What Is Round and Adjust?
Round and adjust applies the compensation principle to multiplication. Round one factor to a friendlier number, multiply, then correct for the rounding difference. This transforms difficult problems like 19 × 8 into easy ones like 20 × 8, with a simple subtraction at the end.
When to Use It
This technique shines when one factor is close to a round number. Numbers ending in 8 or 9 (round up), or 1 or 2 (round down), are ideal candidates. For 98 × 7: round to 100 × 7 = 700, subtract 2 × 7 = 14, giving 686. The adjustment is always the difference multiplied by the other factor.
The Halving and Doubling Trick
Another adjustment technique: if one number is even, halve it and double the other. For 16 × 35: halve 16 → 8, double 35 → 70, then 8 × 70 = 560. Repeat if needed: 8 × 70 = 4 × 140 = 560. This keeps numbers manageable and reduces cognitive load.
Combining Techniques
Expert mental calculators combine round-and-adjust with decomposition. For 24 × 15: split 15 into 10 + 5, compute 24 × 10 = 240 and 24 × 5 = 120, sum to 360. Recognizing which technique fits each problem is the hallmark of mental math mastery.
Practice Examples
Example 1: 19 × 8 = ?
- Round 19 to 20
- 20 × 8 = 160
- Subtract one 8 (you added one extra 19): 160 - 8 = 152
Answer: 152
Example 2: 98 × 7 = ?
- Round 98 to 100
- 100 × 7 = 700
- Subtract 2 × 7 = 14: 700 - 14 = 686
Answer: 686
Example 3: 24 × 15 = ?
- Round 15 to 10: 24 × 10 = 240
- Add 24 × 5 = 120
- 240 + 120 = 360
Answer: 360