Speed calculation · lesson 13 of 25 · free

Check it with nines — Speed Calculation

A fast calculator also checks fast. Add the digits of a number again and again until one digit is left — its nine-check number. Do the same sum with the nine-check numbers. If the result does not match the nine-check number of the answer, the answer is wrong.

The fast method

Casting out nines — “shrink every number to one digit and do the same sum with those”

  1. Find the nine-check number of each number: add the digits until one digit is left.
  2. Do the same sum (× or +) with those digits and shrink the result to one digit too.
  3. Shrink the given answer. Different → wrong. Same → it passes the check.

Use it for: Checking long multiplication and addition in exams, olympiad answers and homework before you hand it in.

Worked example: Check with nines: 38 × 23 = 864. Correct or wrong? Wrong

  1. 38 → 3 + 8 = 11 → 2. 23 → 2 + 3 = 5.
  2. 2 × 5 = 10 → 1.
  3. 864 → 8 + 6 + 4 = 18 → 9. 1 and 9 are different.

Check: 38 × 23 = 874, not 864 ✓

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

Right: 0 · Tried: 0

🏁 Lesson 13 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass — and beat the clock: finish within 4 min.

🏅 Sign in with Google to earn the 🔍 Nine Detective badge when you pass — and a certificate when you finish all 5 lessons of Part 3 · Speed dividing, percentages and checking. You can still take the test without signing in.

🖨️ Casting Out Nines Worksheet

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