SSC MTS · Bite-size lessons

Mathematical Operations

About 7 min · Reasoning Ability and Problem Solving · English

Time worked out from the lesson's 512 words at 150 words a minute, plus a minute for each question.

Mathematical Operations is a reasoning topic that tests your ability to substitute symbols and balance equations according to given rules. Unlike regular arithmetic, these questions replace standard operators (+, −, ×, ÷) with unusual symbols or interchange them, then ask you to evaluate expressions or find which equation becomes true under the new system.

Key ideas

• Symbol Substitution: The question provides a coding scheme where unusual symbols represent standard operations. For example, "If + means ×, − means ÷, × means +, and ÷ means −" then you must mentally or physically replace each symbol before computing.
• Interchanged Operators: Sometimes the question interchanges two standard operators (e.g., + and × are swapped, − and ÷ are swapped). Apply these swaps to the entire expression before evaluating.
• BODMAS After Substitution: Always apply BODMAS/BODMAS order (Brackets, Orders, Division/Multiplication left-to-right, Addition/Subtraction left-to-right) to the expression after you've made all symbol substitutions. The substitution changes what the symbols mean, not the order of operations.
• Balancing Equations: Some questions ask which arrangement of operators makes a given numerical equation true (e.g., 12 ? 3 ? 4 = 8, find the correct operators). Test each option by substituting and calculating.
• Single vs. Multiple Substitutions: Simpler questions substitute all occurrences of one or two symbols. Harder questions may involve four-way or circular swaps. Read the key carefully and apply every rule.

Watch out for

• Forgetting to Apply All Substitutions → Students substitute two operators but miss the other two in a four-way swap. Fix: Write out all four substitution rules before touching the expression. Check each symbol in the expression against your list.
• Ignoring BODMAS After Substitution → After substituting × for +, students add first instead of multiplying. Fix: Treat the substituted expression as a brand-new arithmetic problem. Multiplication and division always come before addition and subtraction, left to right.
• Left-to-Right Without Respecting Precedence → Students compute "18 × 6 + 12 ÷ 4" as (18 × 6 + 12) ÷ 4 by going strictly left to right. Fix: Do all multiplications and divisions first (in any order or left-to-right among themselves), then all additions and subtractions.

Quick reference

• Read the key carefully: Write down or mentally note all substitutions before touching the expression.
• Substitute first, compute second: Replace every symbol, then treat it as a normal arithmetic problem.
• BODMAS is non-negotiable: Multiply/Divide before you Add/Subtract, always left-to-right within each precedence level.
• Check integer results: Complex fractions signal an error.
• Practice 10–15 questions: Symbol substitution becomes automatic with repetition. Aim for under 40 seconds per question.

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.

Read the full noteFlashcards for this topic