in this video we're going to look at how you multiply and divide fractions now multiplying fractions is actually fairly easy because all you have to do is multiply both the numerators and denominators together separately so for 7 over 15 times 3 over 4 you would first multiply your numerators so 7 times 3 to give you 21 as your new numerator and then do the same thing for your denominators so 15 times 4 to give you 60 as your new denominator which means that the answer is 21 over 60. now this answer is entirely correct already but in an exam you'll normally have to simplify your answer which we can do by dividing the top and bottom of our fraction by the common factor of three which will simplify it to seven over twenty for this next question we have to multiply four over seven by nine over five so we multiply 4 by 9 to get 36 and then 7 by 5 to get 35 so we end up with 36 over 35 as our answer and this time there's no need to do anything else because that can't be simplified in this one we're being asked to multiply four-fifths by two and three-quarters which is a mixed number now you can directly multiply fractions by mixed numbers but it's a lot easier if you take the mixed number and convert it to an improper fraction first so to do that we multiply the two by the four to get eight and then add that eight to the numerator of three to get a new numerator of eleven so we get an improper fraction of eleven over four then we can just multiply four fifths by eleven over four like in our other examples so four times eleven is forty 44 and 5 times 4 is 20 which gives us 44 over 20 and then we can simplify that by dividing top and bottom by 4 to get 11 over 5. one other thing to point out about multiplying fractions is that when we multiply together fractions that are less than one like one-half times one-third we actually get an even smaller number because we're taking a small portion of something that was already small for example if we start with half a pizza then by multiplying it by one third we're effectively selecting one third of that half pizza so now we only have one sixth of the whole pizza in order to divide fractions we actually use a trick first of all you want to write out the fraction for example three-quarters divided by five-ninths then you flip the second fraction upside down so change the five over nine to nine over five and then we can rewrite the question with a multiply instead of a divide which means that we'll have three quarters times nine fifths so all we've done is flip the second fraction upside down and change the divide to a multiply then we can just multiply the fractions together as usual so here we're to do 3 times 9 to give us 27 and 4 times 5 to give us 20. so we have 27 over 20 and the last step we need to check if it can be simplified which it can't so the answer stays as 27 over 20. let's try a couple more in this one we're dividing two thirds by four-fifths so we flip the four-fifths upside down to make it five over four and then change the divide to a multiply so that we can multiply them like normal two times five is ten and three times four is twelve so we have ten over twelve which we can simplify by dividing top and bottom by two to get five over six in this question we're dividing three and a half by two-fifths the fact that we need the answer in the form of a mixed number doesn't change how we do the question at all it just means that we're gonna have to convert it into mixed number form at the end the first step though is to convert this three and a half which is a mixed number into an improper fraction to make things easier for ourselves so we do three times two which is six and then add that to the numerator so because six plus one is seven we end up with seven over two and our question now reads seven over two divided by two over five then like always we flip the two over five upside down to get five over 2 and change the divide to a multiply so we're going to have to do 7 times 5 which is 35 and 2 times 2 which is 4. to get 35 over 4 and we can't simplify this at all the last step is to convert this to a mixed number like they ask for in the question so we divide 35 by four to get eight remainder three which means that our mixed number would be eight and three over four anyways that's everything for multiplying and dividing fractions so hope you found it useful and we'll see you again soon