Subtracting Mixed Numbers with Borrowing (Regrouping) | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to subtract mixed numbers with borrowing and we have two examples that we're going to go through together in order to get this down so let's jump into number one where we have 9 and 1 6 minus 5 and a half and the first thing that i like to do is set these problems up vertically so up and down we have 9 and 1 6 minus 5 and a half so the fractions are lined up and the whole numbers are lined up so can we subtract this problem as is no because the fractional part of these mixed numbers do not have common denominators so we can't subtract so we need to find a common denominator and rename so the least common denominator for a six and a two is going to be 6 so let's rename with that common denominator so 9 and how many sixths minus 5 and how many sixths well 1 6 that already has a denominator of 6 so we don't need to rename now as far as one-half we know that 2 times 3 is 6 so we need to do the same thing to the top in order to keep this equivalent 1 times 3 is 3. so now we have renamed fractions with that common denominator of 6 so we are able to subtract but we have 1 6 minus 3 6 so we can't do 1 minus 3 so we need to borrow and just like when we borrow with whole numbers we're going to borrow from the place to the left so we're going to borrow from the whole number nine there so we need to take one from the nine so it's now an eight now we need to add one to that one-sixth but we need to add one whole in fractional form so what we're going to do we are going to use the denominator of 6 because remember we need common denominators when we add fractions and we're going to put 6 over 6 because that equals 1 whole and again i picked 6 over 6 because this denominator is 6 and we need common denominators in order to add fractions so now we have 8 and 1 plus 6 is 7 over 6 minus 5 and 3 6. now we're able to subtract so 7 minus 3 that gives us 4 6 and the whole numbers now 8 minus 5 is 3. so that's our answer but always check to see if you can simplify the fractional part of a mixed number so we have 4 6 which we have a common factor between our numerator the top number and our denominator the bottom number 2 so we can divide both of those by 2 in order to simplify so we end up with 3 and 2 3 as our simplified final answer so let's go on to number two where we have eight and two thirds minus two and six sevenths so let's line this up vertically set it up vertically eight and two thirds minus 2 and 6 7. so can we subtract that problem as is can we subtract those fractions no we need a common denominator so the least common denominator for a 3 and a 7 is going to be 21 so let's rename we have 8 and how many 21sts minus 2 and how many 21st well we know that 3 times 7 is 21 so we need to do the same thing to the top in order to keep this equivalent 2 times 7 is 14. we know 7 times 3 is 21 so we need to do the same thing to the top 6 times 3 is 18. so we have 8 and 14 over 21 minus 2 and 18 over 21. so we are able to move through the process here and go to subtract but we can't subtract we can't do 14 minus 18 so we need to borrow so let's borrow from the 8 and that's now going to be a 7. let's add one whole here and we're going to do it in fractional form 21 over 21 right we need that common denominator in order to add these fractions and we get 7 14 plus 21 that's going to give us 35 over 21 minus 2 and 18 over 21. so now we can subtract after we just borrowed there so 35 minus 18 that's going to give us 17 20 firsts and our whole numbers 7 minus 2 is 5. always look to see if you can simplify the fractional part of a mixed number 17 and 21 the only common factor is 1 so it is in simplest form and 5 and 17 21st is our final answer so there you have it there's how you subtract mixed numbers with borrowing i hope that helped thanks so much for watching until next time peace