 42 divided by 8 so how many times does 8 go into 42 so let's write out the multiples of 8 16 24 32 40. 48 is too much so if we add eight five times you get to forty eight times five is forty and we need to subtract so forty two minus forty is two and we're going to add a decimal point bring down the zero so how many times is eight going to 20 eight goes into 20 at least two times three times to be 24 so that's too much so 8 times 2 is 16 and the difference of that will give us four and we need to add another zero so how many times is eight going to forty as you can see it's five times so we gotta add eight five times to get to forty so we're gonna put a five here and eight times five is forty so the remainder is zero once you get a remainder of zero that's it um you're done so the answer that you're looking for is right here so 42 divided by eight is therefore equal to 5.25 let's try another example actually you can pause the video and try this one so let's say if you want to find out what 22 divided by 4 is so take a minute and try it yourself so how many times does 4 go into 22 so if we write out the multiples of 4 it's 4 8 12 16 20 24 is too much so 4 goes into 22 at least 5 times so 4 times 5 is 20 and the difference is 2. we're going to add a decimal point and then bring down a zero now four goes into 20 five times so we get another five and when we subtract these numbers the remainder is zero so this is equal to 5.5 all right so let's try let's see 28 divided by three now three times six is eighteen three times nine is close is twenty seven three times ten is thirty that's too much so um three goes into twenty eight seven times so now we have to subtract 28 minus set 27 is one we're going to add a decimal point and bring down a zero three goes into ten three times three times three is nine and a difference is one so you bring down another zero you get ten notice that this process will repeat three times three is another nine we're gonna get one and therefore it's like nine point three three three three repeating so what you could write is just 9.3 with a line on top which means 9.3 repeating you can round it to 9.33 if you want it's up to you so now let's try 47 divided by 5. so how many times does 5 go into 47 we know five times nine is forty five five times ten is too much i'll be fifty and forty seven divided by forty five is two so we need to add a decimal point since we don't have a remainder of zero and we gotta add one here as well now five goes into twenty four times so we therefore get nine point four and for the sake of practice let's try one more example 426 divided by 12. so how many times does 12 go into 42 if we write out the multiples of 12 is 12 24 36 48 is too much so 12 goes into 42 at least three times 12 times 3 is 36 so 42 minus 36 is six bring down the other six so how many times does 12 go into 66 well let's keep adding multiples of 12. 48 plus 12 is 60 60 plus 12 is 72 that's too much so we need 5 12 to get up to 60. so 12 times 5 is 60. so that gives us a remainder of six so now we need to add a decimal point we're going to bring down a zero and we know another five will give us sixty twelve times five is sixty and this time the remainder is zero so therefore um 426 divided by 12 is equal to this number which is 35.5 so now let's say if you if the if the numerator is smaller than the denominator so let's say if you have a fraction like one over four how do you convert that into a decimal so the four is on the outside and the one is on the inside well four doesn't go into one so let's add a decimal point and we're gonna add one here so now let's treat the one as if it's a ten four goes into ten two times so it's really a decimal here but you can view it as ten minus eight ten minus eight is two we're going to add a zero four goes into twenty five times and the remainder zero so one over four is equal to point two five what about one over three this is one that's going to repeat so let's add a decimal point so three goes into ten three times three times three is nine so ten minus nine is one add another zero three goes into ten three times so that's going to be nine and this is just going to keep repeating so one over 3 is about 0.33 repeating now there are some common fractions that you simply want to commit to memory you just want to know them um it can help you if you need to do a quick calculation especially in your head one half is point five two over two whenever the numerator which is the top part of the fraction and uh the denominator which is the bottom part of the fraction whenever they have the same value the value of the entire fraction is a whole it's equal to one now here's some other numbers you want to know one over three is about point thirty three two over three is like point six to six six repeating which is really you can round into point sixty seven and three over three as a whole so that's uh equal to one one fourth is a quarter that's 0.25 which is the same as uh 25 2 4 is 0.5 which is about 50 3 4 is 0.75 as a percent that's 75 percent and 4 over 4 that's a whole that's equal to 1 which is 100 percent so one-fifth that's point two and that's about uh twenty percent two over five is 0.4 you simply just multiply 0.2 times 2 and you get 0.4 and so that's like um sets 40 3 over 5 that's point two times three which is point six and so that's sixty percent and four over five that is equal to point eight which is eighty percent and you know five over five is one now the other fractions that you want to know is uh like one over eight one over eight is point one two five which is equivalent to twelve point five percent two over eight is point twenty five three over eight is point three seven five which is thirty seven point five percent four-eighths is point five or fifty percent and five over eight is uh 0.625 which is sixty-two point five percent six over eight if you divide the six and the eight by two you get three-fourths you can reduce the fraction which is equal to 0.75 or 75 percent and 7 8 is 0.875 which is 87.5 percent and then the last one you want to know is the tense so like one over ten is point one which is ten percent two over ten that's point two which is uh twenty percent three over ten is point three which is thirty percent four over ten point four five of ten point five nine over ten point nine so you can see a pattern here and that's like ninety percent so now why is this useful well sometimes you may not want to do long division you can divide fractions in your head so like for example that problem that we had before 39 over 6 you can break that down into two smaller fractions you know 36 goes into six so you can write it as 36 over six now 39 minus 36 is three so 39 over six is equal to 36 over 6 plus 3 over 6 because 36 plus 3 is 39 now by knowing your multiplication tables you know 36 over 6 is equal to 6. now 