Fraction Word Problems – From Simple to Challenging
Word problems are where fractions come to life. They require you to read a situation carefully, choose the right operation, and carry out the calculation. This page walks through many types of fraction word problems from easy to challenging.
Translating a real-world description into the right fraction operation is a skill in its own right, separate from the arithmetic itself — standardised tests and real workplaces (engineering, cooking, finance, construction) rarely hand you a bare calculation like “3/4 ÷ 1/8”; they hand you a scenario and expect you to recognise which operation it demands. This is precisely why maths curricula worldwide place heavy emphasis on word problems: the arithmetic is the easy part once you have correctly identified whether the situation calls for addition, subtraction, multiplication, or division.
A Strategy for Every Word Problem
- Read the problem twice and identify what is given and what you must find.
- Decide which operation is needed: addition, subtraction, multiplication, or division.
- Write the calculation using fractions.
- Solve and simplify your answer.
- Write the answer with the correct unit and check that it makes sense.
Type 1 – Addition Problems
Tom ate 2/8 of a pizza and his sister ate 3/8. How much pizza did they eat in total? 2/8 + 3/8 = 5/8. They ate 5/8 of the pizza.
A gardener planted flowers in 1/3 of a plot on Monday and 2/5 of the plot on Tuesday. How much of the plot has been planted? LCM(3,5)=15. 5/15 + 6/15 = 11/15. 11/15 of the plot is planted.
Type 2 – Subtraction Problems
A bottle was 7/8 full of juice. After breakfast, 3/8 was used. How much juice remains? 7/8 - 3/8 = 4/8 = 1/2. 1/2 of the bottle remains.
A plank is 5 and 1/4 m long. A carpenter cuts off 2 and 3/4 m. How long is the piece that remains? 21/4 - 11/4 = 10/4 = 5/2 = 2 and 1/2 m.
Type 3 – Multiplication Problems
A recipe uses 3/4 cup of sugar. You want to make half the recipe. How much sugar do you need? 3/4 times 1/2 = 3/8. You need 3/8 of a cup.
A field is 3 and 1/2 km long and 2/3 km wide. What is its area? 7/2 times 2/3 = 14/6 = 7/3 = 2 and 1/3 square km.
A factory makes 240 cars in a day. 3/8 of them are red. How many red cars are made? 3/8 times 240 = 720/8 = 90 red cars.
Type 4 – Division Problems
A 3/4 m ribbon is cut into pieces each 1/8 m long. How many pieces are there? 3/4 divided by 1/8 = 3/4 times 8 = 6. 6 pieces.
A tank holds 5 and 1/4 litres of paint. Each tin holds 3/4 litre. How many tins can be filled? 21/4 divided by 3/4 = 21/4 times 4/3 = 84/12 = 7. 7 tins.
Type 5 – Multi-Step Problems
Mia had 2 and 1/2 m of fabric. She used 3/4 m for a cushion and 2/3 m for a bag. How much fabric does she have left?
Step 1: Add fabric used: 3/4 + 2/3. LCM=12: 9/12 + 8/12 = 17/12.
Step 2: 2 and 1/2 - 17/12 = 5/2 - 17/12 = 30/12 - 17/12 = 13/12 = 1 and 1/12 m remaining.
A school bought 3/5 of its supplies on Monday and 1/4 on Wednesday. What fraction is still to be bought?
3/5 + 1/4 = 12/20 + 5/20 = 17/20. Remaining: 1 - 17/20 = 3/20.
Key Takeaways
- Read carefully: the word "of" usually means multiply; "shared equally" means divide; "total" or "altogether" means add; "left over" or "difference" means subtract.
- Always write the calculation before starting to solve.
- Convert mixed numbers to improper fractions for multiplication and division.
- Check your answer against the story — does the size make sense?