Arrange eight-halves, eight-quarters, eight-sixths, and eight-fifths in ascending order.
Often when we’re comparing fractions, they have the same denominator. This means that we can put them into order quickly. For example, we know that two-quarters is less than three-quarters. And the fractions we have here don’t have the same denominator. But they do have something else in common. Can you see? They all have the same numerator. And so, as long as we understand what the numerator and the denominator in a fraction represent, then we can put these into order quickly.
We’re asked to arrange these in ascending order. That’s smallest to largest. Now, as we’ve said already, the numerators in our fractions are all the same. So, we can only look at the denominators. Which is going to be the smallest fraction? Is it going to be the one with the smallest denominator, which we can see here is two, which represents halves? Or is it going to be the one with the largest denominator? Here, it’s a six, which represents sixths.
Let’s remind ourselves what a denominator is. The denominator, or the bottom number in a fraction, is the number of equal parts that one whole has been split into. Now, the really important thing to remind ourselves here is the larger the denominator, the smaller the part. Here, we can see one-half because the whole has been split into two parts. And we can also see one-eighth because the whole has been split into eight equal parts.
And we can use the fact that the larger the denominator, the smaller the part to help us find the answer here. If we apply then what we know about denominator to the question, we are looking for the number with the largest denominator first. This will be the one with the smallest part. And the largest denominator, as we’ve said already, is a six. So, the smallest fraction here is eight-sixths. The next largest denominator is a five, so we have eight-fifths, then a four, eight-quarters, and finally a two, eight-halves.
Our four fractions all have the same numerator, and so the same number of parts that we’ve chosen. And so, to put these fractions in order, we needed to understand that the larger the denominator, the smaller the part. We could then arrange our four fractions in ascending order. And they are eight-sixths, eight-fifths, eight-quarters, and eight-halves.