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Question Video: Finding an Equivalent Fraction Using a Number Line Mathematics • 3rd Grade

Complete the following: 2/3 = .../...


Video Transcript

Complete the following: Two-thirds equals what.

In this question, we’ve been given a pair of equivalent fractions. We can tell that they’re worth the same because there’s an equal sign in between them. Our first fraction is two thirds, but we don’t know what our second fraction is at all. And you know, the interesting thing about this question is that if we weren’t given any more information to help us, there’s actually more than one fraction we could give us an answer. There are several fractions that are worth the same as two-thirds. But thankfully, in this question, we are given some more information to help us. We’re shown two number lines. Let’s look at them one by one.

Our first number line is split up into three equal parts. It shows thirds. And these are labeled for us: one-third, two-thirds, and then three-thirds, which is the same as one whole. So why are we shown this number line? Well, it links with our first fraction. We can see two-thirds on it. Can you see that orange line that goes all the way from zero, two-thirds of the way along the number line? Now, if we look at our second number line, we can spot a few things. Firstly, it begins at zero, and can you see both zeros are lined up? And it ends at twelve twelfths. And twelve twelfths is the same as one whole. In fact, any fraction where the numerator and the denominator are the same is equal to one whole.

So we can say that our second number line goes from zero to one, and it’s completely lined up with the one above it. And because it’s exactly the same length, this means that we can compare one number line with the other. It’s very easy to do so just by looking up and down. Another thing that we can spot is that our second number line isn’t divided into three equal parts. There are much more. If we count them, we can see that there are 12 equal parts. That’s why the denominator that’s labeled here is 12. We’re talking about twelfths: one twelfth, two twelfths, and so on.

So I suppose what the first thing we could do here is to complete part of our missing fraction. We know that whatever we find here is going to be a number of twelfths. And so the denominator in our missing fraction is going to be 12. So we can ask ourselves, two-thirds equals how many twelfths? Let’s draw a line along our second number line until we get one that’s exactly the same as the first. And as we do so, we’re going to count in twelfths: one twelfth, two twelfths, three twelfths, four twelfths. Let’s pause here to look at something interesting. We can see that four twelfths on our bottom number line is the same as one-third on the top.

Now this isn’t the answer to our question, but we could use it to help, because if we know that one-third is the same as four twelfths, surely two-thirds must be worth double this. What do you think? Do you think if one-third is worth four twelfths, then two-thirds must be worth eight twelfths? Let’s carry on shading our line: five twelfths, six twelfths, seven twelfths, eight twelfths. And we can see that this matches up perfectly with two-thirds on our top number line. Our two fractions might look different, but they’re worth exactly the same. Two-thirds is the same as eight twelfths. We’ve used number lines to show that these are equivalent fractions.

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