Adding mixed numbers with like denominators
About this video
The video adds the mixed numbers 3 and 2/8 plus 5 and 3/8. It splits each into a whole number plus a fraction, adds the wholes (3 + 5 = 8) and the fractions (2/8 + 3/8 = 5/8), and gets 8 and 5/8. It also shows the same steps set out vertically.
You'll be able to
- explain what a mixed number is.
- add mixed numbers with like denominators by adding the whole numbers and the fractions separately.
- explain why changing the order of the parts doesn't change the sum.
Key words
- mixed number
- A number with a whole number part and a fraction part, like 3 and 2/8.
- like denominators
- Fractions with the same bottom number, such as 2/8 and 3/8.
- whole number
- A counting number with no fraction part, like 3 or 5.
Transcript
- [Instructor] What we're going to do in this video is to start thinking about adding mixed numbers. Now just as a reminder of what a mixed number is, it'd be something like three and 2/8. It's called mixed because part of the way we represent this number is there's a whole number, the three, and then part is as a fraction, 2/8.
But the numbers three and 2/8ths. So let's think about how we might be able to add three and 2/8ths to five and 3/8ths. 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 three and 2/8ths is the same thing as three plus 2/8ths, and five and 3/8ths is the same thing as five plus 3/8ths. And so if we add these two things together we're just adding really these four things together and the order in which we add doesn't matter so you could view this as three plus five plus 2/8ths plus 2/8ths, plus 3/8ths, notice it's just the same thing, I'm just changing the order with which we are adding, and now what is three plus five?
Three wholes plus five wholes, we'll that's just going to be eight. And then what is 2/8ths plus 3/8ths? 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 gonna have five of that something, in this case 5/8ths.
So this is going to be eight plus 5/8ths. Which we can express as a mixed number as just being equal to eight and 5/8ths. Now there's other ways that you might see folks approaching this. You might see something like this where people will write three plus 2/8ths and then they will write right below that they'll write the five 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 five right below the three and then plus and then the fraction you'd write right below the fraction.
3/8ths. And then we can add vertically like this where first we can look at the fractional part, 2/8ths plus 3/8ths is going to be equal to 5/8ths and then three plus five is going to be equal to eight and if you add these two together, eight and 5/8ths, you get eight and 5/8s.
So different ways to approach it, but that will hopefully start to get you comfortable with adding a mixed numbers.
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