in this lesson we're going to focus on adding and subtracting fractions let's say if we have 3 divided by 5 plus 4 divided by 7. how can we add these two fractions well here's a simple technique first multiply five and seven this will give you a common denominator of thirty five next multiply three and seven three times seven is twenty-one and also there's a plus in between multiply five times four which is twenty twenty-one plus twenty is forty-one so the answer is 41 divided by 35. let's try another example let's say if we want to subtract 7 over 8 minus 2 over 9. let's use the same technique let's multiply the two denominators eight and nine which is uh 72 and then the next one is going to be uh 7 times nine which is sixty-three minus eight times two which is sixteen now let's subtract what is sixty-three minus sixteen this is going to be 47. now 47 is not divisible by 2 nor is it divisible by 3. so this is it that's the final answer so now you know how to add or subtract two fractions now what if we wanted to add or subtract let's say three fractions instead of two what should we do in this case so let's say we wish to combine three over four plus five over three minus seven over two whenever you wish to add or subtract fractions the denominator has to be the same the denominator is the bottom part of the fraction and right now they're all different so how can we make them the same how can we get the common denominator if you want to find the least common denominator make a list all of the multiples of 2 are 2 4 6 8 10 12 14 and so forth multiples of 3 are 3 6 9 12 15 18 and so forth and multiples of 4 are 4 8 12 16 20. what is the least common multiple we're looking for a multiple that is common to all three numbers but is the lowest the least common multiple is 12. 12 is common to 2 3 and 4 and it's the lowest of such numbers now granted 24 is also a common multiple and if you use 24 you can get the right answer you just got to simplify at the end so if you're ever like unsure about how to find the least common denominator you can find any common denominator one simple technique is simply to multiply these three four times three times two is 24 and you could use 24 and still get the right answer so now that we know the least common denominator is twelve let's multiply each fraction in such a way to get twelve the first fraction let's multiply the top and the bottom by three because three times four is twelve the second one let's use four and for the last one let's use six so looking at the first one three times three is nine three times four is twelve four times five is twenty four times three is twelve seven times six is forty two two times six is twelve now that we have the same denominator we can combine the numerators 9 plus 20 is 29 and 29 minus 42 is negative 13. so this is the final answer it's negative 13 divided by 12. so now it's your turn go ahead and try this example 8 over 5 minus 2 over 3 plus 9 divided by four so go ahead and add these three fractions so this time to find the least common multiple we're just going to multiply five three and four it may not be the least common multiple but it is a common denominator just so you know if we multiply 5 times 4 times 3 this will give us 5 times 4 is 20 20 times 3 is 16. so 60 is going to be the common denominator that we're going to try to get so we're going to multiply the first fraction by 12 because 12 times 5 is 60 and the second one by 20 because 20 times 3 is 60. by the way if you want to find out the number divide it 60 divided by 5 will give you the 12. 60 divided by 3 will give you the 20 and 60 divided by 4 will give us the number that we need to multiply this fraction by which is 15. now 12 times 8 that's 96 5 times 12 we know it's 60. 2 times 20 is 40 3 times 20 is 60 and 9 times 15 15 times 10 is 150 so if you take away 15 from that you'll get 15 times 9 so that's 135 and 4 times 15 is 60. now 96 minus 40 that's positive 56. and 56 plus 135. let's go ahead and add those two numbers the old-fashioned way five plus six is eleven carry over the one one plus three plus five is nine plus one so the final answer is 191 divided by sixty in this lesson we're going to focus on multiplying two fractions whenever we need to multiply multiply the numbers across the fractions 3 times seven is equal to twenty one and five times two is equal to ten and so this is it the answer is twenty 21 over 10. that's all you need to do when multiplying fractions but sometimes the numbers may not be that small let's say if we have larger numbers what should we do in this case now we can multiply across we can multiply 24 and 45 which will give us a big number but do we really want to do that when multiplying fractions with large numbers it's in your best interest to break down the large numbers into small numbers for instance 24 is basically six times four 27 is nine times three forty-five is nine times five and 30 is 6 times 5. you want to break it in such a way that you can cancel some numbers here we can cancel a 5 because we have 1 on top and the other on the bottom the same is true for the 9 and we can cancel a six so therefore the final answer is four over three so we were able to get the final answer without multiplying twenty four by forty five that step was necessary plus is going to take some time and you need a calculator doing it this way requires no use of a calculator try this one multiply 56 divided by 77 by 35 over 40. now 56 is 8 times 7 77 is 11 times 7 35 is 7 times 5 and 40 is 8 times 5. so we can cancel an eight we can cancel a seven and we can cancel a five leaving the final answer of seven over eleven so now you know how to multiply two fractions in this lesson we're going to focus on dividing two fractions let's use eight over five as an example and let's divide it by twelve over seven now perhaps you heard of the expression keep change flip it's useful when dividing fractions keep the first fraction the same way change division to multiplication and flip the second fraction and now you can do it so 8 times 7 is 56 but we can simplify it before we multiply 8 is basically 4 times 2 and 12 is four times three so we could cancel a four and now we can multiply two times seven is fourteen and five times three is fifteen so the final answer is fourteen over fifteen try this one what's four divided by three divided by nine over five so using the expression keep change flip let's keep the first fraction the same let's change division to multiplication and let's flip the second fraction now there's nothing to cancel so let's multiply across 4 times 5 is 20 3 times 9 is 27 and so we can't reduce this fraction that's the answer now what if you see a problem that looks like this 36 over 54 divided by 64 over 48 if you have a fraction written this way what should you do this expression is equivalent to saying 36 over 54 divided by 64 over 48 and then we can use the keep change flip principle let's keep the first fraction the same let's change division to multiplication and then let's flip the second fraction and now let's simplify so 36 is basically nine times four fifty four is nine times six forty eight is sixteen times three and sixty four is sixteen times four so right now we can cancel a nine we can cancel a 16 and we can cancel a four so what we have left over is three over six now three over six can be reduced we can divide both numbers by three three divided by three is equal to one six divided by three is two so the final answer is one over two you