Skip to main content

Fractions Worksheet - GCSE - Intermediate

Fractions worksheet for Key Stage 4 / GCSE (Ages 14-16). Intermediate level maths practice, aligned to the UK National Curriculum. Print-ready with answer key included.

MathsKey Stage 4 / GCSE (Ages 14-16)Fractionsintermediate
0 views
0 downloads

Mastering Fractions: Intermediate Challenges

Key Stage 4 / GCSE Maths (Ages 14-16) - Intermediate Level

Name:
Date:
Score:
/8

Instructions: This worksheet is designed to deepen your understanding of fractions. You'll tackle a variety of problems, from simplification to complex operations involving fractions. Work through each activity carefully, showing all your calculations.

1

Simplifying Fractions

Simplify each fraction to its lowest terms. Show your working clearly for each step.

1. \( \frac{18}{24} \)

2. \( \frac{45}{60} \)

3. \( \frac{56}{64} \)

4. \( \frac{81}{99} \)

5. \( \frac{100}{150} \)

2

Adding and Subtracting Fractions

Add or subtract the following fractions. Ensure you find a common denominator and simplify your answer.

1. \( \frac{3}{4} + \frac{2}{5} \)

2. \( \frac{7}{8} - \frac{1}{4} \)

3. \( \frac{5}{6} + \frac{3}{9} \)

4. \( \frac{11}{12} - \frac{2}{3} \)

3

Multiplying Fractions

Multiply the following pairs of fractions. Simplify your answers where possible.

1. \( \frac{2}{3} \times \frac{4}{5} \)

2. \( \frac{7}{9} \times \frac{3}{8} \)

3. \( \frac{5}{6} \times \frac{2}{7} \)

4. \( \frac{9}{10} \times \frac{11}{12} \)

4

Dividing Fractions

Divide the following fractions. Remember to multiply by the reciprocal of the divisor.

1. \( \frac{3}{4} \div \frac{2}{5} \)

2. \( \frac{7}{8} \div \frac{1}{6} \)

3. \( \frac{5}{9} \div \frac{4}{7} \)

4. \( \frac{11}{15} \div \frac{3}{5} \)

5

Converting Recurring Decimals to Fractions

Convert the following recurring decimals into fractions. Show all your working steps.

1. 0.\overline{3}

2. 0.\overline{56}

3. 0.\overline{142}

4. 0.\overline{7}

6

Fraction Word Problems

Solve the following word problems involving fractions. Show all your calculations.

1. If \( \frac{3}{5} \) of a cake is left and you eat \( \frac{1}{3} \) of the remaining cake, how much of the whole cake have you eaten?

2. A recipe requires \( \frac{2}{3} \) cup of sugar. If you want to make half the recipe, how much sugar do you need?

3. A tank is \( \frac{3}{4} \) full. After using \( \frac{1}{5} \) of the tank's capacity, how much is left?

7

Comparing Fractions

Compare the following pairs of fractions using >, <, or =. Show your reasoning.

1. \( \frac{7}{12} \) and \( \frac{2}{3} \)

2. \( \frac{5}{8} \) and \( \frac{3}{4} \)

3. \( \frac{9}{10} \) and \( \frac{4}{5} \)

4. \( \frac{11}{14} \) and \( \frac{5}{7} \)

8

Fractional Indices

Evaluate the following expressions with fractional indices. Simplify your answers.

1. \( 16^{\frac{1}{2}} \)

2. \( 27^{\frac{1}{3}} \)

3. \( 64^{\frac{2}{3}} \)

4. \( 81^{\frac{3}{4}} \)

Answer Key

Activity 1: 3/4 ; 3/4 ; 7/8 ; 9/11 ; 2/3

Activity 2: 23/20 ; 5/8 ; 17/18 ; 1/4

Activity 3: 8/15 ; 7/24 ; 5/21 ; 33/40

Activity 4: 15/8 ; 21/4 ; 35/36 ; 11/9

Activity 5: 1/3 ; 28/45 ; 142/999 ; 7/9

Activity 6: 1/5 ; 1/3 ; 11/20

Activity 7: < ; < ; > ; =

Activity 8: 4 ; 3 ; 16 ; 27

Want a customised worksheet?

Create your own AI-generated worksheet tailored to your exact needs.

Fractions Worksheet - GCSE - Intermediate | Free Printable PDF - WorksheetsGenerator | Worksheets Generator