Ordering Fractions

Hi there. In this mathematics post, I go over ordering fractions between 0 and 1. This topic is suitable for grades 5, 6, 7. It is assumed that the reader is familiar with lowest common multiples and common denominators.

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Fractions Above Half & Less Than Half

When it comes to ordering fractions (smallest to largest) from a list of fractions such as 1/5, 1/10, 2/5, 1/2, 3/7 and 7/8, it is a good idea to use half as a guide. We can determine which fractions are below half and which one are above half.

From the list of 1/5, 1/10, 2/5, 1/2, 3/7 and 7/8, we have the fractions less than half being 1/5, 1/10, 2/5 and 3/7. For the fraction 3/7 you can determine that this is less than half as half of 7 is 3.5 and the top number of 3 is less than 3.5. The only fraction above half is 7/8.

So far we have the largest fractions as 1/2 and 7/8. We need to sort the fractions 1/5, 1/10, 2/5 and 3/7.

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Comparing Fractions With Common Denominators

There are a couple ways of comparing fractions but I do recommend finding common denominators as it is easy to compare fractions.

From the fractions 1/5, 1/10, 2/5 and 3/7, we need to find the lowest common multiple (LCM) between the denominators of 5, 10 and 7. The LCM of these three numbers is 70.

To get 70 from 5 is from 5 x 14. Obtaining 70 from 10 is from 10 x 7 and obtaining 70 from 7 is from 7 x 10.

The equivalent fraction for 1/5 is 14/70, the equivalent fraction for 1/10 is 7/70, for 2/5 it is 28/70 and the equivalent fraction for 3/7 is 30/70.

Original Fraction	Multiply Top & Bottom By	Equivalent Fraction
1/5	14	14/70
1/10	7	7/70
2/5	14	28/70
3/7	10	30/70

The equivalent fractions which correspond to their original fractions can be used to order fractions from smallest to largest. For the fractions less than half here the order is 1/10, 1/5, 2/5 and 3/7.

The full ordered list is 1/10, 1/5, 2/5, 3/7, 1/2 and 7/8.