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Same tens digit, units that add to 10

This is a narrow shortcut, but when it applies, it's almost as fast as the "ending in 5" squares trick — two two-digit numbers collapse into two tiny multiplications.

When it applies

Both numbers need the same tens digit, and their units digits need to add up to exactly 10. 42 and 48 qualify (both have tens digit 4; units 2 and 8 sum to 10). 42 and 47 don't (units sum to 9).

The rule

Let t be the shared tens digit, and u₁, u₂ be the two units digits (which sum to 10). Then:

Why it works

Write the two numbers as (10t + u) and (10t + (10 − u)). Multiplying them out: 100t² + 10t(10 − u) + 10tu + u(10 − u) = 100t² + 100t + u(10 − u) = 100·t(t+1) + u(10−u). The first term gives the leading digits, and u(10−u) — which is exactly u₁ × u₂ — gives the trailing two.

Worked examples

42 × 48 — t=4, units 2 and 8. Leading: 4×5=20. Trailing: 2×8=16. Combine → 2016.

61 × 69 — t=6, units 1 and 9. Leading: 6×7=42. Trailing: 1×9=09 (pad to two digits). Combine → 4209.

73 × 77 — t=7, units 3 and 7. Leading: 7×8=56. Trailing: 3×7=21. Combine → 5621.

Watch the padding

The trailing part always needs exactly two digits. In the 61×69 example, 1×9=9 has to be written as "09," not "9" — otherwise the digits don't land in the right place and the answer comes out wrong by a factor of ten.

Practice it

Practice arithmetic → · See the rest of the shortcuts guide →