Multiplication tricks

Multiplication doesn't always need long working. Many numbers have tricks that make them easy to multiply in your head. Once you know the tricks, you can do mental maths like a pro.

What is this?

Multiplying by 10, 100, 1,000 , just add zeros.

• 47 × 10 = 470.
• 23 × 100 = 2,300.
• 5 × 1,000 = 5,000.

Multiplying by 5 , multiply by 10, then halve.

• 26 × 5 = (26 × 10) ÷ 2 = 260 ÷ 2 = 130.
• 48 × 5 = 480 ÷ 2 = 240.

Multiplying by 9 , multiply by 10, then subtract the original.

• 7 × 9 = 70 − 7 = 63.
• 12 × 9 = 120 − 12 = 108.

Multiplying by 11 (for two-digit numbers) , add the two digits, put the answer in the middle.

• 23 × 11: 2 + 3 = 5. Answer = 2 _ 5 _ 3 = 253.
• 35 × 11: 3 + 5 = 8. Answer = 385.

If the middle sum is more than 9, carry 1 to the left digit. 78 × 11: 7 + 8 = 15. Carry: 8 _ 5 _ 8 with carry → 858.

Multiplying by 2 repeatedly is doubling. 16 × 4 = double 16 = 32, double 32 = 64.

Doubling and halving: if one number is even, halve it and double the other.

• 35 × 8 = 70 × 4 = 140 × 2 = 280.

These tricks save time and make you feel powerful with numbers. Try them often.

Worked examples

Example 1. 64 × 5.

• Trick: × 10 then halve.
• 64 × 10 = 640. 640 ÷ 2 = 320.

Example 2. 8 × 9.

• Trick: × 10 then subtract.
• 8 × 10 = 80. 80 − 8 = 72.

Example 3. 45 × 11.

• Trick: add digits and place in the middle.
• 4 + 5 = 9. Answer: 4 _ 9 _ 5 = 495.

Try it

1. 36 × 5 (using the trick).
2. 9 × 9 (using the trick).
3. 27 × 11 (using the trick).
4. 56 × 10.
5. 12 × 9 (using the trick).

Hands-on

Mental-maths race. Pick 5 multiplications. Try the tricks above. Race a family member , them with a calculator, you with your head. Who finishes faster?

Trick discovery. Try multiplying any two-digit number ending in 5 by 5. Notice a pattern? Try 15 × 5, 25 × 5, 35 × 5. They all end in 25 or 75. Why?