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Mathematical Operations

Outline & Learning Goals

In this chapter you will learn to:

• Decode questions where symbols are given fake meanings (e.g., '+' means '×')
• Interchange signs or numbers and check which equation becomes correct
• Balance equations by choosing the right set of signs
• Apply BODMAS confidently under time pressure

The Hook: When '+' Tells a Lie

Imagine a world where '+' means multiply, '−' means divide, and nothing is what it looks like. Sounds like a puzzle from a movie? That is exactly what SSC, Banking and Railway exams do to you. They take a simple arithmetic sentence and secretly change the meaning of every symbol. Your job is not heavy calculation — your job is translation. Once you learn to translate, these questions become some of the fastest marks in the whole reasoning paper.

The Common Struggle (You Are Not Alone)

Most students lose marks here for three reasons:

1. They start calculating before rewriting the equation in real symbols.
2. They forget BODMAS order while simplifying.
3. In "interchange" questions, they test options randomly instead of smartly.

We will fix all three, one small chunk at a time.

Chunk 1: Symbol Substitution (The Core Type)

Rule: The question says things like: "If '+' means '×', '−' means '+', '×' means '÷', and '÷' means '−'…" Then it gives you an expression.

Method — always follow these two steps:

1. Rewrite first. Take the given expression and replace every symbol with its real meaning, on paper. Never do this in your head.
2. Then solve by BODMAS.

Example: If '+' means '×', '−' means '÷', '×' means '+', '÷' means '−', find the value of:
`8 + 4 − 3 × 2`

Step 1 (rewrite): 8 × 4 ÷ 3 + 2
Step 2 (BODMAS): 32 ÷ 3 + 2 = 10.67 + 2 ≈ 12.67

If the answer looks odd, recheck the rewriting — 90% of errors happen in Step 1, not Step 2.

🧠 Active Recall: Close the book. What are the two steps of symbol substitution, and in which step do most mistakes happen?

Chunk 2: BODMAS — Your Only Calculator Rule

Brackets → Of (×) → Division → Multiplication → Addition → Subtraction

Key points examiners exploit:

• Division and Multiplication have equal priority — solve left to right.
• Addition and Subtraction have equal priority — solve left to right.
• 'Of' (जैसे "1/2 of 8") is solved before division/multiplication.

Example: 24 ÷ 4 × 2 = ?
Wrong: 24 ÷ 8 = 3 (multiplied first — trap!)
Right: left to right → 6 × 2 = 12

🧠 Active Recall: Between ÷ and ×, which comes first in BODMAS? (Answer: neither — left to right!)

Chunk 3: Interchanging Signs or Numbers

Type A — Interchange two signs: "If '+' and '×' are interchanged, which equation is correct?"

Smart method: Don't test all four options fully. Take the new meaning, rewrite each option, and check only the division/multiplication part first — if that doesn't give a whole number, reject the option instantly and move on.

Type B — Interchange two numbers: "If 3 and 5 are interchanged, which equation becomes correct?" Swap the two digits in every option, then check.

Type C — Interchange sign AND number together: Do both swaps in one rewrite, then BODMAS.

🧠 Active Recall: In interchange questions, why should you check the division part of an option first? (Because a non-whole result lets you reject the option in 5 seconds.)

Chunk 4: Balancing the Equation (Insert the Signs)

Type: "Which set of signs makes the equation true? 15 ⃝ 3 ⃝ 5 ⃝ 2 = 10"

Method — work backwards from the answer:

• Look at the result (10). Is it small? Then division/subtraction is probably involved.
• Try the option that creates a clean division first (e.g., 15 ÷ 3 = 5).
• Verify the full chain by BODMAS.

Example: 15 ÷ 3 + 5 × 2 = 5 + 10 = 15 ✗ … try 15 ÷ 3 × 5 − 2? No wait — check options one by one, but always start with the option containing '÷' if the numbers divide cleanly.

🧠 Active Recall: When balancing an equation, which sign should you usually test first and why?

Chunk 5: Coded Inequalities & Statements

Some questions code relations: 'A + B' means 'A > B', 'A − B' means 'A < B', etc. Treat these exactly like symbol substitution: translate the whole statement into real symbols first, then judge the conclusion. Never mix coded and real meanings in the same line.

Mnemonic Trick 🎯

"Rewrite Before You Write" — chant this before every question of this chapter. Your pen's first job is translation, not calculation.

For BODMAS order, remember: "Big Orange Dogs Make Angry Sounds" (Brackets, Of, Division, Multiplication, Addition, Subtraction).

Summary Table

⚠️ Caution: Examiner's Trap

1. More than one plausible relation in options: In balancing/interchange questions, two options may *look* correct at first glance. The examiner designs one option that works only if you forget BODMAS (e.g., solving left-to-right blindly). Always verify with full BODMAS before marking.

2. Confusing wording to rattle you: Phrases like "interchanged with each other" vs "replaced by" mean different things. "A is replaced by B" is one-way; "A and B are interchanged" is two-way. Read the instruction line twice — it is the most important line of the question.

3. Double-relation questions: Some questions swap two pairs of symbols (e.g., '+'↔'−' AND '×'↔'÷'). Students often apply only one swap and get a confidently wrong answer. Count the swaps given, tick each one off as you rewrite.

📌 Review this chapter after 2 days. Redo the examples without looking at the solutions — if you can rewrite and solve each in under 45 seconds, this chapter is exam-ready.