The grid below shows five different fractions. Write down the fractions in order from smallest to largest.
This is sometimes called ascending order. To compare fractions, we first need to ensure that each fraction has the same
denominator. Before we do though, notice that nine-eighths is the only fraction in this list which
is improper. That is to say, it’s the only fraction where the numerator is greater than the
denominator. This means that this fraction is larger than one. By definition, it has to be the largest fraction in the list. This means that we just need to compare the remaining four fractions.
In order to find the lowest common denominator of these remaining four fractions, we
need to find the lowest common multiple of 40, four, two, and 20. In fact, the lowest common multiple of these numbers is 40. It’s the smallest number that is in the 20 times tables, the two times tables, the
four times tables, and of course the 40 times tables. We will therefore leave nineteen fortieths as it is.
To convert three-quarters into fortieths, we need to multiply the denominator by
10. To ensure that we create an equivalent fraction, we need to do the same to the
numerator. Three multiplied by 10 is 30, so our fraction becomes thirty fortieths. To change one-half into fortieths, we need to multiply the denominator by 20. Once again, we do the same to the numerator to create an equivalent fraction. One multiplied by 20 is 20, so one-half is equal to twenty fortieths.
Finally, we multiply the numerator and the denominator of seven twentieths by
two. Seven twentieths is equivalent to fourteen fortieths. We can see that the smallest number in this list now is fourteen fortieths, since 14
is smaller than 19, 30, and 20. The next number in the list is nineteen fortieths, followed by twenty fortieths and
then thirty fortieths. When we write these in order of size, it’s very important that we use the original
The smallest fraction was fourteen fortieths which was equivalent to seven
twentieths. The next was nineteen fortieths which remained unchanged from our original
question. Then we had twenty fortieths, which is equal to one-half, and so on. In order of size from smallest to largest, we have seven twentieths, nineteen
fortieths, one-half, three-quarters, and nine-eighths.