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.
Mastering Fractions: Intermediate Challenges
Key Stage 4 / GCSE Maths (Ages 14-16) - Intermediate Level
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.
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. \( \frac{100}{150} \)
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. \( \frac{11}{12} - \frac{2}{3} \)
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. \( \frac{9}{10} \times \frac{11}{12} \)
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. \( \frac{11}{15} \div \frac{3}{5} \)
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}
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?
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 \( \frac{5}{7} \)
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. \( 81^{\frac{3}{4}} \)
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
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