Home  ›  Learning Centre  ›  Maths  ›  Decimals  ›  Decimal Problem Solving
11+ Maths Guide · Year 5–6 · Free lesson

Decimal Problem Solving

This is where decimals earn their keep: money, distances and multi-step word problems — the exact style the 11+ and SATs love. The lesson teaches a four-step routine: read, plan, calculate, check.

D14Decimal Problem Solving
Put it all together with real problems.
Decimal problems mix money, measures and multi-step thinking.
Mia buys a pencil for £0.85 and a notebook for £1.20. How much change from £5?
£0.85 + £1.20 = £2.05
£5.00 − £2.05 = £2.95
Two steps: add the costs, then subtract from what she paid.
1

Learn the 4-Step Method

1Read the problem twice.

What is the question actually asking? Underline the numbers and the goal.

❓→📝

2Plan the steps.

Most problems take two steps: often an add THEN a subtract.

+ then −

3Calculate carefully.

Line up decimal points; treat money as two decimal places.

£2.05

4Check it makes sense.

£2.95 change from £5 after spending about £2 — sensible ✓

💡 Key IdeaMoney is decimals in disguise: £1.20 means 1 pound and 20 hundredths. Every decimal skill transfers.
2

Worked Example

A relay team runs 2.4 km, 1.35 km and 1.85 km. How far is that in total — and how much short of 6 km are they?

Step 1 · Add the legs
 2.40
 1.35
+1.85
5.6 km
Step 2 · Compare with 6 km
6.00 − 5.60 = 0.4
✓ Answer
Total 5.6 km — they are 0.4 km short.
3

Watch Out! Common Mistakes

Answering the wrong question.

Careful! The problem asked for the change, not the total cost. Always re-read the question before writing the answer.

Treating £5 as 5 pence or 500 pounds.
£5 − £2.05 = £2.5 ✕

Wrong! Write money with two decimal places: £5.00 − £2.05 = £2.95.

Skipping the sense-check.
2.4 + 1.35 + 1.85 = 56 km ✕

Impossible! Three short runs can’t make 56 km. An estimate (≈ 2 + 1 + 2 = 5) catches this instantly.

📄 Free printable: Download the Decimal Problem Solving cheat sheet (PDF) — keep it by your child's desk.

Quick summary

Frequently asked questions

How should children approach decimal word problems?

With a routine: read the question twice, plan the steps, calculate with decimal points lined up, then check the answer against an estimate.

What's the most common mistake in money problems?

Misaligning place value — treating £5 as 5.0 pence or forgetting money has two decimal places. Writing every amount with two decimal places prevents it.

How do these problems appear in the 11+?

Usually as two-step problems: find a total then find change, or add lengths then compare with a target — exactly the patterns practised in this lesson.

← Previous lesson
D13 Fractions to Decimals
All lessons
Decimals Hub
Topic complete 🎉
Back to the Decimals Hub
🛡️ Curriculum aligned⭐ Builds confidence💜 Made for 9–13 year olds
© MindBlaze. Free to read, share and link to. Learning Centre