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T.1 Complete multiples of unit fractions

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What are multiples of unit fractions?

Multiples of unit fractions are fractions that come from adding the same unit fraction more than once. A unit fraction has the number 1 in the numerator (top number).

Examples:
  • The unit fraction is 1/4.
  • 2 × (1/4) = 2/4
  • 3 × (1/4) = 3/4
Note

A multiple of a unit fraction is just that unit fraction added again and again.

How to identify multiples of unit fractions

To identify a multiple of a unit fraction, check if the fraction’s numerator shows how many times the unit fraction has been added.

Steps:
  • Start with a unit fraction: 1/5.
  • Multiply by 4 → 4 × (1/5).
  • The result is 4/5. This means we added 1/5 four times.
Note

The numerator always tells how many unit fractions are in the multiple.

Common examples of multiples of unit fractions

Here are some multiples of unit fractions that appear often when working with fractions:

Examples:
  • 3 × (1/2) = 3/2
  • 5 × (1/6) = 5/6
  • 7 × (1/8) = 7/8
  • 9 × (1/10) = 9/10
Note

Even if the numerator is larger than the denominator, the rule is the same: the fraction is still a multiple of a unit fraction.

Using multiples of unit fractions in problems

Multiples of unit fractions help in understanding repeated addition of fractions, multiplication with fractions, and fraction word problems.

Examples:
  • “Sam ate 3 pieces of cake. Each piece is 1/8 of the cake.” → 3 × (1/8) = 3/8
  • “A rope is cut into 1/6 pieces. Using 5 pieces makes 5/6 of the rope.”
Note

Always think of multiples of unit fractions as groups of equal parts being combined.