The strategy
How it works
Choose a nearby base such as 10 or 100.
Write each factor as the base plus or minus its offset.
Use distribution to combine the base product and offset terms.
See it in action
Worked examples
Example 19 × 8
- Use base 10: 9 = 10 − 1 and 8 = 10 − 2.
- 10 × 10 − 10 × 1 − 10 × 2 + 1 × 2.
- 100 − 10 − 20 + 2 = 72.
Answer: 72
Example 212 × 11
- Use base 10: (10 + 2)(10 + 1).
- 100 + 10 + 20 + 2.
- 132.
Answer: 132
A quick heads-up
Common mistakes to avoid
- Forgetting the product of the two offsets; in 9 × 8, include (−1) × (−2) = +2.
- Using a base that is not actually close; splitting into place values may be simpler for distant numbers.
Your turn
Check your understanding
Choose an answer to see instant feedback and a short explanation. You can take the quiz again any time.
Question 1 of 3
What is 9 × 7?
Think 10 × 7 = 70, then remove one group of 7: 63.
Which is 11 × 12?
(10 + 1)(10 + 2) = 100 + 20 + 10 + 2 = 132.
What base is most useful for 98 × 97?
Both numbers are close to 100, so 100 is the friendly base.
Keep the momentum
Try a few practice problems
Choose a comfortable range and work through a short round with the free mental math trainer.