How to Multiply and Divide Mixed Numbers | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to multiply and divide mixed numbers we'll go through one example of each and i'll explain each step as we work through the problems let's jump into our examples starting with number one where we have four and two-thirds times two and one-fifth now the first thing that we wanna do here is to convert these mixed numbers to improper fractions we do that by multiplying and then adding let's convert four and two-thirds to an improper fraction so we start at the bottom and work our way to the top and again we multiply and then add so 3 times 4 is 12 plus 2 is 14. 14 is our numerator we keep the denominator of 3 the same so fourteen thirds is four and two thirds and we converted it to that improper fraction let's bring our multiplication sign down and then convert two and one-fifth to an improper fraction so we multiply and then add 5 times 2 is 10 plus 1 is 11. so 11 is our numerator and then keep our denominator of 5 the same now the reason we convert these to improper fractions is to have a numerator a top number and then a denominator a bottom number now we can multiply straight across so 14 times 11 that gives us 154 3 times 5 is 15. so we get 154 15 or 154 over 15. that's an improper fraction so we want to convert this back to a mixed number for our final answer so we do that by dividing 154 by 15. how many whole groups of 15 can we pull out of 154 well 10 that gets us to 150. now we did not hit 154 exactly we had a remainder of 4 so that's our numerator and then keep our denominator of 15 the same always look to see if you can simplify the fractional part of a mixed number 4 15 well the greatest common factor between 4 and 15 here is 1 so this is simplified and done 10 and 4 15. so to recap convert to improper fractions and then we can multiply straight across let's move on to number two where we have eight and a half divided by three and six sevenths so we need to convert these two improper fractions start at the bottom work our way to the top multiply and then add so 2 times 8 that's 16 plus 1 is 17. keep our denominator of 2 the same bring our division sign down here and then three and six sevenths so multiply and then add seven times three is 21 plus six is 27 so that's our numerator keep our denominator of 7 the same so now we have numerators and denominators only and we can go through our dividing fractions steps keep switch flip so we always keep our first fraction so let's rewrite this problem using those steps keep 17 over 2. switch division to multiplication the opposite of division here so switch to multiplication and since we switch to the opposite of division we're going to flip our second fraction meaning the 7 is going to be our numerator and the 27 is going to be our denominator this is called the reciprocal so the 7 is now the numerator and the 27 is now the denominator now we can multiply straight across so 17 times 7 and then 2 times 27 now just a side note here if you need to solve something to the side for example 17 times 7 you can come to the side and let's multiply here 17 times 7 well 7 times 7 is 49 7 times 1 is 7 plus 4 is 11. so 119 it's okay to come to the side to solve things if need be so 119 is our numerator and then 2 times 27 is 54. so we get 119 50 fourths or 119 over 54. that's an improper fraction we do not want to leave our final answer as an improper fraction so let's convert it to a mixed number so 119 divided by 54. how many whole groups of 54 can we pull out of 119 well two whole groups that gets us to 108 we did not hit 119 exactly we had a remainder of 11 and we keep our denominator of 54 the same now 11 54 is in simplest form the greatest common factor between 11 and 54 is 1 so we are done here 2 and 11 50 fourths so there you have it there's how you multiply and divide mixed numbers convert everything to improper fractions and then go through your steps as far as multiplying or dividing fractions i hope that helped thanks so much for watching until next time peace you