Adding Mixed Numbers: A Step-By-Step Review | How to Add Mixed Numbers with Unlike Denominators

[Music] welcome to math with mr j [Music] in this video i'm going to cover how to add mixed numbers now i'll go through one example which should be helpful for anyone looking for a quick review or refresher whether you learned this recently or years ago if you need more help or examples i dropped links to other videos on this topic down in the description let's jump into our example where we have five and two-sevenths plus four and two-thirds now the first thing that i'm going to do i'm going to rewrite this problem vertically so up and down lining up the fractions and whole numbers so we'll start with five and two-sevenths plus four and two thirds so once we do that we need to find a common denominator we're not able to add because we have a 7 and a 3 for our denominators we need a common denominator in order to add the fractional part of these mixed numbers so in order to find a common denominator we need to find a least common multiple and that's going to be our least common denominator now you may be able to figure out what the least common multiple between 7 and 3 is without writing out the multiples but as a review i'm going to come to the side here and we'll write out our multiples and i'll show you how to find the least common multiple and again that's going to be our least common denominator so let's start with seven and i'm going to write out the first four multiples of seven now the multiples go on forever so my suggestion write four or five see if you have any in common if not you can always extend your lists so 7 14 21 28 now we'll write the first four multiples of three so 3 6 9 12. and we don't have any matches there we don't have anything in common so let's extend our lists now seven we're already at 28 and for our multiples of three we're only at 12 so let's extend that list so then we have 15 18 still nothing in common and then we have 21 so 21 is going to be our least common multiple and therefore our least common denominator so that's what we're going to use so once we have that common denominator we're going to rename the fractional part of our mixed numbers with that common denominator that way we'll be able to add so let's go over to our mixed numbers here and rename we do not need to do anything with the whole numbers so this is going to be 21 so let's use equivalent fractions to rename that 2 7 with a denominator of 21 so we need to think how do we get 7 to equal 21 well 7 times 3 is 21. whatever we do to the bottom we must do to the top in order to keep this equivalent two times three is six so six twenty firsts is equivalent to two sevenths we're not changing the value of the problem at all these are equivalent fractions we're just renaming using that common denominator let's bring the addition sign over and then we need to do four and two thirds again we do not need to do anything with the whole number and we have a common denominator of 21. so let's think how do we get 3 to equal 21 well 3 times 7 is 21. whatever we do to the bottom we must do to the top in order to keep this equivalent so 2 times 7 is 14. so now we're ready to add to recap we found our common denominator of 21 then we renamed the fractions of our mixed numbers using that common denominator of 21. now that we have a common denominator between our fractions we're able to add so let's add our fractions and then whole numbers so for our fractions add the numerators 6 plus 14 is 20 and then we keep our denominator of 21. so 6 21sts plus fourteen twenty firsts equals twenty twenty first so we added our fractions now let's add the whole numbers so five plus four is nine so our final answer is 9 and 20 21sts always check to see if you can simplify the fractional part of a mixed number well 20 21st is in simplest form the only common factor between 20 and 21 is one so we are done and our final answer is nine and twenty twenty firsts so there you have it there's how you add mixed numbers i hope that helped thanks so much for watching until next time peace