SOF NSO · Bite-size lessons

Mathematical Operations

About 7 min · Logical Reasoning · English

Time worked out from the lesson's 537 words at 150 words a minute, plus a minute for each question.

Mathematical Operations is a topic in the Logical Reasoning section of SOF NSO where students must evaluate expressions after substituting given symbols for standard operators (+, −, ×, ÷). The challenge lies not in complex arithmetic but in careful symbol substitution and strict adherence to BODMAS/BODMAS order of operations. This topic tests your attention to detail and ability to execute multi-step calculations without errors.

Key ideas

• Symbol Substitution: The problem defines new meanings for standard operators. For example, if "A + B means A ÷ B," you must mentally (or on paper) replace every + with ÷ throughout the expression before calculating.
• BODMAS/BODMAS Rule: After substitution, evaluate strictly in this order: Brackets, Orders (powers/roots), Division and Multiplication (left to right), Addition and Subtraction (left to right). Ignoring this order is a common cause of wrong answers.
• Four Operation Types: Problems usually substitute the four basic operations (+, −, ×, ÷) with each other or with symbols like @, #, $, ★. Less common variations include interchange with comparison operators (>, <, =) in "find the true statement" questions.
• Two Question Formats: (1) Direct evaluation — "If A $ B means A + B and A # B means A × B, find the value of 8 $ 4 # 3." (2) Statement verification — "Which equation becomes true after applying the given substitutions?"
• No Actual Math Complexity: Once substituted correctly, the arithmetic is typically at Class 5–7 level (whole numbers, simple fractions). The difficulty is procedural, not computational.

Watch out for

• Forgetting to Substitute All Operators: Writing "12 + 3 × 2" when the problem says + means × and × means +, but only substituting one. Always scan the entire expression and replace every symbol.
• Ignoring BODMAS: Calculating left to right without respecting order of operations. For example, in 8 + 4 × 2, students wrongly do (8+4) × 2 = 24 instead of 8 + (4×2) = 16. Fix: Always do multiplication/division before addition/subtraction unless brackets override.
• Mixing Up Substitution Direction: If the problem says "A + B means A × B," students sometimes reverse it and think "× means +." Fix: Write down the substitution key clearly: "+ symbol in the problem → × operator in calculation."

Quick reference

• Substitution → BODMAS — Always perform substitution completely, then apply BODMAS strictly.
• BODMAS = Brackets, Orders, Div/Mult (L→R), Add/Sub (L→R) — Equal-priority operations go left to right.
• Write It Out — Don't skip steps in rough work; transcription errors are the most common mistake.
• Check Every Option — In multiple-choice verification, test all statements before finalizing your answer.
• Practice Symbol Sets — Familiarize yourself with common substitution patterns (swap addition/subtraction, rotation of all four operators).

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain. The questions are from Shishya's validated question bank.

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