Year 8 Fractions Worksheet - Intermediate

Year 8 Fractions worksheet for Year 8 (Key Stage 3 / Year 7-9 (Ages 11-14)). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

Maths•Key Stage 3 / Year 7-9 (Ages 11-14)•Fractionsintermediate

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Fraction Focus: Year 8 Skills

Year 8 (ages 12–13) | Intermediate

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Instructions: Work through each activity and show your working clearly in the answer spaces. Simplify fractions where possible and include units in contextual answers. For recurring decimals, use a dot above the recurring digit or digits.

Calculate with Fractions

Complete each calculation, showing your working. Convert mixed numbers to improper fractions when helpful, and simplify each answer fully. Check that your answer is reasonable.

1. 2 1/3 + 1 5/6 =

2. 4 1/5 − 1 3/4 =

3. 3/7 × 2 1/3 =

4. 2 2/5 ÷ 3/10 = [3 marks]

Use the Reciprocal

To divide by a fraction, multiply by its reciprocal. Rewrite each division as a multiplication, then simplify. Show the reciprocal you use in your working.

1. 5/6 ÷ 2/3 =

2. 7/8 ÷ 1/4 =

3. 1 1/2 ÷ 3/5 =

4. 2 1/4 ÷ 1 1/2 = [3 marks]

Fractions, Decimals and Percentages

Convert each value to the requested form. Give fractions in their simplest form. For recurring decimals, mark the repeating digit or block with dots, for example 0.333… = 0.3̇.

1. Convert 3/8 to a decimal and a percentage.

2. Convert 0.625 to a fraction in simplest form and a percentage.

3. Convert 45% to a fraction in simplest form and a decimal.

4. Write 2/9 as a recurring decimal, using dots to show the recurring digit.

5. Write 0.1̇6̇ as a fraction in simplest form. [3 marks]

Fractions of Amounts: Multi-step Problems

Read each problem carefully and show each step. Find the fraction of the amount first where appropriate, then use the result to complete the remaining calculation. Include the unit in each final answer.

1. A library has 240 books. Three-eighths are fiction. How many fiction books are there?

2. A class has 32 pupils. Three-quarters attend a lunchtime club, and one-third of those pupils choose chess. How many pupils choose chess?

3. A water tank contains 60 litres. First, 2/5 of the water is used; then 1/4 of the remaining water is used. How many litres remain?

4. A baker makes 48 rolls. He sells 5/8 of them in the morning and 2/3 of the remaining rolls in the afternoon. How many rolls are left? [3 marks]

Mixed-Number Operations Challenge

Solve each problem using an efficient method. Show conversions and intermediate steps, and give each answer as a simplified fraction or mixed number. Remember that multiplication and division are completed before addition and subtraction.

1. 1 3/4 + 2/3 × 3/8 =

2. (2 1/2 − 3/4) ÷ 7/8 =

3. 3 1/3 × 1 1/5 − 2 1/2 =

4. 4 1/2 ÷ 3/4 + 1 1/3 = [3 marks]

Answer Key

Activity 1: 4 1/6 ; 2 9/20 ; 1 ; 8

Activity 2: 5/4 (1 1/4) ; 7/2 (3 1/2) ; 5/2 (2 1/2) ; 3/2 (1 1/2)

Activity 3: 0.375 and 37.5% ; 5/8 and 62.5% ; 9/20 and 0.45 ; 0.2̇ ; 1/6

Activity 4: 90 books ; 8 pupils ; 27 litres ; 10 rolls

Activity 5: 2 ; 2 ; 3/2 (1 1/2) ; 7 1/3