Subtracting mixed numbers with regrouping

So let's see how we could approach 4 and 1/4 minus 2 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 rewrite this as 4 and 1/4 minus 2 and 2/4. The reason why it's useful to write it this way is we could say look, each of these mixed numbers have a whole number part and then they have a fractional part. 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 two-fourths from one-fourth?" Two-fourths is larger than one-fourth. 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.

That's that we're not just subtracting two-fourths from one-fourth; we're subtracting two and two-fourths from four and one-fourth. 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 four-fourths, four-fourths and one-fourth is five-fourths.

So I can rewrite this as three and five-fourths minus two and two-fourths. Once again, why is that useful? Because five-fourths is greater than two-fourths. What is five-fourths minus two-fourths? Well, that's going to be three-fourths. And then what is three minus two? Well, that's going to be one, and we get one and three-fourths.

Another way we could have thought about it is this is the same thing as four minus 2 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 4. Instead of 4, we could rewrite that as 3 plus 4/4. That's the same thing as 4, and of course you have minus 2 plus 1/4 minus 2/4 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 3 minus 2, that's that part in that part. And then you're going to have, if you have the four-fourths and the one-fourth, so plus five-fourths minus two-fourths. That's exactly what we have here: three and five-fourths minus two and two-fourths.

So three minus two is one, and five-fourths minus two-fourths is three-fourths.