Doubling & Halving

Technique: Double one factor, halve the other

The key insight

a × b = (a÷2) × (b×2). If one factor is even, halve it and double the other to get an easier multiplication.

Examples

• 14 × 16 → halve 14, double 16 → 7 × 32 = 224
• 24 × 15 → halve 24, double 15 → 12 × 30 = 360
• 36 × 15 → halve 36, double 15 → 18 × 30 = 540
• 48 × 25 → halve 48, double 25 → 24 × 50 = 1200

When to double-halve twice

If one factor is divisible by 4, you can halve twice:

• 16 × 35 → 8 × 70 → 4 × 140 = 560
• 44 × 25 → 22 × 50 → 11 × 100 = 1100

Why does this work?

Multiplication is commutative and associative: a × b = (a × 2) × (b ÷ 2). You're not changing the product, just rearranging the factors.

Every question has a 30 second shot clock.