3 over 6 you can reduce that if you divide both numbers by three top and bottom whatever you do to the top you must do to the bottom of the fraction so if we divide the top fraction by three three divided by three is one six divided by three is two three over six is equivalent to one-half and we know one-half as a fraction is 0.5 so 6 plus 0.5 is therefore 6.5 and that's what we got for long division when we divided 39 by 6. the other example that we had was 42 over 8. now the highest multiple of 8 just under 42 is 40. so you want to separate this fraction one of which will be a multiple of eight and the other is the remainder 42 minus 40 is two so two is the remainder now eight goes into forty five times or 40 divided by eight is five now two over eight we know that to be the same as one-fourth if you divide the top and the bottom by two you can reduce the fraction to one-fourth and one-fourth as a decimal we know it's 0.25 so therefore we add 5 plus 0.25 which is equivalent to 5.25 and so 42 over 8 is 5.25 so with this method go ahead and practice a few problems try nine over two and seven over three convert it into a decimal and you can also convert it to a percentage as well nine over two we can break it into eight over two plus one over two eight divided by two is four and one over two is point five so this is equal to four point five by the way as a percentage one is a hundred percent if you want to convert a decimal into a percentage multiply by a hundred so four point 4.5 is 450 percent a quaker method is you can move the decimal point two units to the right so you get 450. now what about seven over three what is that as a decimal seven over three we can break that into six over three and one over three now we know six divided by three is two and one third is about point thirty three so we get two point thirty three as a percentage that's 233 percent so now let's try five over four and you can also try eight over five so pause the video and see if you can get the answer on paper so five over four we can rewrite that as four divided by four plus one over four now four divided by four that's just one and one over four is point two five so this is equal to one point two five or one hundred and twenty-five percent eight over five um that's five over five plus three over five so five over five is one three over five is point six now if you remember one over five that's point two and then you multiply point two by three you get point six so this is equal to one point six or 160 okay let's not worry about the percentage anymore let's just convert the rest into decimals so try these two 15 over 2 and uh 19 over 3. so we can make this fourteen over two plus one over two fourteen divided by two is seven one half is point five so this is equal to seven point five now three goes into nineteen six times three times six is eighteen so we can write this as eighteen over three and one third eighteen divided by three is six one third is point thirty three so as a decimal this is six point thirty three so try these two 11 over 4 and 24 over 5. 11 over 4 is 8 over 4 and 11 minus 8 is 3 that's the remainder so 8 over 4 is 2 3 4 is 0.75 so therefore 11 divided by 4 is 2.75 so 24 over 5 that's 20 over five plus four over five so if you think of the multiples of five that's five ten fifteen twenty twenty five is too much it exceeds twenty four so we need to stop at twenty that's why we choose this number and then to get this number simply subtract 24 minus 20 it gives you the remainder four so 20 divided by five is four and four over five is point eight so that therefore 24 over 5 is 4.8 try this one 23 over 8. so multiples of 8 are 8 16 24 24 is too high so we'll stop at 16. 23 minus 16 is 7. so 8 16 divided by 8 is 2 and 7 8 is about as a decimal 0.875 so this is 2.875 by the way if you get like 9 as a fraction um one over nine is about point one one one one repeating so two over nine is about point twenty two repeating three over nine is point thirty three repeating four over nine is point forty four repeating five over nine point fifty five repeating and so forth so six over nine is point six six repeating eight over nine is like point eight eight repeating so let's say if you have uh 15 over 99 that's going to be 0.15 repeating so it's like .151515 it keeps on going forever so 27 over 99 it's going to be 0.272727 repeating so you can write it as just 0.27 so 46 over 99 and 73 over 99 this will be 0.46 repeating 0.73 repeating now let's say if you have like 246 over 999 this would be 0.246 repeating and if you have like 375 over 999 it's 0.375 repeating now some of these um you may be able to reduce this fraction but if you quickly want to get the decimal value this is what it is so just in case if it's based on nine now what about this one what's 76 divided by a hundred now remember the last actually before we do that let's do this one 76 divided by 10. now when we said 5 over 10 we said that was 0.5 3 over 10 was 0.3 so what do you think 76 over 10 is equal to 76 over 10 is equal to 7.6 you see what you need to do is move the decimal one unit to the left so it's right now it's right here you move it to the left it becomes 7.6 so notice the pattern so 76 over 10 is 7.6 76 over 100 you move the decimal 2 units to the left that's going to be 0.76 76 over a thousand point zero seven six seventy six over ten thousand it's going to be .0076 so with that in mind divide these numbers by go ahead and simplify these fractions convert them into a decimal let's say if you have 54 divided by 10 23 divided by 100 um 8 over 10 4.6 over 10 try those so 54 divided by 10 that's 5.4 23 divided by 100 is 0.23 so you move the decimal place two units to the left here just one unit eight divided by ten um that's point eight four point six divided by ten is point four six so try these point 43 divided by 10 7.1 divided by 10 84 divided by 100 and .25 divided by 100 so if you divide it by 10 move the decimal point one unit to left so this is going to be .043 this is 0.071 actually that's too far that's 0.71 um this is going to be .84 and for this one i'm going to move it two units to left so it's going to be .0025 so try these 36 divided by a thousand four hundred seventy five divided by a hundred three thousand eight hundred fifty six divided by ten and uh 4.92 divided by a thousand so 36 divided by a thousand let's move the decimal point three units to left one two three so it's point zero three six four hundred seventy five divided by a hundred move it two units to left so this is four point seven five here this movement one unit to left so it's going to be 385.6 and for this one move it three units to the left one two three so we gotta fit in two zeros here the decimal point is now here so it's going to be point zero zero four nine two so that's how you can divide numbers if it's ten a hundred or a thousand you