Subtracting a mixed number from a whole number
Narrator says 'rewrite this seven as 9 8/8' when he means 6 8/8; an on-screen note corrects it.
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The video works out 7 - 4 5/8. Because 7 has no eighths, it rewrites 7 as 6 + 8/8, written as the unusual mixed number 6 8/8. Then it subtracts the eighths (8/8 - 5/8 = 3/8) and the wholes (6 - 4 = 2) to get 2 3/8.
You'll be able to
- rewrite a whole number as a mixed number with eighths, like 7 = 6 8/8.
- subtract a mixed number from a whole number by subtracting fractions and wholes separately.
- explain why we regroup one whole into fractional parts.
Key words
- mixed number
- A number made of a whole number and a fraction, like 4 5/8.
- eighths
- The 8 equal parts a whole is split into; 8/8 is one whole.
- whole
- One complete amount, which can be written as 8/8 when we use eighths.
Transcript
- [Lecturer] Figure out what seven minus 4 5/8 is equal to. And pause this video and try this on your own before we do this together. All right, now let's do this together. Now there's different ways that you could approach this, but one way we could think about lining up the whole numbers.
So we have seven, and then from that we're going to subtract four wholes and 5/8. Now we have an issue here because this top number here doesn't have any eighths. So where do we subtract that 5/8 from? Well, one thing that we could do is we can rewrite seven. Seven is the same thing as six plus one.
Why did I write it this way? Because I can re-express one as a certain number of eighths. One is the same thing as what? Well, one is the same thing as 8/8. So seven is the same thing as six plus eight over eight. Why is this useful? Well, I could write this, and it's a little unusual to write it this way, but I could write this as 6 8/8.
I know that's a very strange-looking mixed number, but if we were to write it here, it would actually make the subtraction pretty straightforward. If we rewrote the seven. Let me change the color to make it clear what I'm writing. So if we were to rewrite this seven as 9 8/8 and we from that, we are subtracting 4 5/8.
The reason why this whole exercise was useful is now we could even think of this as the eighth place if you wanted to think of it that way. But now we have enough eighths here to subtract 5/8 from it. 8/8 minus minus 5/8. This part right over here is going to be equal to 3/8.
And then we could focus on the wholes. So six wholes minus four wholes is going to be two wholes, and we're done. 2 3/8. As I said, there's other ways that you could have expressed this. You could have converted this second, you could have converted both of them into pure fractions instead of mixed numbers.
But this is actually the way that my head would probably handle it, especially if I'm trying to do it in everyday life.
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