Fraction Word Problems
Fraction word problems combine fractional arithmetic with contextual scenarios, requiring learners to translate written descriptions into mathematical operations. These problems typically involve finding parts of quantities, comparing fractional amounts, or determining remainders after portions have been used or consumed. The key skill lies in identifying which operation the problem requires and interpreting the word 'of' as multiplication.
Why it matters
Fraction word problems appear throughout daily life, from calculating cooking measurements to determining sale discounts and managing budgets. A baker calculating 34 of a 200g flour recipe needs 150g, whilst a shopper finding 13 off a £24 jumper saves £8. These skills prove essential in GCSE mathematics, where complex multi-step problems involving fractions appear regularly across topics like ratio, percentage, and probability. Year 7 students encounter these problems as preparation for more advanced applications in algebra and geometry. Professional contexts like construction, nursing, and finance rely heavily on fractional calculations — a nurse administering 23 of a 15ml dose gives exactly 10ml. Understanding fraction word problems builds the foundation for percentage calculations, decimal operations, and proportional reasoning that students will use throughout secondary education and beyond.
How to solve fraction word problems
Fraction Word Problems
- Read carefully: identify what fraction of what quantity.
- 'Of' usually means multiply: 23 of 12 = 23 × 12 = 8.
- For remaining/left over: subtract the fraction from the whole.
- Draw a diagram if the problem is hard to visualise.
Example: 34 of 20 students like maths: 34 × 20 = 15 students.
Worked examples
Poppy has 8 cookies. She uses 14 of them. How many did she uses?
Answer: 2
- Find 14 of 8 → 8 ÷ 4 = 2 — To find 1/4 of 8, divide 8 by 4.
- Answer → 2 — She uses 2 cookies.
A pizza is cut into 4 slices. Oscar eats 2 slices. What fraction did he eat?
Answer: 24 = 12
- Write as fraction → 24 — Eaten (2) over total (4).
- Simplify → 12 — Divide both by 2.
A rope is 24 m long. Another rope is 12 m long. How long are they together?
Answer: 1 m
- Find common denominator → LCM(4, 2) = 4 — The common denominator is 4.
- Rewrite and add → 24 + 24 = 44 — Convert both to 4ths and add.
- Simplify → 1 m — Simplify and express as a mixed number if needed.
Common mistakes
- Misinterpreting 'of' as addition rather than multiplication, leading to errors like calculating 1/3 of 12 as 1/3 + 12 = 12 1/3 instead of 1/3 × 12 = 4.
- Adding fractions incorrectly by adding numerators and denominators separately, producing results like 1/4 + 1/3 = 2/7 instead of the correct answer 7/12.
- Forgetting to simplify final answers, leaving results like 6/8 instead of reducing to 3/4, or expressing improper fractions like 9/4 rather than converting to 2 1/4.
- Confusing 'what fraction remains' problems by subtracting from the wrong starting point, calculating 3/4 - 1/2 = 1/4 when the question asks what fraction of the original 1 remains after using 3/4.