Question Video: Comparing Unit Fractions Visually Mathematics • 3rd Grade

Video Transcript

Complete one-ninth what one-third, using the symbol for is less than, is equal to, or is greater than.

These symbols that we have at the end of this question are those that we use when we compare two values together. And in this question, we need to choose the correct symbol to write in between two fractions. So, in other words, we’re comparing two fractions. Is one-ninth less than one-third, is it equal to one-third, or is it greater than one-third? And you might’ve noticed we’ve got some fraction strips underneath that can help us. And we could look at them straight away and be able to compare one-ninth with one-third.

But before we do that, let’s look at the fractions themselves in the question. Both fractions have the same top number or numerator. But look at these bottom numbers. One-ninth has a bottom number or denominator of nine, but the other fraction’s denominator is only three. Nine is greater than three, isn’t it? So don’t you think that’s going to mean one-ninth is greater than one-third? Think it might be time to look at our fraction strips, don’t you? The first thing that we can say about our fraction strips is they’re both the same length. This is really important when we’re comparing fractions. It shows that the whole amount is the same.

Now, the first fraction that’s labeled is one-ninth. And we know that the denominator or the bottom number in a fraction shows how many equal parts the whole amount has been split into. So although we can’t see them all, this fraction strip has been split into nine equal parts. In fact, should we draw them on? There we go. Now, the numerator or the top number in this fraction shows us how many of these parts we’re talking about. And because it’s one, we’re only talking about one out of these nine parts. That’s where this blue part comes from. Now, if we look at our second strip for a moment, we can see that the bottom number or the denominator is smaller. But this doesn’t mean it’s a smaller fraction.

Remember, the denominator shows us how many equal parts we’re splitting the whole amount into. And if we’re splitting it into three parts rather than nine, each of our three parts is going to be larger. And because our numerator is one again, we’re only thinking about one out of these three parts. So that’s where our fraction strips come from. Now we understand them; we can use them to help. We can see that one out of nine equal parts is a lot smaller than one out of three equal parts. One-ninth is less than one-third. The symbol that we need to use in between these two fractions to compare them is the one that means is less than.