Complete five-ninths what four-ninths using the symbol for is less than, is equal to, or is greater than.
In this problem, we have two values that we need to compare, and they’re both fractions. We have five-ninths, and we need to compare this to the second fraction, four-ninths. Is five-ninths less than four-ninths? Is it the same as four-ninths? Or is it greater than four-ninths? How can we compare these two fractions together? Well, if we look closely, our two fractions have got something in common. They both have nine as a denominator. This means both fractions are showing an amount of ninths.
Just like we’d be able to compare five balloons with four balloons or five elephants with four elephants, we’re able to quickly compare five-ninths with four-ninths. Ninths is what we get when we split a whole amount into nine equal parts. Each part has a value of one-ninth. And so, five-ninths is what we get when we show five of these parts. Five out of a possible nine, five-ninths. And we can show four-ninths the same way. We start with one whole, split it into nine equal parts, ninths. And because our denominator is still nine, notice that each of the parts is the same size as in the previous diagram.
So, four-ninths would look like this, four out of a possible nine. The diagrams show what we probably knew already. Five-ninths is greater than four-ninths. Remember that when we use the comparison symbols less than and greater than, we always point the widest part of the symbol towards the greater value. And so, if five-ninths is greater than four-ninths, we need to point the wider part of the symbol towards five-ninths. This way we can be sure that we’ve chosen the correct symbol. It’s easy to get them muddled up.
Both of our fractions showed an amount of ninths. And so to compare them, all we had to do was look at the numerator, look at the number of ninths that they showed. Five-ninths is greater than four-ninths. So, the correct symbol to use in between the fractions is the one that represents is greater than.