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Tricks · Checking and divisibility

Check with nines

Checking a multiplication (or an addition) you have already done, such as 347 × 26 = 9022.

casting out nines

The trick, step by step

  1. Add the digits of each number until one digit is left: 347 → 3 + 4 + 7 = 14 → 5; 26 → 8.

  2. Multiply those digits and do the same: 5 × 8 = 40 → 4.

  3. Do the same to your answer: 9022 → 9 + 0 + 2 + 2 = 13 → 4.

  4. They match, so the answer passes. If they do not match, the answer is surely wrong.

given working answer taken away

Why it works

10 is 9 + 1, so every place value leaves remainder 1 when divided by 9: a number and its digit sum leave the same remainder. Remainders multiply like the numbers do, so a right product must match. A wrong answer usually shows a different digit, but swapped digits (9022 and 9202) are not caught.

Practise this trick