Maths Library

Unit and Non-Unit Fractions: Grade 3 math

Students distinguish between unit fractions (with numerator 1) and non-unit fractions, writing and identifying them from representations. Worksheets build understanding of the role of the numerator and denominator.

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What this covers

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

Worked example

A strip is divided into 5 equal parts and 3 parts are shaded. Write the fraction shaded and state whether it is a unit fraction.

  1. Total equal parts = 5, shaded parts = 3, so the fraction is 35
  2. Check numerator: numerator is 3, which is greater than 1
  3. Conclude that 35 is a non-unit fraction

Answer: 35, non-unit fraction

Difficulty scale

The sheet generator offers five difficulty settings for this topic.

  1. Find a half, third or quarter of a number
  2. Unit fractions of larger multiples, denominators 2 to 4
  3. Find 15, 16, 18 or 110 of a quantity
  4. Larger quantities with denominators up to 10
  5. Mixed denominators, answers linked to division facts

Common mistakes

  • Thinking 1/8 is larger than 1/4 because 8 is larger than 4
  • Swapping the positions of numerator and denominator

Curriculum links

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

  • 3.NF.A.1 Understand a unit fraction 1/b as one part of a whole divided into b equal parts.

Sample sheet and answers

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

Unit and Non-Unit Fractions

Grade 3 math

Qs
6
Marks
12
NameDateScore / 12
1.
Find 15 of 30.
[2]
2.
Find 16 of 24.
[2]
3.
Find 18 of 16.
[2]
4.
Find 110 of 70.
[2]
5.
Find 18 of 32.
[2]
6.
Find 15 of 50.
[2]

Answer key

  1. 615 of 30 means 30 ÷ 5; 30 ÷ 5 = 6
  2. 416 of 24 means 24 ÷ 6; 24 ÷ 6 = 4
  3. 218 of 16 means 16 ÷ 8; 16 ÷ 8 = 2
  4. 7110 of 70 means 70 ÷ 10; 70 ÷ 10 = 7
  5. 418 of 32 means 32 ÷ 8; 32 ÷ 8 = 4
  6. 1015 of 50 means 50 ÷ 5; 50 ÷ 5 = 10