Mental Math Tricks with Worked Examples

Learn practical mental arithmetic with decomposition, percentage shortcuts and rounding checks you can verify.

Break numbers into useful parts

For 48 × 25, use 25 = 100 / 4: 48 × 100 / 4 = 1200. For 19 × 7, use 20 × 7 − 7 = 133. These transformations preserve the value; the aim is to replace an awkward operation with two easy ones.

Find percentages without a calculator

10% means dividing by 10 and 1% means dividing by 100. To find 15% of 240, add 24 and 12 to get 36. For 12%, add 10% and twice 1%: 24 + 4.8 = 28.8. For 2.5%, find a quarter of 10%.

Compensate after rounding

To add 398 and 257, first add 400 and 257, then subtract 2: 655. To subtract 199 from 530, subtract 200 and add 1: 331. Write the compensation sign before calculating if you tend to reverse it.

Check the scale of the answer

Estimate first. Since 48 is close to 50, 48 × 25 should be close to 1250; 1200 fits, while 120 does not. Estimation detects misplaced decimal points but does not prove every digit correct. Use the expression calculator to verify an exact result.

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English edition: 16 September 2026.