Library

Tricks

30 mental maths tricks. Each shows a worked example in colour, explains why it works (so it is maths, not magic), and has a game to practise it until it is automatic.

Multiplying

n × 11Multiply by 1136 × 11 = 396 n × 5Multiply by 546 × 5 = 230 n × 25Multiply by 2536 × 25 = 900 n × 50Multiply by 5068 × 50 = 3400 n × 9Multiply by 947 × 9 = 423 n × 99Multiply by 9934 × 99 = 3366 n × 15Multiply by 1524 × 15 = 360 n × 101Multiply by 10147 × 101 = 4747 a × bDouble and halve16 × 35 = 8 × 70 43 × 47Same start, ends add to 1043 × 47 = 2021 97 × 94Multiply numbers near 10097 × 94 = 9118 47 × 53Numbers either side of a round number47 × 53 = 2500 − 9

Squares and roots

(a5)²Square a number ending in 565² = 4225 (50 ± d)²Square a number near 5053² = 2809 (100 ± d)²Square a number near 10097² = 9409 √nSquare root of a perfect square√5476 = 74 ³√nCube root of a perfect cube³√175,616 = 56

Adding and taking away

a + 38Add by rounding47 + 38 = 85 a − 29Subtract by rounding83 − 29 = 54 1000 − nSubtract from 100, 1000 or 10,0001000 − 367 = 633 a + b + c + dMake tens first17 + 26 + 13 + 4 = 60 a + bAdd from the left347 + 285 = 632 meanAverage from a basemean of 47, 52, 49, 56 = 51

Dividing and percentages

n ÷ 5Divide by 5235 ÷ 5 = 47 n ÷ 25Divide by 25675 ÷ 25 = 27 p% of nPercentages from 10% and 1%23% of 400 = 92 x% of y = y% of xSwap the percentage8% of 50 = 50% of 8 = 4 p/q = ?%Fractions as percentages3/8 = 37.5%

Checking and divisibility

casting out ninesCheck with nines347 × 26 = 9022 passes is n divisible by d?Divisibility rules7524 is divisible by 9