How to Order Fractions?

order fraction

When you vvrite fractions in order of size, you must first compare them. You can ordering fractions in two ways:

Ordering Fractions using Common Denominator

When putting fractions in order from smallest to largest (ascending order) or largest to smallest (descending order), it helps to find a common denominator first.

Fractions can be compared and ordered by determining their equivalent fractions with the common denominator. Common denominators are created by using common multiples of the two numbers. For example, 18 is the least common multiple of 6 and 9.
6 x 3 = 18
9 x 2 = 18

Yet 6 and 9 have several other common multiples; however, 18 is the lowest.

Ordering Fractions from Least to Greatest

Let’s learn this with the help of examples.

Example 1 Put the following fractions in order from least to largest value. 
12 , 38 , 34
Solution
First, identify all the denominators of the fractions. The denominators are 2, 4, and 8. Calculate the least common multiple of all the denominators. Use the LCD to rename the fractions as equivalent fractions with the same denominator.

The least common multiple of denominators 2, 4 and 8 is 8. The next step is to rewrite each fraction as an equivalent fraction with the denominator 8.

12 x 44 = 48
38 x 11 = 38
34 x 22 = 68

Now that all the fraction shares a common denominator, it is easier to place the fractions in ascending order (smallest to largest) by comparing their numerators. 

The fraction with the smallest numerator is the smallest. Finally, write the answer, using the original fractions given in the question.
38 , 12 , 34
Let's write using symbols. 
38 < 12 < 34

Convert Fractions to Decimals and then Ordering

Example 2 Arrange the following fractions in ascending order.

45 , 12 , 35

Solution
First, write any improper fractions as mixed numbers.
45 = 0.8
12 = 0.5
35 = 0.6

Since all the fractions have zero in their unit’s digit, compare them by checking the tenths digit.

Now arrange the decimals in ascending order.
0.5 , 0.6 , 0.8

Here is the correct ordering:
12 , 35 , 45

Example 3 Put the following fractions in order from largest to least value.
14 , 23 , 512
Solution
Calculate the least common multiple of all the denominators. The least common multiple of denominators 3, 12 and 4 is 12.
The next step is to rewrite each fraction as an equivalent fraction with the denominator 12.

14 x 33 = 312
23 x 44 = 812
512 x 11 = 512

By comparing the numerators, the final answer becomes
23 , 512 , 14