__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

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