When students encounter a multiplication problem like 16 × 25, they often brace themselves for multi-step paper calculations. But there is an elegant mathematical principle called doubling and halving that turns this into a problem you can solve in your sleep.
The Core Concept
If you halve one factor and double the other factor, the product remains identical:
A × B = (A ÷ 2) × (B × 2)
Let's Solve 16 × 25
- Halve 16 to get 8.
- Double 25 to get 50.
- Now solve
8 × 50. - Halve again if you want: Halve 8 to get 4, double 50 to get 100.
4 × 100 = 400!
So 16 × 25 = 400 without writing down a single number.
Another Example: 18 × 15
- Halve 18 = 9
- Double 15 = 30
9 × 30 = 270
This works especially well whenever one number is even and the other ends in 5 or 25!