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.
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.
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.
Order these lists of fractions from smallest to largest.
1/7, 8/11, 1/9, 2/3 and 2/5
1/10, 2/9, 7/10, 1/3, 1/4 and 3/5
2/11, 2/7, 3/10, 1/2, 5/9 and 9/11
1/9, 1/7, 2/5, 2/3, 8/11
1/10, 2/9, 1/4, 1/3, 3/5, 7/10
2/11, 2/7, 3/10, 1/2, 5/9, 9/11
Thank you for reading.
