[Music] welcome to math with mr j [Music] in this video i'm going to cover how to multiply fractions using cancellation and cancellation is a way to simplify fractions before we multiply this gives us smaller and easier numbers to work with understanding and using cancellation can make problems a lot simpler and easier to work through so let's get into our four examples here and start with number one where we have 14 15 times 5 16. what we need to do first is look for common factors between the numerators the top numbers here and the denominators so top and bottom we are not looking for common factors horizontally or side to side so always top and bottom think of it like simplifying fractions but you can use all of the numbers within the problem so for example looking for common factors here i know that 15 and 5 have a common factor of 5. so let's divide both 15 and 5 by that common factor of 5. 15 divided by five is three five divided by five is one let's take a look at fourteen and sixteen to see if they have any common factors besides one and they do they have a common factor of two so let's divide both of those by two fourteen divided by two is seven sixteen divided by two is eight so i'm going to rewrite my problem here and we have seven over three times one over eight and we multiply fractions by going straight across so we get seven twenty-fourths always check to see if we can simplify further here but 7 24 is in simplest form the only common factor between 7 and 24 is 1 so we are done so you can see that we got much simpler and easier numbers to work with compared to the original problem so let me rewrite the original problem here fourteen fifteenths times five sixteenths so fourteen times five is going to give us seventy and 15 times 16 is going to give us 240. so you can see that those multiplication problems there are a little more complex and the numbers are greater in value than our cancellation version there of seven over three times one over eight and also seventy over two hundred forty that's going to take a lot more simplifying and work there so you can see that the cancellation made everything simpler now 70 over 240 is equivalent to what we got with the cancellation we would just need to simplify that and break that down and it would eventually get to seven twenty fourths on to number two where we have seven eighteenths times six sevenths so we need to look at numerators and denominators top and bottom and we can see that we have a seven and a seven here so a common factor of seven between those sevens so divide each by seven and we get one seven divided by seven is one all right let's take a look at eighteen and six here so do we have any common factors yes two three and six let's use the greatest common factor of six that way we have less simplifying in the end once we get our answer if you don't use the greatest common factor between two numbers that's fine you're just going to have more simplifying in the end so we'll divide eighteen and six by six so eighteen divided by six is three and six divided by six is one so we end up with one over three times one over one and that's going to get us one third and one third is in simplest form so we are done now again you can do 7 18 times 6 7 and keep it as is and you will get the same answer it's just going to take more simplifying at the end there and you do have larger numbers in value to work with seven times six and eighteen times seven so on to number three where we have two-thirds times 27 so a fraction times a whole number what we need to do here is we'll write two-thirds and we need to make 27 into a fraction so we have a numerator and a denominator and all we need to do if we have a whole number we put it over one and that's equivalent to 27. we didn't change the value of 27 we just converted it to a fraction where we have a numerator and a denominator so let's see if we have any common factors between our numerators and denominators and yes we do three and 27 both have a common factor of three so let's divide both by three three divided by three is one twenty-seven divided by three is nine so let's multiply straight across two times nine is eighteen and one times one is one so we get eighteen over one which is just eighteen and lastly number four where we have a mixed number times a fraction so whenever we have a mixed number we want to convert it to an improper fraction here so we have a numerator and a denominator and we can do that by multiplying and then adding so multiply the denominator by the whole number 9 times 2 is 18 plus the numerator of 2. so again 9 times 2 is 18 plus 2 gives us 20 ninths and if you need more help with converting mixed numbers to improper fractions i'll drop that link down in the description and four fifths we keep as is so let's see here if we have any common factors between the numerators and the denominators so 20 and five both have a common factor of five there so let's divide 20 and 5 by 5. 20 divided by 5 is 4 5 divided by 5 is 1. so we get to 4 times 4 is 16 and 9 times 1 is 9. so we get an improper fraction of 16 9 so we need to convert it to a mixed number here so 16 divided by 9 is going to give us our whole number so how many whole nines out of 16 well one whole nine with a remainder of seven and we keep our denominator the same so one and seven ninths so again what i did there 16 divided by 9 how many whole groups of 9 out of 16 well 1 with a remainder of 7 that's going to be our numerator here and we keep the denominator of 9 the same so there you have it there's how you multiply fractions using cancellation and before i end here i do want to mention that this only works for fraction multiplication and fraction division and for fraction division once a fraction division problem is converted to a multiplication problem that's when you can use this this does not work for adding and subtracting fractions i hope that helped thanks so much for watching until next time peace