Mathematical Operations • Topic 2 of 4

Symbol Substitution

You are told what each symbol really means (e.g., 'P means +, Q means −, R means ×'). Rewrite the whole expression with the real operations, then apply BODMAS. Do the substitution in writing first.

Rewrite first, compute second

Replace every symbol with its real operation on paper, then evaluate the rewritten expression using BODMAS. Trying to hold the mapping in your head while computing is where errors creep in.

Example: if "+" means "×" and "−" means "+", then "4 + 2 − 3" becomes "4 × 2 + 3" = 8 + 3 = 11.

BODMAS still applies after substitution. Once rewritten, the real ÷ and × happen before the real + and −, regardless of how the symbols looked.

✅ Solved examples

1. If + means ×, − means +, evaluate 4 + 2 − 3.
Becomes 4×2+3 = 8+3 = 11.
2. If × means −, ÷ means +, evaluate 10 × 2 ÷ 5.
Becomes 10−2+5 = 13.
3. If + means ÷, evaluate 12 + 4.
Becomes 12÷4 = 3.
4. If − means ×, + means −, evaluate 6 − 2 + 1.
Becomes 6×2−1 = 12−1 = 11.

✏️ Practice — try these, take hints as needed

1. If + means ×: 3 + 5
3×5.
—
—
15
2. If × means +, − means ×: 4 × 2 − 3
4+2×3.
BODMAS: 4+6.
—
10
3. If ÷ means −: 9 ÷ 4
9−4.
—
—
5
4. If + means −, − means +: 8 + 3 − 2
8−3+2.
—
—
7
5. If × means ÷: 20 × 4
20÷4.
—
—
5

📝 Topic test — 8 questions

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