Symbol Substitution — Rewrite, Then BODMAS

🎯 Learning Objective

Solve 'if + means × ...' questions by rewriting the expression with real signs and applying BODMAS strictly.

💡 Concept

• The question redefines symbols: 'if + means ×' tells you every + in the expression is actually a ×
• Step 1: REWRITE the whole expression with the real signs — never solve with the fake signs in your head
• Step 2: apply BODMAS on the rewritten expression: Brackets, Of, Division, Multiplication, Addition, Subtraction
• Division and multiplication settle before addition and subtraction — this is where most marks are lost
• Substitution goes ONE way: replace the symbol in the expression with its given meaning, not the reverse

🧮 Key Formulas

BODMAS: Brackets → Of → Division → Multiplication → Addition → Subtraction

✏️ Easy Example

Q. If + means − and − means +, find the value of 12 + 5 − 3.

1. Rewrite with real signs: 12 − 5 + 3
2. 12 − 5 = 7, then 7 + 3

Answer: 10

🇮🇳 Real-Life Example

Typing on a friend's phone where autocorrect swaps words — you first translate back what was really meant, then read the sentence. Rewrite first, solve second.

📝 Exam-Level Example

Q. If + means ×, − means ÷, × means − and ÷ means +, find 8 + 4 − 2 × 6 ÷ 3.

1. Rewrite: 8 × 4 ÷ 2 − 6 + 3
2. Divide/multiply first: 8 × 4 ÷ 2 = 16
3. Then: 16 − 6 + 3 = 13

Answer: 13

📝 Exam-Level Example

Q. If × means +, ÷ means −, + means ÷ and − means ×, find 36 + 6 − 3 × 5 ÷ 3.

1. Rewrite: 36 ÷ 6 × 3 + 5 − 3
2. 36 ÷ 6 = 6, then 6 × 3 = 18
3. 18 + 5 − 3 = 20

Answer: 20

🪄 Memory Trick

Write the swap table at the top of your rough space (+→×, −→÷ ...) and convert the expression in ONE pass, pointing at each symbol. Never convert while calculating.

⚠️ Common Mistakes

• ❌ Solving left to right and ignoring BODMAS after rewriting (16 − 6 + 3 is 13, not 16 − 9 = 7)
• ❌ Substituting only some of the symbols and leaving one in its fake form
• ❌ Reversing the mapping — 'if + means ×' converts + to ×, not × to +

🏆 Exam Tips

• ✅ After rewriting, underline all × and ÷ parts and settle them before touching + and −
• ✅ If two options are close, recompute only the multiplication/division block — that is where slips happen

📌 Summary

• Rewrite the full expression with real signs first
• Then strict BODMAS — divide/multiply before add/subtract
• Convert in one pass using a swap table
• Left-to-right solving is the classic trap