Imagine being asked to compute 16 × 35 in your head. Most adults will pause and try to imagine a sheet of paper. But with the Doubling and Halving Strategy, that intimidating calculation can be rewritten in one second as 8 × 70, which is an effortless times-table fact: 560. Here is how this technique works, why it is mathematically sound, and when to deploy it.
The Principle: Conservation of Area
Think of multiplication as the area of a rectangle: Area = Width × Height. If you take a chocolate bar that is 16 cm long and 35 cm wide, cut it exactly in half lengthwise, and place the two halves side by side, what happens? The width doubles (to 70 cm), the length halves (to 8 cm), but the total amount of chocolate remains completely unchanged.
Step-by-Step Examples
Worked Example 1: 18 × 15
- Cut the even number in half:
18 ÷ 2 = 9. - Double the other number:
15 × 2 = 30. - Multiply the new numbers:
9 × 30 = 270. - Therefore: 18 × 15 = 270!
Worked Example 2: 24 × 25
- Halve 24:
12. Double 25:50. Problem is now12 × 50. - Let's do it again! Halve 12:
6. Double 50:100. - Problem is now
6 × 100 = 600! - Therefore: 24 × 25 = 600!
Worked Example 3: 14 × 45
- Halve 14 →
7. - Double 45 →
90. 7 × 90 = 630.- Result: 630 in two seconds.
⚡ Practice with the Gamified Mental Math Speed Trainer
Test your 11s trick, doubling/halving, left-to-right addition, and times tables in timed speed sprints!
Frequently Asked Questions
Because multiplying by 2 and dividing by 2 cancel each other out: (A × 2) × (B / 2) = A × B × (2 / 2) = A × B × 1 = A × B. The total area or product remains strictly invariant.
Use this method whenever one factor ends in 5 (like 15, 25, 35, 45) or is difficult, while the other factor is an even number (like 14, 16, 24, 32). Doubling the 5-number creates a round multiple of 10.
Yes! You can double and halve as many times as you like until you reach factors that are trivial to compute.