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Non-calculator arithmetic tricks practice questions with answers

Foundation and Higher · Grade 3 · Non-calculator

A second set of non-calculator arithmetic tricks questions for GCSE Maths. They are different from the ones on the topic page, so work through both. Try each question, then open the answer to check your working.

More questions

Question 1 Easy

Work out 21 × 8 by using 20 × 8.

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Answer: 168

  1. 21 is 1 more than 20, so 21 × 8 = 20 × 8 + 8.
  2. 20 × 8 = 160, and 160 + 8 = 168.
  • Method (1): 21 is 1 more than 20, so 21 × 8 = 20 × 8 + 8.
  • Accuracy (1): Answer 168

Question 2 Easy

Work out 29 × 9 by using 30 × 9.

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Answer: 261

  1. 29 is 1 less than 30, so 29 × 9 = 30 × 9 − 9.
  2. 30 × 9 = 270, and 270 − 9 = 261.
  • Method (1): 29 is 1 less than 30, so 29 × 9 = 30 × 9 − 9.
  • Accuracy (1): Answer 261

Question 3 Medium

Work out 41² by writing 41 as 40 + 1.

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Answer: 1681

  1. 41² = (40 + 1)², which is 40² + 2 × 40 × 1 + 1².
  2. 1600 + 80 + 1 = 1681.
  • Method (1): 41² = (40 + 1)², which is 40² + 2 × 40 × 1 + 1².
  • Accuracy (1): Answer 1681

Question 4 Medium

Work out 91 ÷ 7 by splitting 91 into 70 + 21.

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Answer: 13

  1. Split 91 into 70 + 21, because both parts divide by 7.
  2. 70 ÷ 7 = 10 and 21 ÷ 7 = 3, so 10 + 3 = 13.
  • Method (1): Split 91 into 70 + 21, because both parts divide by 7.
  • Accuracy (1): Answer 13

Question 5 Hard

Work out 7 × 15 by splitting 15 into 10 + 5.

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Answer: 105

  1. 7 × 10 = 70 and 7 × 5 = 35.
  2. Add the two parts: 70 + 35 = 105.
  • Method (1): 7 × 10 = 70 and 7 × 5 = 35.
  • Accuracy (1): Answer 105

Question 6 Hard

Work out 16 × 25 by halving one number and doubling the other.

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Answer: 400

  1. Halve 16 and double 25: 16 × 25 = 8 × 50.
  2. 8 × 50 = 400.
  • Method (1): Halve 16 and double 25: 16 × 25 = 8 × 50.
  • Accuracy (1): Answer 400

Exam-style question

A longer question with marks, in the style of a written paper. This is a Yumio practice question, not a past paper question.

Exam-style question 12 marks

Work out 78 ÷ 6 by splitting 78 into 60 + 18.

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Answer: 13

  1. Split 78 into 60 + 18, because both parts divide by 6.
  2. 60 ÷ 6 = 10 and 18 ÷ 6 = 3, so 10 + 3 = 13.
  3. The result is 13.
  • Method (1): Split 78 into 60 + 18, because both parts divide by 6.
  • Accuracy (1): Answer 13

Quick checks

Short one-step questions. Pick an option before you open the answer.

Check 1

Work out 28 × 50 by halving one number and doubling the other.

  1. 1400
  2. 1402
  3. 1410
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1400 The result is 1400.

Check 2

Work out 21² by writing 21 as 20 + 1.

  1. 441
  2. 443
  3. 451
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441 The result is 441.

Check 3

Work out 84 ÷ 4 by splitting 84 into 80 + 4.

  1. 21
  2. 23
  3. 31
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21 The result is 21.

Check 4

Work out 51 × 8 by using 50 × 8.

  1. 408
  2. 410
  3. 418
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408 The result is 408.

Check 5

Work out 19 × 9 by using 20 × 9.

  1. 171
  2. 173
  3. 181
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171 The result is 171.

Check 6

Work out 7 × 18 by splitting 18 into 10 + 8.

  1. 126
  2. 128
  3. 136
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126 The result is 126.

Check 7

Work out 32 × 25 by halving one number and doubling the other.

  1. 800
  2. 802
  3. 810
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800 The result is 800.

Check 8

Work out 91² by writing 91 as 90 + 1.

  1. 8281
  2. 8283
  3. 8291
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8281 The result is 8281.

Check 9

Work out 96 ÷ 6 by splitting 96 into 60 + 36.

  1. 16
  2. 18
  3. 26
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16 The result is 16.

Check 10

Work out 21 × 5 by using 20 × 5.

  1. 105
  2. 107
  3. 115
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105 The result is 105.

Check 11

Work out 29 × 6 by using 30 × 6.

  1. 174
  2. 176
  3. 184
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174 The result is 174.

Check 12

Work out 9 × 15 by splitting 15 into 10 + 5.

  1. 135
  2. 137
  3. 145
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135 The result is 135.

Check 13

Work out 22 × 50 by halving one number and doubling the other.

  1. 1100
  2. 1102
  3. 1110
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1100 The result is 1100.

Check 14

Work out 81² by writing 81 as 80 + 1.

  1. 6561
  2. 6563
  3. 6571
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6561 The result is 6561.

Check 15

Work out 133 ÷ 7 by splitting 133 into 70 + 63.

  1. 19
  2. 21
  3. 29
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19 The result is 19.

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