If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

### Course: Arithmetic>Unit 13

Lesson 5: Adding and subtracting mixed numbers with unlike denominators

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

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.

## Want to join the conversation?

• Why can't I convert the mixed numbers into improper fractions and then add them together?
• It is okay if you add them as improper fractions, but you need to show your answer as a mixed number
• I know what to do now! Thanks for the video to help me! Merry Christmas!! 🎄⛄
• 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.
• I don't get this. Help!
• I don't get it either!! :( (I wanted to help but I dunno how)
1.you need to find a common denominator if the denominator for both of the fractions is not the same
Steps to find out common denominator:
ex: 4/49+3/7 - 49 is a multiple of 7 , to get 49 you multiply 7x7
2.now all you have to do is multiply 4x7 which gives you 28
so then your fraction will become 28/49+3/7
3.then you just add the numerator

I hope this helps!
• How come we can’t just add it like a regular adding problem?
• Because this is fractions. is where he starts to add both of them
• If I have 1 9/9 and 6 7/8 do I still have to convert it since 8/8 equals to one whole? :)
• Because you're adding you have to do what you did with adding regular fractions, make the denominators of your proper fractions in the mixed fractions the same, and then you can start adding the whole numbers then the numerators of the proper fractions :) Same when subtracting mixed fractions. Then simplify at the end if you can do.
• I have a test tommorow, Lets hope i dont fail. :o
• practice makes perfect.
• are there tricks to simplifying odd fractions?
• i do not git this video. merry Christmas!
• It is okay if you add themas improper fractions, but you need to show your anwser as a mixed number

## 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.