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### Unit 14: Lesson 31

Adding and subtracting mixed number with unlike denominators- Adding mixed numbers: 19 3/18 + 18 2/3
- Subtracting mixed numbers: 7 6/9 - 3 2/5
- Add and subtract mixed numbers with unlike denominators (no regrouping)
- Adding mixed numbers with regrouping
- Subtracting mixed numbers with regrouping (unlike denominators)
- Add and subtract mixed numbers with unlike denominators (regrouping)

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# Adding mixed numbers: 19 3/18 + 18 2/3

CCSS.Math:

To add two mixed numbers, you can separate the whole number and fraction parts. Add the whole numbers together as you normally would, and then find a common denominator to add the fractions. Once you have your sum, you may need to simplify the fraction for your final answer. Created by Sal Khan.

## Video transcript

Let's add 19 and
3/18 to 18 and 2/3. So I like to separate out
the whole number parts from the fraction parts. So 19 and 3/18 is the same
thing as 19 plus 3/18. And to that, we are
going to add 18 and 2/3, which is the same
thing as 18 plus 2/3. Now we can separately add
the whole number parts. So we could add
the 19 to the 18. So we could do 19 plus 18. And then we can add
the fraction parts-- let me do this in green--
plus 3/18 plus 2/3. Now 19/18, pretty
straightforward. That is what? Let's see. 19 plus 19 would be 38. So this is going to
be 1 less than that. It's going to be 37. So that gives me 37. And then 3/18 plus
2/3, to add them, I need to have the
same denominator. And the least common
multiple of 18 and 3 is 18. So let's convert 2/3
to something over 18. So 2/3, if I want to write
it as something over 18, well, I multiplied
the denominator by 6, so I'd also have to
multiply the numerator by 6. So it's the same thing as 12/18. So I can rewrite 2/3 as 12/18. And now I can add these
two things together. That's going to be-- so
I have 37 plus-- it's going to be something over
18-- plus something over 18. 3 plus 12 is 15, plus 15/18. And so expressing this
as a mixed number, I get 37 and 15/18. And that's the right number. But we can simplify
it even more. We can simplify the 15/18. Both the numerator and the
denominator are divisible by 3. So let's divide them both by 3. And we're not changing
the value because we're doing the same thing to the
numerator and the denominator. And so this gives us,
we still have our 37, but the numerator is now 5,
and the denominator is now 6. So we get 37 and 5/6. And we're done.