Adding Mixed Numbers with Regrouping | Math with Mr. J

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to add mixed numbers with regrouping so once we get to our answer it's going to require some regrouping because the fractional parts of these mixed numbers are going to add to give us something more than a whole so we're going to have an improper fraction within that answer and we do not want to leave it with an improper fraction so you'll see exactly what i mean as far as with regrouping as we go through our two examples here so let's jump into number one where we have six and three-fourths plus two and a half so the first thing i like to do i like to rewrite the problem vertically so up and down six and three fourths plus two and a half so i have my fractions lined up and my whole numbers lined up now we can go through our process so we are able to add our fractions if we have a common denominator in the case of number one we have three fourths and a half so we don't have a common denominator so we need to find one so the least common denominator for a four and a two is going to be a 4 so that's our common denominator now we need to rename so let's rename with that common denominator of 4. so 6 and 3 4 that doesn't need renamed it already has a denominator of four plus two and how many fourths so we need to rename that half so it has a denominator of four we need to keep it equivalent it's still going to equal a half be equivalent to a half so how do we get 2 to equal 4 well we know 2 times 2 equals 4 so whatever we do to the bottom we have to do to the top in order to keep it equivalent so 1 times 2 is 2. so now we're ready to add because we have a common denominator so 3 4 plus 2 4 is 5 4. six plus two our whole numbers is eight so we get eight and five-fourths so we just add it now we need to regroup and simplify so five-fourths is an improper fraction it's greater than one whole we don't want to leave our answer like this so what we need to do we need to convert that 5 4 to a mixed number we don't want to leave it improper so we do 5 divided by four how many whole groups of four out of five well one whole group of four out of five does it hit five exactly no we have a remainder or one left over and keep our denominator of four the same so 5 4 equals 1 and 1 4 but that's not our final answer there don't forget about this eight holes here so let's bring that down and what we need to do we need to combine our whole numbers here we are regrouping that one whole with the eight combine our whole numbers so we get nine wholes and then don't forget about our fraction so nine and one 4. so to recap we converted this improper fraction to a mixed number and regrouped the whole number from that mixed number with the 8. now i do want to mention that you should always check to see if you can simplify the fractional part of your answer but in the case of number one one-fourth is in simplest form the only common factor between your numerator and denominator the 1 and 4 is 1 so it's simplified and we are done let's do another example so we'll move on to number two here where we have seven and four-fifths plus four and two-thirds so let's line these mixed numbers up okay so we need a common denominator in order to add our fractions so 5 and there for our denominators obviously they are not the same so we need a least common denominator for a five and a three it's going to be fifteen so let's rename so seven and how many fifteenths plus four and how many fifteenths so let's rename we know five times three is fifteen so four times three gives us twelve whatever we do to the bottom we have to do to the top in order to keep it equivalent so we know three times five gives us a denominator of fifteen so do the same thing to the top two times five is 10. now we're ready to add so let's add our fractions 12 plus 10 is 22 and this is 15. 7 plus 4 is 11. so we have a mixed number here with a whole 11 and then 22 15. so an improper fraction we don't want to leave it like that so we need to convert that to a mixed number so we do 22 divided by 15. how many whole groups of 15 out of 22 well 1 with 7 left over because we did not hit 22 exactly 115 out of 22 we have a remainder of 7. keep our denominator of 15 the same don't forget about our 11. so we need to regroup or combine our whole 11 and then that one for our final answer so 11 plus that one whole gives us 12 i'm running out of room so i will write it below 12 and then our fractional part of 7 15. now always check to see if you can simplify the fractional part of an answer 7 15 the only common factor between 7 and 15 is 1 so it is simplified and we are done so there you have it there's how you add mixed numbers with regrouping all you need to do is convert that improper fraction to a mixed number and then combine your whole numbers and bring your fractional part down with your answer as well so i hope that helped thanks so much for watching until next time peace