Compensation Magic

Multiplying by 9 and 99 (Rounding & Compensation)

Numbers adjacent to round powers of ten (9, 99, 999) are easiest to calculate by overshooting to the clean power of ten and compensating backwards.

Mathematical Symmetry & Identity

$$N \times 9 = 10N - N, \quad N \times 99 = 100N - N$$

Visual Mental Pipeline

Step-by-Step Execution Rules

1 Multiply by 9: Multiply by 10 (add a 0) and subtract the number once. Example: 43 × 9 = (43 × 10) - 43 = 430 - 43 = 387.
2 Multiply by 99: Multiply by 100 (add two 0s) and subtract the number once. Example: 26 × 99 = 2600 - 26 = 2574.
3 Subtractions in your head: Subtract the tens first, then the units (e.g. 430 - 40 = 390; 390 - 3 = 387).

43 × 9 Example 1

Step 1: 43 × 10 = 430

Step 2: 430 - 43 = 387

= 387

68 × 9 Example 2

Step 1: 68 × 10 = 680

Step 2: 680 - 68 = 612

= 612

26 × 99 Example 3

Step 1: 26 × 100 = 2600

Step 2: 2600 - 26 = 2574

= 2574

57 × 99 Example 4

Step 1: 57 × 100 = 5700

Step 2: 5700 - 57 = 5643

= 5643

Put this shortcut into practice with 10 procedural, timed questions. Sharpen your reaction time and track your accuracy.