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Adding Mixed Numbers. Created by Sal Khan and Monterey Institute for Technology and Education.
Video transcript
Add and simplify the answer and write as a mixed number. So we have two mixed numbers here. We have a whole number part and a fraction part. We need to add them. Now, there's two ways to do this. You could convert both of these into improper fractions, then add them, and then convert that back into a mixed number. Or you could just look at this and say, well, you know what? 17 and 2/9 is the exact same thing as 17 plus 2/9, and then 5 and 1/9 is the exact same thing as 5 plus 1/9, so 17 and 2/9 plus 5 and 1/9 is the same thing as 17 plus 2/9 plus 5 plus 1/9. These two statements are completely equivalent. And we know that when you're just adding a bunch of numbers, it doesn't matter what order you do it in, so you can swap the order. So you could say that this is the same thing as 17 plus 5 plus 2/9 plus 1/9. And we could do this in any order. And we know what 17 plus 5 is. We've done that before. 17 plus 5 is 22, so that part right there is 22. So we have 22 plus-- now what is 2/9 plus 1/9? Well, they have the same denominator, so it's going to be over 9, and then you add the numerators. 2 plus 1 is 3. So it's 22 plus 3/9, but this can be simplified. Both the numerator and the denominator are divisible by 3. Divide the numerator by 3, you get 1. Divide the denominator by 3, you get 3. So this is 22 plus 1/3, which is the exact same thing as 22 and-- let me write it in that other blue color-- which is the exact same thing as 22 and 1/3.