Maths Library

Comparing and Ordering Fractions: Grade 3 math

Pupils practise comparing and ordering fractions by finding common denominators or comparing to benchmarks like one half. The worksheet builds fluency in using inequality symbols and ordering lists from smallest to largest.

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What this covers

Comparing and Ordering Fractions is taught in Grade 3 (age 8 to 9) as a topic to introduce. It sits in the Fractions strand.

Worked example

Which fraction is larger: 34 or 56

  1. Find a common denominator for 4 and 6, which is 12.
  2. Convert 34 to 912 and 56 to 1012.
  3. Compare numerators: 9 < 10, so 1012 is larger.

Answer: 56

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Fractions with identical denominators, compare using <, > or =
  2. Fractions with identical numerators or where one denominator is a multiple of the other
  3. Two proper fractions with unrelated denominators up to 12
  4. Ordering sets of three or four fractions, including unit and non-unit fractions
  5. Ordering mixed sets containing improper fractions and mixed numbers

Common mistakes

  • Assuming a larger denominator always means a larger fraction
  • Comparing numerators directly without finding a common denominator

Curriculum links

Indicative matches to Common Core State Standards. Check wording and codes against the official document.

  • 3.NF.A.3 Recognize and generate simple equivalent fractions and compare fractions with the same numerator or denominator.

Sample sheet and answers

Six questions at the level's usual difficulty. Open the editor to change, add or regenerate any of them.

Comparing and Ordering Fractions

Grade 3 math

Qs
6
Marks
6
NameDateScore / 6
1.
Write < or >: 45 25
[1]
2.
Write < or >: 47 67
[1]
3.
Write < or >: 13 23
[1]
4.
Write < or >: 35 65
[1]
5.
Write < or >: 47 37
[1]
6.
Write < or >: 57 17
[1]

Answer key

  1. >Use a common denominator of 25; 20/25 and 10/25, so 4/5 > 2/5
  2. <Use a common denominator of 49; 28/49 and 42/49, so 4/7 < 6/7
  3. <Use a common denominator of 9; 3/9 and 6/9, so 1/3 < 2/3
  4. <Use a common denominator of 25; 15/25 and 30/25, so 3/5 < 6/5
  5. >Use a common denominator of 49; 28/49 and 21/49, so 4/7 > 3/7
  6. >Use a common denominator of 49; 35/49 and 7/49, so 5/7 > 1/7