SSC GD · Bite-size lessons

Simplification

About 6 min · Elementary Mathematics · English

Time worked out from the lesson's 375 words at 150 words a minute, plus a minute for each question.

Simplification is a time-sensitive topic in the SSC GD Elementary Mathematics section. The core skill is applying the BODMAS rule (order of operations) systematically while handling fractions, decimals, surds, and roots.

Key ideas

• BODMAS Rule: Operations must be performed in strict order—Brackets first, then Orders (powers/roots), then Division and Multiplication (left to right), finally Addition and Subtraction (left to right). Never work left-to-right blindly.
• Brackets hierarchy: When nested brackets appear, solve innermost first: ( ) then { } then [ ]. Always clear all brackets before moving to other operations.
• Division and Multiplication are equal priority: These two operations have the same precedence. Perform them as they appear from left to right, not all division first or all multiplication first.
• Addition and Subtraction are equal priority: Similarly, addition and subtraction share equal status. Execute them left to right after all higher operations are complete.
• Surds: A surd is an irrational root that cannot be simplified to a rational number, written as √n. Operations on surds follow algebraic rules: √a × √b = √(ab) and √a / √b = √(a/b).

Watch out for

• Left-to-right calculation without BODMAS: Students often compute 5 + 3 × 2 as (5+3)×2 = 16 instead of 5 + (3×2) = 11. → Always apply BODMAS: Multiplication before addition gives 5 + 6 = 11.
• Treating Division/Multiplication or Addition/Subtraction as separate passes: Performing all multiplications first, then all divisions creates errors. → Division and Multiplication have equal priority—solve left to right. Same applies to Addition and Subtraction.
• Forgetting to clear innermost brackets first: Jumping to outer brackets leads to wrong results. → Always solve ( ) before { } before [ ]. Work inside-out systematically.

Quick reference

• BODMAS order: Brackets → Orders → Div/Mult (left-right) → Add/Sub (left-right)
• Surd multiplication: √a × √b = √(ab); √3 × √12 = √36 = 6
• Surd division: √a / √b = √(a/b); √50 / √2 = √25 = 5
• Rationalize 1/√a: Multiply by √a/√a to eliminate surd in denominator
• Memorize squares 1–25 and cubes 1–12: instant recognition saves time

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 18 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