How to multiply two-digit numbers in your head

Two-digit multiplication feels impossible mentally because the paper method makes you hold four partial products at once. These three methods only ever ask you to hold one or two numbers.

Method 1: split one factor

Break the easier number into tens and units, multiply each piece, then add. Always add as you go, so you only carry one running total.

Tip: split the number whose units digit is smaller — 3 × 27 is easier than 7 × 43.

Method 2: round and adjust

When one factor sits just below a round number, use the round number and subtract the overshoot.

This is the fastest method for anything ending in 8 or 9: 39 × 16 = 40 × 16 − 16 = 624.

Method 3: difference of squares

If the two numbers are the same distance from a midpoint, the answer is the midpoint squared minus the distance squared. It looks like algebra, but it's the fastest trick here when it applies.

It works whenever the two numbers are both odd or both even: 34 × 26 = 30² − 4² = 900 − 16 = 884.

Squaring a two-digit number

Squares are a special case of Method 3. Round up and down by the same amount, multiply those, and add back the square of the amount:

Numbers ending in 5 are even quicker: multiply the tens digit by one more than itself and append 25. 65² → 6 × 7 = 42 → 4225.

Which method to use

Practise until it's automatic

Reading a method takes a minute; using it without thinking takes a few weeks of short sessions. R3CK0N's Math mode on Hard gives you nothing but two-digit by two-digit multiplication, and its Secret mode has dedicated timed drills for 2×2-digit products and two-digit squares. Every problem is timed, so you can see which ones still slow you down.

These techniques are covered in far more depth in Arthur Benjamin and Michael Shermer's Secrets of Mental Math, which R3CK0N's Secret mode is built around.