Maths Library

Equivalent Fractions: Grade 3 math

This topic focuses on identifying, generating, and proving equivalence between fractions using visual models and arithmetic scaling. Pupils multiply or divide numerator and denominator by a common factor to complete equivalent pairs.

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What this covers

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

Worked example

Find the missing number: 35 = /20.

  1. Determine the multiplier for the denominator: 205 = 4
  2. Multiply the numerator by the same value: 3 × 4 = 12
  3. The missing numerator is 12

Answer: 12

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Find the missing number in an equivalent fraction, multiplier 2 to 4
  2. Same, with multipliers up to 4 and small denominators
  3. Missing numerator in equivalent fractions with multipliers up to 9
  4. Larger denominators, still a single multiplier
  5. Mixed denominators up to 9 with multipliers up to 9

Common mistakes

  • Adding the same number to both numerator and denominator instead of multiplying (e.g. 2/3 = 3/4)
  • Multiplying the numerator but forgetting to multiply the 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.

Equivalent Fractions

Grade 3 math

Qs
6
Marks
6
NameDateScore / 6
1.
12 = 2
[1]
2.
23 = 6
[1]
3.
17 = 4
[1]
4.
14 = 4
[1]
5.
13 = 4
[1]
6.
89 = 24
[1]

Answer key

  1. 42 × 2 = 4; Multiply the top by 2 as well: 1 × 2 = 2
  2. 93 × 3 = 9; Multiply the top by 3 as well: 2 × 3 = 6
  3. 287 × 4 = 28; Multiply the top by 4 as well: 1 × 4 = 4
  4. 164 × 4 = 16; Multiply the top by 4 as well: 1 × 4 = 4
  5. 123 × 4 = 12; Multiply the top by 4 as well: 1 × 4 = 4
  6. 279 × 3 = 27; Multiply the top by 3 as well: 8 × 3 = 24