Multiplication Tricks

Five techniques that let you multiply large numbers in your head. No memorization tables — just patterns your brain can exploit.

1. Squaring Numbers Ending in 5

Any number ending in 5 can be squared instantly. Take the tens digit, multiply it by one more than itself, and append 25.

The problem 35² = ? Tens digit times next number 3 \times 4 = 12 Append 25 35² = 1225

45² = ?

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75² = ?

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To multiply any two-digit number by 11, insert the sum of the two digits between them. If the sum exceeds 9, carry the 1.

The problem 36 \times 11 = ? Sum the digits 3 + 6 = 9 Insert between 3 [9] 6 = 396

72 × 11 = ?

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85 × 11 = ?

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Multiply by 10 and subtract the original number. Since 9 = 10 − 1, this turns every ×9 into a trivial subtraction.

The problem 47 \times 9 = ? Multiply by 10 47 \times 10 = 470 Subtract the original 470 - 47 = 423

Since 5 = 10 ÷ 2 and 25 = 100 ÷ 4, you can turn multiplication by 5 or 25 into division problems, which are often simpler.

Multiply by 5 48 \times 5 = 48 \times 10 \div 2 = 480 \div 2 = 240 Multiply by 25 48 \times 25 = 48 \times 100 \div 4 = 4800 \div 4 = 1200

Break one number into easier parts. This is the most flexible technique and works for any multiplication.

The problem 23 \times 14 = ? Break 14 into 10 + 4 23 \times 10 = 230 Then the remaining part 23 \times 4 = 92 Add them up 230 + 92 = 322

32 × 15 = ?

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