How to Order Fractions From Least to Greatest

Step-by-Step Guide

1. 1

   Step 1: Find a common denominator for all the fractions.

   Use one of these methods to find a denominator, or lower number of a fraction, that you can use to rewrite every fraction in the list, so you can easily compare them.
   
   This is called a common denominator, or the lowest common denominator if it is the lowest one possible:
   Multiply every different denominator together.
   
   For example, if you are comparing 2/3, 5/6, and 1/3, multiply the two different denominators: 3 x 6 =
   18.
   
   This is a simple method, but will often result in a much larger number than the other methods, which can be difficult to work with.
   
   Or list the multiples of each denominator in a separate column, until you notice a number that shows up on every column.
   
   Use this number.
   
   For example, comparing 2/3, 5/6, and 1/3, list a few multiples of 3: 3, 6, 9, 12, 15,
   18.
   
   Then list the multiples of 6: 6, 12,
   18.
   
   Since 18 shows up on both lists, use that number. (You could also use 12, but the examples below will assume you are using
   18.)
2. 2

   Step 2: Convert each fraction so it uses the common denominator.

   Remember, if you multiply a fraction's top and bottom by the same amount, the fraction is still the same size.
   
   Use this technique on each fraction, one by one, so that each one uses the common denominator as the bottom number.
   
   Try it for 2/3, 5/6, and 1/3, using the common denominator 18: 18 ÷ 3 = 6, so 2/3 = (2x6)/(3x6)=12/18 18 ÷ 6 = 3, so 5/6 = (5x3)/(6x3)=15/18 18 ÷ 3 = 6, so 1/3 = (1x6)/(3x6)=6/18 , Now that they all have the same denominator, the fractions are easy to compare.
   
   Use their top number, or numerator, to rank them from least to greatest.
   
   Ranking the fractions we found above, we get: 6/18, 12/18, 15/18. , Keep the fractions in the same order, but return each one back to its original form.
   
   You can do this by remembering how each fraction transformed, or by dividing the top and bottom of each fraction again: 6/18 = (6 ÷ 6)/(18 ÷ 6) = 1/3 12/18 = (12 ÷ 6)/(18 ÷ 6) = 2/3 15/18 = (15 ÷ 3)/(18 ÷ 3) = 5/6 The answer is "1/3, 2/3, 5/6"
3. 3

   Step 3: Use the top number to order the fractions.

4. 4

   Step 4: Return each fraction to its original form.

Detailed Guide

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