Common fractions (halves)

- [Voiceover] 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. .5 and one half are equivalent or equal but let's not just accept that that's true, let's see, 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 zero to one and it's divided into one, two, three, four, five, six, seven, eight, nine, 10 equal pieces so that means each of these pieces is one of the 10 equal pieces or one tenth. So looking back at this decimal up here, this five is in the tenths place so we can also say 0.5 is five tenths is another way to read that decimal or we could say five tenths. So if this distance here is one tenth, if we travel another one, we've gone two of the tenths, two of the 10 equal spaces. So to get to five tenths, we're going to travel one, two, three, four, five of the tenths and right here, we have five tenths. We could write is as a fraction or we could write is 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, going to mark it off, this point right here where we said five tenths, this distance, this whole distance that we traveled is this much and 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 one to show they're equivalent. Another way we can 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 and now, let's try to show that this is equal to five tenths. Remember, this five is in tenths place. So now, instead of halves, we're going to divide our rectangle into tenths, five tenths, so let's do that. Here we go. So we'll make 10 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 0.5 or five tenths.