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Word problems are questions where you need to read a real-life situation, decide which mathematics to use, and then work through the calculation. The GL 11+ exam includes many word problems — some require just one step, but the hardest ones need multiple steps. This lesson gives you a reliable strategy for tackling any word problem.
Use this method for every word problem:
| Step | What to do |
|---|---|
| 1 | Read the question carefully (twice!) |
| 2 | Decide what operation(s) you need |
| 3 | Calculate — show your working |
| 4 | Check — does the answer make sense? |
Top Tip: Underline the key numbers and the question being asked. Many marks are lost by answering the wrong thing!
Certain words in a question tell you which operation to use:
| Key words | Operation |
|---|---|
| total, altogether, sum, combined, more than | Addition |
| difference, less than, fewer, reduce, left | Subtraction |
| times, product, each, every, groups of | Multiplication |
| share, split, divide, per, each (sharing) | Division |
| of (with fractions/percentages) | Multiplication |
Be careful: "How many more" usually means subtraction, not addition!
Tom has 145 stickers. He gets 78 more for his birthday. How many does he have now?
A school has 520 pupils. 287 are girls. How many are boys?
A box holds 24 crayons. A teacher orders 15 boxes. How many crayons is that?
Sarah has 156 sweets to share equally among 12 friends. How many sweets does each friend get?
Multi-step problems require two or more calculations. The key is to break them down into separate steps.
A shirt costs £18.50 and a pair of trousers costs £24.99. Mum buys 2 shirts and 1 pair of trousers. She pays with a £100 note. How much change does she get?
Step 1: Cost of 2 shirts = 2 × £18.50 = £37.00
Step 2: Total cost = £37.00 + £24.99 = £61.99
Step 3: Change = £100 - £61.99 = £38.01
A train travels at 60 miles per hour. It leaves at 09:15 and arrives at 11:45. How far does it travel?
Step 1: Time taken = 11:45 - 09:15 = 2 hours 30 minutes = 2.5 hours
Step 2: Distance = speed × time = 60 × 2.5 = 150 miles
A baker makes 180 cakes. He sells ²⁄₃ of them in the morning and ¼ of the remainder in the afternoon. How many cakes are left?
Step 1: Sold in morning = ²⁄₃ × 180 = 120
Step 2: Remainder after morning = 180 - 120 = 60
Step 3: Sold in afternoon = ¼ × 60 = 15
Step 4: Cakes left = 60 - 15 = 45 cakes
Tom and Jasmine share £72 in the ratio 5 : 4. Tom then spends £15 on a book. How much money does Tom have left?
Step 1: Total parts = 5 + 4 = 9
Step 2: One part = £72 ÷ 9 = £8
Step 3: Tom's share = 5 × £8 = £40
Step 4: Tom's money after buying the book = £40 - £15 = £25
Shop A: 3 pencils for £1.35. Shop B: 5 pencils for £2.10. Which shop is cheaper per pencil?
A shopkeeper buys 50 toys at £3.20 each and sells them at £4.50 each. What is the total profit?
Step 1: Total cost = 50 × £3.20 = £160
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