Mental math tricks

Make a 10

Move part of one number to the other to make a 10 first. 8 needs 2 more, so take 2 from the 5: 8 + 5 = 10 + 3.

1. 8 + 5
2. 8 + 2 = 10
3. 10 + 3 = 13

Why it works: Tens are the easiest numbers to add to, and moving 2 across doesn't change the total.

Add 9

Add 10, then take away 1. Adding 10 is easy: the tens digit goes up by one.

1. 47 + 9
2. 47 + 10 = 57
3. 57 − 1 = 56

Why it works: 9 is 10 − 1.

Subtract by counting up

Count up from the smaller number to the bigger one, in easy jumps to the next 10. The jumps add up to the answer.

1. 52 − 47
2. 47 + 3 = 50
3. 50 + 2 = 52
4. 3 + 2 = 5

Why it works: Subtraction asks how far apart two numbers are, and counting up measures exactly that.

Multiply by 5

Multiply by 10, then halve. It works for any number: 5 × 37 is 370 ÷ 2 = 185.

1. 5 × 46
2. 10 × 46 = 460
3. 460 ÷ 2 = 230

Why it works: 5 is half of 10.

Multiply by 9

Multiply by 10, then take the number away once.

1. 9 × 23
2. 10 × 23 = 230
3. 230 − 23 = 207

Why it works: 9 is 10 − 1, so 9 groups is 10 groups minus 1 group.

Multiply by 25

Divide by 4, then multiply by 100.

1. 25 × 16
2. 16 ÷ 4 = 4
3. 4 × 100 = 400

Why it works: 25 is a quarter of 100.

Halve one, double the other

Halve one number and double the other, and the answer stays the same. Keep going until one of them is easy.

1. 14 × 15
2. 14 ÷ 2 = 7
3. 15 × 2 = 30
4. 7 × 30 = 210

Why it works: Dividing one number by 2 and multiplying the other by 2 cancel out.

Square a number ending in 5

Multiply the tens digit by the next number up, then write 25 after it. 35 × 35: 3 × 4 = 12, so 1225.

1. 35 × 35
2. 3 × 4 = 12
3. 12 | 25
4. 1225

Why it works: A number ending in 5 is 10 × a + 5. Its square is 100 × a × (a + 1) + 25.

Multiply a two-digit number by 11

Split the digits and put their sum in the middle. If the sum is 10 or more, carry the 1.

1. 11 × 72
2. 7 + 2 = 9
3. 7 | 9 | 2
4. 792

Why it works: 11 × 72 is 720 + 72, and adding those puts 7 + 2 in the middle.

More on the 11s: how to multiply by 11 in your head.