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GCSE Maths · Number
Four operations GCSE Questions and Worked Answers
The four operations combine amounts, find differences, count equal groups and share or measure groups. Place value keeps each digit attached to the correct-sized unit.
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Start with the meaning
What you need to know about four operations
You have £8.37 and receive £2.46. To find the total, add pounds to pounds and pence to pence. In a decimal, the first digit after the point counts tenths and the next counts hundredths. Ten hundredths make one tenth, just as ten pennies make ten pence. This is why lining up decimal points matters: it puts equal-sized parts in the same column.
See the idea first
Exchange ten smaller parts for one larger part
Seven hundredths plus six hundredths make thirteen hundredths. Keep three hundredths and exchange the other ten for one tenth. The tenths column then totals eight. The pounds total ten, giving £10.83.
| Tens | Ones | Tenths | Hundredths |
|---|---|---|---|
| 0 | 8 | 3 | 7 |
| 0 | 2 | 4 | 6 |
| 1 | 0 | 8 | 3 |
From problem to method
Typical problems you need to be able to solve
These are the main kinds of question in this topic. Each card first states the problem, then explains how to solve it.
Find a total or difference
What the problem asks: Find 6.4 + 2.85 and 6.4 − 2.85.
How to solve it: Write 6.4 as 6.40. Add matching columns for 9.25; subtract matching columns for 3.55, exchanging a tenth for ten hundredths, then a whole for ten tenths.
Find the cost of equal groups
What the problem asks: Three notebooks cost £1.24 each. Find the total.
How to solve it: Three copies of 124p total 372p, or £3.72. Multiplication counts equal groups.
Count how many groups fit
What the problem asks: How many 0.4 m strips fit into 3.2 m?
How to solve it: Count equal lengths. Express both lengths in tenths: 32 ÷ 4 = 8. Scaling both quantities equally does not change how many groups fit.
A reliable routine
Choose a written method for the required operation
For integer and decimal calculations, preserve the value represented by each digit. Addition and subtraction align units; multiplication counts partial products; division can scale both numbers equally.
- For addition or subtraction, align decimal points and pad missing places with zeros.
- For multiplication, split one factor into convenient parts and add their products.
- For division by a decimal, multiply both dividend and divisor by the same power of ten.
- Estimate first or use the inverse operation afterwards to check the size.
Check: This page focuses on integer and decimal arithmetic. Fraction operations and signed-number reasoning have their own linked guides. Division by zero is undefined.
Fully worked
Four operations GCSE worked examples
Each solution explains the clue, why the method fits and how to check the result.
Example 1
Add decimal amounts
Question
Work out 5.68 + 3.47.
Hundredths: 8 + 7 = 15, so carry one tenth. Tenths: 6 + 4 + 1 = 11, so carry one whole.
Check: about 6 + 3 = 9.
Example 2
Exchange across a zero
Question
Work out 10.02 − 3.76.
Exchange one whole for ten tenths, then exchange one of those tenths for ten hundredths. This writes 10.02 as 9 wholes, 9 tenths and 12 hundredths. Subtract 3 wholes, 7 tenths and 6 hundredths.
Check: 6.26 + 3.76 = 10.02.
Example 3
Multiply two integers
Question
Work out 34 × 26 without a calculator.
Split 26 into 20 + 6.
Include both partial products.
Example 4
Multiply decimals
Question
Work out 1.8 × 0.35.
There are 18 tenths and 35 hundredths.
Each product unit is a thousandth, so
Multiplying by a positive number below one makes this amount smaller.
Example 5
Divide by a decimal
Question
Work out 7.56 ÷ 0.6.
Multiply both numbers by ten.
Check: 12.6 × 0.6 = 7.56.
Example 6
Interpret a remainder
Question
A club has 157 passengers. Each minibus has 12 passenger seats. How many minibuses are needed?
Thirteen minibuses leave one passenger without a seat. Therefore 14 minibuses are needed. A count of vehicles must be a whole number.
10 original questions · total 23 marks
Four operations GCSE exam-style questions
Try each question before opening its fully worked answer. The difficulty rises through the set.
Before you startAllow about 28 minutes · Show your working. Give exact answers unless a question asks you to round, and include units where needed. · answers start collapsed
Decimal total
Calculate 4.7 + 2.86.
Show worked answer
Align as 4.70 + 2.86.
Decimal difference
Calculate 6 − 2.48.
Show worked answer
Write 6.00 and exchange between columns.
Check by adding 2.48.
Partial products
Calculate 47 × 18.
Show worked answer
Decimal product
Calculate 0.7 × 0.08.
Show worked answer
Seven tenths times eight hundredths gives 56 thousandths.
Short division
Calculate 936 ÷ 8.
Show worked answer
8 goes into 9 once, remainder 1; into 13 once, remainder 5; into 56 seven times.
Decimal divisor
Calculate 5.04 ÷ 0.12.
Show worked answer
Scale both by 100.
Missing amount
A rope loses 1.85 m and has 4.6 m left. Find its original length.
Show worked answer
Put the removed length back.
Split a bill
Four friends share £18.60 equally. How much each?
Show worked answer
Divide into four equal shares.
Each pays £4.65.
Whole strips
How many complete 0.8 m strips can be cut from 6 m? Ignore cutting waste.
Show worked answer
Only 7 complete strips fit. The remaining 0.4 m is too short.
Check an error
A pupil says 3.2 × 4 = 1.28. Correct the answer.
Show worked answer
The original 3.2 is 32 tenths, so the product is 128 tenths: 12.8. Four copies of 3.2 must exceed 3.2.
Examiner-style feedback
Common four operations mistakes
Align decimal points for addition and subtraction, not the rightmost digits.
To preserve a quotient, scale both dividend and divisor equally.
Round vehicle counts up when everyone needs a seat, but count complete strips down. Use the situation.
30-second recap
Choose, carry out, check
Translate the wording before you reach for a rule.
- Keep place values aligned.
- Show partial products.
- Check with an inverse operation.
- Interpret remainders in context.
Quick answers
Four operations FAQ
Do I need written methods in GCSE Maths?
Yes. Practise them for non-calculator work and show enough working to explain your calculation.
Does multiplication always make a number bigger?
No. Multiplying a positive number by 0.5 halves it.
Content standards
Curriculum and rights review
N2–N3 integer and decimal operations, place value and contextual remainders across tiers. Questions, suggested marks, solutions and diagrams are original practice material, not official past-paper questions.
Official specification references