Adding mixed numbers with like denominators

What we're going to do in this video is to start thinking about adding mixed numbers. Now, just as a reminder, what a mixed number is, it'd be something like 3 and 2/8. It's called mixed because part of the way we represent this number is as a whole number, the 3, and then part is as a fraction, 2/8. But the number is 3 and 2/8.

So let's think about how we might be able to add 3 and 2/8 to 5 and 3/8. So pause this video and see if you can have a go at this before we work through this together.

All right, now let's work through this together. Now, there's a couple of ways that we could approach this. You might recognize that 3 and 2/8 is the same thing as 3 plus 2/8, and 5 and 3/8 is the same thing as 5 plus 3/8. So if we add these two things together, we're just really adding these four things together, and the order in which we add doesn't matter.

So you could view this as 3 plus 5 plus 2/8 plus 3/8. Notice it's just the same thing; I'm just changing the order with which we are adding. Now, what is 3 plus 5? Three wholes plus five wholes? Well, that's just going to be 8. And then what is 2/8 plus 3/8? Well, if I have two of something, in this case, eighths, and I add three more of that something, in this case, eighths, I'm going to have 5 of that something—in this case, 5/8.

So this is going to be 8 plus 5/8, which we can express as a mixed number as just being equal to 8 and 5/8. Now there's other ways that you might see folks approaching this. You might see something like this where people will write 3 plus 2/8, and then they will write right below that.

They'll write the 5 in the ones place, or in the whole number, and there's only a ones place in these whole numbers. So you'd write the 5 right below the 3, and then plus, and then the fraction you'd write right below the fraction 3/8. Then we can add vertically like this, where first we can look at the fractional part. 2/8 plus 3/8 is going to be equal to 5/8, and then 3 plus 5 is going to be equal to 8.

If you add these two together, 8 and 5/8, you get 8 and 5/8. So different ways to approach it, but that will hopefully start to get you comfortable with adding mixed numbers.