Arithmetic techniques and time saving tricks
Working quickly on paper and being able to carry out calculations in one’s head are useful skills.
The ISEB Mathematics Common Entrance examinations from Autumn 2022 are changing their aural mental arithmetic examination to a quick-fire written exam where pupils are tested on 40 short arithmetic questions in 10 minutes.
Some helpful time saving tricks are listed below. These are types of questions set at CE level but also taught lower down the school with appropriate numbers for the age group.
Double and halving
Example 1)
Twenty-four books are bought at a cost of £3.50 each. What is the total cost?
Working
24 × 3.50
÷ 2 × 2
= 12 × 7
= £84
Example 2)
Sixteen lollies are bought at a cost of £2.25 each. What is the total cost?
Working
16 × 2.25
÷ 2 × 2
= 8 × 4.50
÷ 2 × 2
= 4 × 9
= £36
Further examples
68 × 5 = 34 × 10 = 340 16 × 15 = 8 × 30 = 240 52 × 25 = 26 × 50 = 13 × 100 = 1300
Multiplying by 9, 19, 21, 29 etc.
19 footballs are bought at a cost of £25 each. What is the total cost?
Working
19 × £25 (19 lots of 25)
= 20 × 25 – 1 × 25 (20 lots of 25 subtract 1 lot of 25)
= 500 - 25
= £475
Using Approximations
Example 1)
12 T-shirts are bought at a cost of £7.99 each. What is the total cost?
Working
12 × £7.99
= 12 × £8 – 12 × 1p
= £96 – 12p
= £95.88
Example 2)
A TV sports programme starts at 14 : 35 and last for 2 hours and 55 minutes.
When does it end?
Working
Add 3 hours then jump back 5 mins. 17 : 30
Re-arranging products
Example 1)
2 × 7 × 11 × 5
= 2 × 5 × 7 × 11
= 10 × 77
= 770
Example 2)
25 × 6 × 5 × 4 × 3 × 2
= 25 × 4 × 6 × 3 × 5 × 2
= 100 × 18 × 10 = 18 000
Factorising numbers
Example 1)
437 × 99 + 437
= 437 × (99 + 1)
= 437 × 100
= 43700
Example 2) Extension
34 × 42 + 68 × 29
= 34 × (42 + 2 × 29)
= 34 × (42 + 58)
= 34 × 100
= 3400
R. Farnan
24/11/2021
Posted on
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