Word problems with decimals

Word problems with decimals

Word problems with decimals

Decimal numbers show up everywhere in real life — prices, lengths, weights, times. The arithmetic is the same as for whole numbers, with one extra rule you already know: line up the decimal points.

Money problems

A pencil costs £0.45. How much do 6 pencils cost?

Multiply: 6 × 0.45.

  • Ignore the decimal point: 6 × 45 = 270.
  • 0.45 has two decimal places → answer has two decimal places.
  • Cost: £2.70.

Lena has £10.00. She buys a notebook for £3.75 and a pen for £1.20. How much change does she get?

  • Total spent: 3.75 + 1.20 = £4.95.
  • Change: 10.00 − 4.95 = £5.05.

A box of cereal costs £2.40. It contains 480 g. How much does 100 g cost?

  • 480 g costs 240 pence (or £2.40).
  • 100 g costs 240 ÷ 480 × 100 = 50 pence = £0.50.

Or: 100 ÷ 480 of the box × £2.40 = £0.50.

Length problems

A rope is 2.45 m long. Tom cuts off a piece 0.85 m long. How long is the remaining rope?

Subtract: 2.45 − 0.85 = 1.60 m.

A snail moves 0.4 m every minute. How far in 15 minutes?

Multiply: 0.4 × 15 = 6.0 → 6 m.

A walking track is 3.6 km long. If Anna walks it 3 times, how far has she walked?

3.6 × 3 = 10.8 km.

Other decimal contexts

A liter of milk costs €1.45. How much do 4 liters cost?

4 × 1.45 = €5.80.

A runner's time was 12.07 seconds in the first race and 11.83 seconds in the second. By how much did she improve?

12.07 − 11.83 = 0.24 seconds.

A handy trick: re-read in whole numbers

Decimal problems can feel scary just because of the dots. If they confuse you, multiply everything by 10 or 100 to make the numbers whole, solve, then divide back.

What is 0.4 + 0.7?

Multiply both by 10: 4 + 7 = 11. Divide by 10: 1.1.

Use this trick when you're stuck — but the column method on paper is usually faster once you're confident.

Common pitfalls

  • Lining up the digits, not the points. Always align the decimal points in column work. Then the columns of digits align by place value automatically.
  • Forgetting trailing zeros that aren't shown. If you subtract 2.4 − 0.85, rewrite as 2.40 − 0.85 first.
  • Misreading money totals as cents. "£3.75" is three pounds and 75 hundredths of a pound, not 375.
  • Skipping the unit in the answer. "5.05" without a "£" or "m" is not a complete answer.

Practice