Complete four-ninths what seven-ninths using the symbol for is less than, is equal to, or is greater than.
In this question, we’re being asked to compare two fractions, four-ninths and seven-ninths. And we can see in between them in the question there’s a gap. We need to complete this gap using a symbol that compares both fractions together. Is four-ninths less than seven-ninths, equal to seven-ninths, or greater than seven-ninths? To help us choose the right symbol, let’s take a moment to look more closely at these fractions. What do we notice?
Well, the first thing we can see is that they both show a number of ninths. The denominator in both fractions is the same. We know that a denominator shows the number of equal parts as a whole that has been split into. So if they’re both split into the same amount, we can say that the size of these parts is the same. And because, as we’ve said, the size of the parts in these fractions is the same, all we have to do is to compare the numerators, to compare the number of these parts.
Comparing fractions when they both have the same denominator is quite straightforward. We know that four is less than seven. So four-ninths is less as a fraction than seven-ninths. Let’s show this using our diagram. Here’s what four-ninths looks like, four out of nine. And here is what seven-ninths looks like, seven out of a possible nine. And this diagram shows us visually that four-ninths is less than seven-ninths. So the symbol we need to use in between both of these fractions is the one that represents is less than.
Because our two fractions have the same denominator, we compared them just by looking at the numerator. Having the same denominator meant that the size of each part was the same. So we simply needed to look at the number of parts that each fraction was referring to. Four parts is less than seven parts. So we can say that four-ninths is less than seven-ninths.
The correct symbol to compare these fractions is the one that represents is less than.