Quick mental methods, decimal-place shortcuts and sense-checks that save time and rescue marks on the non-calculator paper. It is on Foundation and Higher, aimed at grade 3. Free questions with answers are on this page. Worked examples show each line before you try the questions.
Non-calculator papers reward rewriting, not grinding. 25×16 is 100×4 once you notice 25×4=100 and 16=4×4. Fractions full of 5s and 2s cancel if you factor first. A decimal multiplication can be done as whole numbers, then the point is counted back in.
Show the rewrite. The method mark is on '25×16=100×4', not on a mysterious 400. If a product looks ugly, try splitting, factoring, or pairing a 4 with a 25 or a 5 with a 2.
These are Paper 1 speed marks: decimal place-count for products, ×25=×100÷4, and 'make the divisor whole' for decimal division. Write the equivalent calculation, then the arithmetic — two lines, two marks.
Objectives
19 × 4 = 20 × 4 − 4.
16 × 25 = 8 × 50 = 4 × 100.
7 × 13 = 7 × 10 + 7 × 3.
Key points
Multiply and divide decimals by moving digits, using a whole-number fact.
Use a given calculation (like 34×26=884) to answer related decimal calculations.
Multiply by 5, 25, 0.5 and 0.25 using halving, doubling and quartering.
Use 'round and adjust' for prices like £3.95.
Worked examples
Example 1
Work out 19 × 3 by using 20 × 3.
2 marks
19 is 1 less than 20, so 19 × 3 = 20 × 3 − 3.
20 × 3 = 60, and 60 − 3 = 57.
The result is 57.
Answer: 57
Common slips
Slip: 21 is 1 less than 20, so 19 × 3 = 20 × 3 − 3. That changes a number from the question, so it answers a different question.
Slip: 23 × 3 = 60, and 60 − 3 = 57. That changes a number in the working, so the step no longer follows from the one before.
Slip: The result is 61. That does not match the working above it.
Example 2
Work out 7 × 12 by splitting 12 into 10 + 2.
2 marks
7 × 10 = 70 and 7 × 2 = 14.
Add the two parts: 70 + 14 = 84.
The result is 84.
Answer: 84
Common slips
Slip: 9 × 10 = 70 and 7 × 2 = 14. That changes a number from the question, so it answers a different question.
Slip: Add the two parts: 73 + 14 = 84. That changes a number in the working, so the step no longer follows from the one before.
Slip: The result is 88. That does not match the working above it.
Example 3
Work out 12 × 25 by halving one number and doubling the other.
2 marks
Halve 12 and double 25: 12 × 25 = 6 × 50.
6 × 50 = 300.
The result is 300.
Answer: 300
Common slips
Slip: Halve 14 and double 25: 12 × 25 = 6 × 50. That changes a number from the question, so it answers a different question.
Slip: 6 + 50 = 56. That uses addition, but this step needs multiplication.
Slip: The result is 304. That does not match the working above it.
Questions and answers
GCSE Maths non-calculator arithmetic tricks questions and answers. Try each one, then open the answer. Easy questions come first.
Question 1 Easy2 marks
Work out 51² by writing 51 as 50 + 1.
Show answer
Answer: 2601
51² = (50 + 1)², which is 50² + 2 × 50 × 1 + 1².
2500 + 100 + 1 = 2601.
M1 — 51² = (50 + 1)², which is 50² + 2 × 50 × 1 + 1².
A1 — Answer 2601
Question 2 Easy2 marks
Work out 112 ÷ 8 by splitting 112 into 80 + 32.
Show answer
Answer: 14
Split 112 into 80 + 32, because both parts divide by 8.
80 ÷ 8 = 10 and 32 ÷ 8 = 4, so 10 + 4 = 14.
M1 — Split 112 into 80 + 32, because both parts divide by 8.
A1 — Answer 14
Question 3 Medium2 marks
Work out 9 × 18 by splitting 18 into 10 + 8.
Show answer
Answer: 162
9 × 10 = 90 and 9 × 8 = 72.
Add the two parts: 90 + 72 = 162.
M1 — 9 × 10 = 90 and 9 × 8 = 72.
A1 — Answer 162
Question 4 Medium2 marks
Work out 14 × 50 by halving one number and doubling the other.
Show answer
Answer: 700
Halve 14 and double 50: 14 × 50 = 7 × 100.
7 × 100 = 700.
M1 — Halve 14 and double 50: 14 × 50 = 7 × 100.
A1 — Answer 700
Question 5 Hard2 marks
Work out 31 × 5 by using 30 × 5.
Show answer
Answer: 155
31 is 1 more than 30, so 31 × 5 = 30 × 5 + 5.
30 × 5 = 150, and 150 + 5 = 155.
M1 — 31 is 1 more than 30, so 31 × 5 = 30 × 5 + 5.
A1 — Answer 155
Question 6 Hard2 marks
Work out 39 × 6 by using 40 × 6.
Show answer
Answer: 234
39 is 1 less than 40, so 39 × 6 = 40 × 6 − 6.
40 × 6 = 240, and 240 − 6 = 234.
M1 — 39 is 1 less than 40, so 39 × 6 = 40 × 6 − 6.
A1 — Answer 234
Question 7 Exam-style3 marks
Work out 31² by writing 31 as 30 + 1.
Show answer
Answer: 961
31² = (30 + 1)², which is 30² + 2 × 30 × 1 + 1².
900 + 60 + 1 = 961.
The result is 961.
M1 — 31² = (30 + 1)², which is 30² + 2 × 30 × 1 + 1².
M1 — 900 + 60 + 1 = 961.
A1 — Answer 961
Common mistakes
Most lost marks on this topic are one slip.
Subtracting 1 instead of one whole group.
19 × 4 is 4 less than 20 × 4.
Adding the adjustment when it should be taken away.
For 19 × 4, start from 20 × 4 and take away one group of 4.
Splitting 13 as 10 + 3 but only multiplying one piece.
Both pieces are multiplied by 7.
Spot the slip
19 × 4 is the same as
20 × 4 − 4
20 × 4 − 1
19 × 10
Show the slip
20 × 4 − 4 Nineteen groups are one group less than twenty groups.
Exam tips
Be ready to do this without a calculator. Paper 1 is the non-calculator paper.
If the question says “show that”, the result is given. The marks are for the steps that reach it.
The method is the same on AQA-style and Edexcel-style papers.
Write the whole-number fact you are using — 'since 6×15=90' — so the marker can see the method.
On money questions, keep two decimal places all the way through.
Printable worksheet
The same questions are in a PDF you can print. Answers start on a later page.