How to multiply in your head without losing the numbers.

1. Split a factor into easy parts

For 23 × 14, split 14 into 10 + 4. Ten groups of 23 make 230. Four groups make 92. Add them for 322. This is the distributive law in a form that keeps the intermediate numbers manageable.

23 × 14 = 230 + 92 = 322

The same idea works with bigger numbers: 208 × 34 = 208 × 30 + 208 × 4 = 6,240 + 832 = 7,072. For a large product, jotting down an intermediate total is sensible; mental math does not have to mean doing every step without paper.

2. Use a nearby round number

For 97 × 96, both numbers are close to 100. They are 3 and 4 below it. Multiply the shortfalls, 3 × 4 = 12. Cross-subtract 97 − 4 = 93. Because the base is 100, the shortfall product needs two digits: 93 followed by 12 gives 9,312.

97 × 96 = (100 − 3)(100 − 4) = 9,312

This works because expansion gives 10,000 − 300 − 400 + 12. It is especially convenient when both factors sit near the same power of ten. For numbers far from a round base, splitting a factor may be simpler. This near-base pattern is also taught in Vedic mathematics.

3. Use a digit rule for a familiar multiplier

The Trachtenberg ×11 rule adds neighbouring digits. For 47 × 11, begin with 7. The middle sum is 4 + 7 = 11: write 1 and carry 1. Add that carry to the leftmost 4 to get 5. The result is 517. Check it as 470 + 47.

47 × 11 = 517

Read the full Trachtenberg multiplication guide for longer examples and the related ×12 rule.

How to choose a method and check your answer

If a factor is near 10 or 100, try compensation. If a factor splits cleanly, distribute. If you recognise a multiplier with a rule you already know, use the rule. Estimate before calculating: 208 × 34 is around 200 × 35 = 7,000, so 7,072 is plausible. A result of 70,720 would fail that quick check even before you redo the arithmetic.

For other operations and a short practice plan, see our mental math methods guide.