Common fractions (halves) | Math | 4th grade | Khan Academy

Let's try to show that 0.5 is equal to one-half. We often hear people use these interchangeably; they use them back and forth. Maybe someone would say, "I have a 2.5 pound rat," and then someone would say back to them, "Wow, a two and a half pound rat! That's enormous!"

If we get past thinking about how enormous that rat is, what we can notice is they first said 2.5, and then they changed it to two and a half. They use them interchangeably because they're equal, and that's fine. You can use these back and forth because they are equal to each other.

0.5 and one-half are equivalent or equal. But let's don't just accept that that's true; let's see if we can prove it. Let's try to show that.

So, the first way we can show it is down here with a number line. We have a number line that goes from 0 to 1, and it's divided into 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 equal pieces. So, that means each of these pieces is one of the 10 equal pieces, or 1/10.

Looking back at this decimal up here, this 5 is in the tenths place. So, we can also say 0.5 is 5/10 is another way to read that decimal, or we could say 5/10. So, if this distance here is one-tenth, if we travel another one, we've gone two of the tenths, two of the ten equal spaces.

To get to five-tenths, we're gonna travel one, two, three, four, five of the tenths, and right here we have five tenths. We could write it as a fraction or we could write it as a decimal.

So, we found five tenths on this number line, but let's see if that really is the same as one-half. This distance here from zero to one, if we were to block that off, kind of mark it off, this point right here where we said five tenths, this distance, this whole distance that we traveled is this much.

We can see here that this is, in fact, half of the distance between zero and one. This is halfway. So, 0.5 and one-half are at the same point on a number line.

So, that's one way to show their equivalent. Another way we could show that five tenths and one-half are equal is with a fraction model. So here we have a rectangle, and let's try to show one-half. Let's start with one-half this time.

So, if we split this rectangle in half here, we're trying to show half, one out of two equal pieces. So, we'll shade one half, one of the two pieces. So, this is one-half. Now let's try to show that this is equal to five-tenths. Remember, this five is in the tenths place.

So now, instead of halves, we're going to divide our rectangle into tenths: five-tenths. So, let's do that. We'll make ten equal pieces for tenths, and we will shade five of them. We want to see five of the tenths, so let's do that: one, two, three, four, and five.

Here, we've shown five tenths, and we can see that it is equal to one-half. One-half and five-tenths cover the same amount, so they are equal.

So, we've shown two ways now: one-half and five-tenths were at the same spot on a number line, which means they're equal, and they cover the same amount of area, which is another way to show they're equal. So, one-half is definitely equal to zero point five or five-tenths.