welcome to a lesson on multiplying and dividing mixed numbers let's first talk about multiplying mixed numbers step one we're going to convert the mixed numbers to improper fractions step two we'll simplify if possible step three we'll multiply and then the last step step four will convert our answers back to a mixed number let's go and look at some examples so the most important thing about multiplying mixed numbers is we have to convert these to improper fractions remember to do that we multiply the denominator times the whole number and then add the numerator so 3 * 2 would be 6 + 1 that would be 7 so we have 7/3 times here we have 4 * 1 that would be 4 + 3 and that would be 7 over 4 or 74s now we go and treat this like a normal multiplication problem involving fractions we try to simplify first nothing simplifies here so we multiply across the top that would be 49 multiply across the bottom that would be 12 this is our product but typically we're asked to convert this back to a mixed number so now we have to take 49 and divide by 12 so let's go ahead and do that 49 / 12 there's 4 12 and 49 4 * 12 is 48 with a remainder of 1 so remember what that tells us is that 491 12ths is the same as 4 and 1 over 12 or 1 12th we put the remainder over the divisor and that gives us our fraction okay let's go ahead and try another one again the first step is to convert 6 and 2/3 to an improper fraction so 3 * 6 is 18 + 2 that' be 20 so we have 20/3 * 1/4 now again before we multiply across the top and bottom we should try to simplify notice the four and the 20 would simplify we can rewrite 20 as 4 * 5 and now we can see that they have a common factor of four so now we can go ahead and multiply across the top and bottom we' have 5 * 1 that's 5 3 * 1 that would be three so our product is 5/3 converting this to a mixed number 5 / 3 there's 1 three and five with the remainder of two so 5/3 the same as one whole and 2/3 let's go ah and try one more and then we'll talk talk about division here we have 8 * 2 and 5 6 we need to write 8 in fraction form so write this as 8 over 1 times converting this to an improper fraction we'd have 6 * 2 that's 12 + 5 17 over 6 now 6 and 8 do simplify they have a common factor of two so there's three twos and six and four 2os and 8 now we can go ahead and multiply across the top and bottom 4 * 17 that' be 68 1 * 3 is 3 this is our product but let's go ahead and convert it to a mixed number 68 / 3 there are two threes in six subtract bring down the eight and there are 2 3 is in 8 2 * 3 is 6 we have a remainder of two so this tells us that 683 is the same as 22 and 23 okay let's go and talk about division now the process will be pretty much the same we're going to convert our mixed numbers to improper fractions then we're going to rewrite the division problem as a multiplication problem simplify multiply and then convert back to a mixed number so it's pretty much the same except we have to rewrite the division problem as the multiplication problem let's try a couple again the first step is to write these as improper fractions so we'll have 10 over one divided by this would be 5 * 3 + 1 that's 165s now the only difference here is now we have to convert this division problem to a multiplication problem so remember dividing by 16 fths is the same as multiplying by the reciprocal so this will be 10 over 1 * 516 notice how we did not take the reciprocal of the first fraction only the second fraction dividing by 16 fths is the same as multiplying by 516 and now it's just like the previous problems we need to simplify this again 10 and 16 have a common factor of two there are five twos and 10 and 8 2s and 16 multiply across the top we have 25 multiply across the bottom we have 8 25 / 8 there are 38s in 25 with a remainder of one so this is equal to 3 and 1/8 and I think we have time for one more here we have 1 and 78 / 1 and 2/3 converting these to improper fractions we'd have 8 * 1 + 7 that's 158 divided 3 * 1 + 2 that' be 5/3 now we need to rewrite this as a multiplication problem so it be 158 times the reciprocal or times 35ths and again let's go ahead and simplify first first notice we have a common factor of five here there's one five and five and three fives and 15 multiply across the top we have nine across the bottom we have eight and 9/8 would be the same as 1 and 1/8 okay that's going to do it for this video thank you for watching for