Year 6 Arithmetic (SATs) · Fractions · Lesson 3.1

Year 6 Arithmetic (SATs): Equivalent fractions and simplifying

Part of the Year 6 Arithmetic (SATs) fractions chapter. Chapter overview · whole chapter on one page

3.1

Equivalent fractions and simplifying

Year 6
Identify, name and write equivalent fractions, and use common factors to simplify (Year 5-6)

Practice material. Non-calculator practice. This book is practice in the style of the Year 6 arithmetic test. It is not the official test, and no official test item is used. Do every question without a calculator. Marks and timings are a practice guide only.

Story. Maya makes a fruit salad. The recipe says 36/48 of the bowl should be apples. She wants the simplest way to write that fraction, so that she can check it on the recipe card.

Rule

Equivalent fractions have the same value but different numbers. Multiply the top and the bottom by the same number to make an equivalent fraction.

To simplify, divide the top and bottom by a common factor. A fraction is in its simplest form when no number divides into both except 1.

For the full explanation, read Year 6 maths, chapter 2.

Key ideas

Multiply or divide the top and bottom by the same number to get an equivalent fraction.
The highest common factor (HCF) gives the simplest form in one step.
Check a simplified fraction by seeing whether the top and bottom still share a factor.

Worked example 3.1.1

Simplify 36/48.

Method. Find the highest common factor of the top and bottom, then divide both by it.

Find a number that divides into both the top and the bottom. The highest common factor of 36 and 48 is 12.
HCF of 36 and 48 is 12
Divide the top and the bottom by it. Dividing both by the same number keeps the fraction the same size.
36 ÷ 12 = 3, 48 ÷ 12 = 4
Write the answer.
3/4

Check. 3 × 12 = 36 and 4 × 12 = 48, so 3/4 is the same fraction. ✓

Watch out. Dividing by 2 only gives 18/24, which can still be simplified.

Worked example 3.1.2

Write 3/5 as an equivalent fraction with denominator 20.

Method. Find what 5 is multiplied by to make 20, then do the same to the top.

Multiply the top and the bottom by the same number. Both are multiplied by 4, so the value of the fraction does not change.
3 × 4 = 12 and 5 × 4 = 20
Check the bottom. 5 × 4 = 20, which is the new bottom number.
5 × 4 = 20
Write the answer.
3/5

Check. 20 ÷ 5 = 4, so the top is 3 × 4 = 12. ✓

Worked example 3.1.3

Fill in the missing number: 5/8 = ☐/40.

Method. Multiply the bottom by 5, and do the same to the top.

Multiply the top and the bottom by the same number. Both are multiplied by 5, so the value of the fraction does not change.
5 × 5 = 25 and 8 × 5 = 40
Check the bottom. 8 × 5 = 40, which is the new bottom number.
8 × 5 = 40
Write the answer.
5/8

Check. 40 ÷ 8 = 5, so the top is 5 × 5 = 25. ✓

Year 6 Arithmetic (SATs): Equivalent fractions and simplifying

Equivalent fractions and simplifying

Rule

Key ideas

Exercise 3A Practice: equivalent fractions and simplifying