__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 |