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Subtracting mixed numbers with regrouping

Sal practices subtracting mixed numbers with common (like) denominators. Items require regrouping (borrowing).

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Video transcript

- [Instructor] So let's see how we could approach four and 1/4 minus two and 2/4. Pause this video and have a go at that before we work on this together. All right, so the first thing that you might try to do is re-write this as four and 1/4 minus two and 2/4. And the reason why it's useful to write it this way is we could say look, each of these mixed number have a whole number part and then they have a fractional part. And so I could try to subtract the fractional part from the fractional part and then the whole number part from the whole number part. And that will often work. But when we go to just the fractional parts and we say hey, how do I subtract 2/4 from 1/4, 2/4 is larger than 1/4. You immediately might find yourself in something of a conundrum. So what do you do? Well, what comes to the rescue is a notion called regrouping and that's that we're not just subtracting 2/4 from 1/4. We're subtracting two and 2/4 from four and 1/4. So what we could do is we could take some of the value that's in this four and regroup it into the fraction. What do I mean by that? Well instead of four, if I view four as three and 4/4, 4/4. And so 4/4 plus 1/4 is 5/4, 5/4. So I could re-write this as three and 5/4 minus two and 2/4. Once again, why is that useful? Because 5/4 is greater than 2/4. What is 5/4 minus 2/4? Well that's going to be 3/4. And then what is three minus two? Well that's going to be one. And we get one and 3/4. Another way we could of thought about it is this is the same thing as four minus two plus 1/4, plus 1/4, minus 2/4, minus 2/4. And we have trouble with the 1/4 minus 2/4. That's what we saw right over here. So what we do is we take some of that value from the four. Instead of four we could re-write that as three plus 4/4. That's the same thing as four. And of course you have minus two plus 1/4 minus 2/4. And then if you add the 4/4 to the 1/4 that's going to give us 5/4. So you're going to have three minus two. That's that part and that part. And then you're going to have if you add the 4/4 and the 1/4, so plus 5/4 minus 2/4. And that exactly what we have here. Three and 5/4, three and 5/4 minus two, minus two, and minus 2/4. And so three minus two is one. 5/4 minus 2/4 is 3/4.