Same tens digit, units adding to 10

When 43 × 47 shows up, the answer takes five seconds.

The question

What is 43 × 47?

The trick

If both numbers share a tens digit and their units add to 10: multiply the tens digit by the next number up for the left half, and multiply the two units for the right half.

4×53×72021

Worked example

1Both numbers have tens digit 4, and 3 + 7 = 10 — the pattern applies
2Left half: 4 × 5 = 20
3Right half: 3 × 7 = 21
4Join them: 2021

So: 2021

Remember it like this

Same tens, units that make ten — front shakes hands with the next number, units multiply on their own.

In the exam

Check both conditions before using it. 43 × 46 does not qualify, because 3 + 6 is 9, not 10. And pad the right half to two digits: 81 × 89 → 72 and 9 → 7209.

Why it works

The numbers are (10n+a) and (10n+b) where a+b = 10. Multiplying out gives 100n² + 100n + ab, which is 100 × n(n+1) + ab.

Explain this to my childGet the words to teach it, in your language

Try it yourself

0/4 correct

1
62 × 68
62 × 68
2
81 × 89
81 × 89
3
34 × 36
34 × 36
4
95 × 95
95 × 95