5 MENTAL MATH TRICKS FOR FASTER MULTIPLICATION

There is no single best multiplication trick. Look at the numbers first. A nearby round number, an even factor, or a familiar square usually tells you which method will be quickest.

1. Multiply numbers close to 100

For 95 × 93, both numbers are close to 100. Their shortfalls are 5 and 7.

1. Cross-subtract: 95 − 7 (or 93 − 5) = 88.
2. Multiply the shortfalls: 5 × 7 = 35.
3. Combine them: 88 | 35 = 8,835.

Why it works: (100−a)(100−b) = 100(100−a−b) + ab. The right-hand part needs two digits, so pad a one-digit result with a zero: 98 × 97 = 95 | 06 = 9,506.

2. Halve one number and double the other

The product stays unchanged when you halve one factor and double the other. Use this when one number is even and the other becomes round:

24 × 35 = 12 × 70 = 6 × 140 = 840.

3. Use the difference of two squares

Numbers equally spaced around a midpoint fit (a−b)(a+b) = a²−b². For 47 × 53, the midpoint is 50 and both numbers are 3 away:

47 × 53 = 50² − 3² = 2,500 − 9 = 2,491.

4. Round, multiply, then adjust

Move one factor to a nearby round number, then correct for what you added or removed. For 49 × 18:

50 × 18 − 1 × 18 = 900 − 18 = 882.

5. Split one factor into easy pieces

Use the distributive rule and choose pieces you can calculate quickly. For 32 × 17:

32 × (10 + 5 + 2) = 320 + 160 + 64 = 544.

A five-minute practice routine

Do five questions with each trick, untimed, and name the trick before solving. Then mix the question types and time the set. You are training the moment before the calculation: spotting which shortcut fits. For a full training schedule, continue with the mental math guide.