Doubling and Halving Method
- Trick / Shortcut
- Doubling and Halving Method
- Topic
- Multiplication
- How It Works
For multiplications with awkward numbers, double one factor and halve the other. This preserves the product:
$n \times m = \left(\frac{n}{2}\right) \times (2m)$
Repeat this process until one of the numbers becomes easy to multiply, such as a power of 10 or a single digit.
- Example
Example 1: 24 × 35
$24 \times 35$ $= 12 \times 70$ $= 6 \times 140$ $= 3 \times 280 = \textbf{840}$
Example 2: 125 × 48
$125 \times 48$ $= 250 \times 24$ $= 500 \times 12$ $= 1000 \times 6 = \textbf{6000}$