Word problem subtracting fractions with like denominators

After a rainstorm, Lily measures the depth of several puddles in her backyard. She records her results in a table. So, here are three different puddles, and she measures the depth in inches.

Then we're asked: how much deeper was the puddle under the swing than the puddle on the sidewalk? So pause this video and see if you can figure that out.

They say, "How much deeper was the puddle under the swing?" So that's this one right over here; that's one and one-fourth inches deep. It's under the swing. How much deeper was that than the puddle on the sidewalk?

Let me do that in a different color. The puddle on the sidewalk - and we see here the puddle on the sidewalk is two-fourths inches deep. So what we could do is subtract the two-fourths from the one and one-fourth. We could write one and one-fourth minus two-fourths.

We could write it like that, and we could try to subtract the fraction part, two-fourths, from the fraction part of this mixed number up here, from one-fourth. But we immediately have a problem because two-fourths is a larger fraction than one-fourth.

So, how do we deal with that? Well, the key is to realize that one can be rewritten as a fraction. One and one-fourth is the same thing as one and one-fourth, the same thing as one plus one-fourth, which is another way to write one in terms of fourths: four-fourths.

So this is four-fourths plus one-fourth, plus one-fourth, which is going to be equal to five-fourths. Now you can view this as five-fourths. This number is the same thing as five-fourths minus two over four.

Let me rewrite it: minus two-fourths. That's pretty straightforward. If I have five of something and I subtract two of it, I'm going to have three of that something. In this case, I'm talking about three-fourths.

So how much deeper was the puddle under the swing than the puddle on the sidewalk? Well, three-fourths of an inch.

Just another way that you could have visualized this is: look, I'm going to subtract two-fourths from one and one-fourth. At first, we could have thought of one and one-fourth as a whole like this.

So let me shade the whole in; that's one, and then I would have a fourth of a whole. So let me divide this into four equal sections. This is one and one-fourth. At first, we said, "Well, how do we take away two-fourths from just that?" I only have one-fourth right over here.

And our key realization is, well, look, I actually – this whole right over here is actually four-fourths. I could think of it as four-fourths. So I could think of it like this, and now I have five-fourths: one, two, three, four, five-fourths.

Now, I could take away two of the fourths. So I could take away one of the fourths and two of the fourths. And what am I left with? Well, then I'm going to be left with these three-fourths right over there.