Logical reasoning · lesson 26 of 30 · free

Symbol substitution — Logical reasoning for kids

If + means × and × means +, what is 12 − 4 + 3 × 6? Do not calculate yet! First rewrite the whole sum with the real signs, then use BODMAS: × and ÷ before + and −.

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How to think it through

Swap, then BODMAS — “rewrite the sum with the real signs before you calculate anything”

  1. Rewrite the sum, swapping every sign for what it means.
  2. BODMAS: do × and ÷ first, from left to right.
  3. Then do + and −, from left to right.

Use it for: Mathematical operations questions in reasoning tests, and getting BODMAS right in school maths.

Worked example: If + means ×, − means ÷, × means + and ÷ means −, what is 12 − 4 + 3 × 6? → 15

  1. Swap the signs: 12 ÷ 4 × 3 + 6.
  2. × and ÷ first: 12 ÷ 4 = 3, 3 × 3 = 9. Then 9 + 6 = 15.

Check: (12 ÷ 4) × 3 + 6 = 9 + 6 = 15 ✓

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✓ Written and checked by the TalentJR team · Updated 27 Oct 2026 · How we make our lessons

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🖨️ Symbol Substitution Worksheet

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