HSSC CET · Bite-size lessons

Simplification

About 6 min · Quantitative Ability · English

Time worked out from the lesson's 344 words at 150 words a minute, plus a minute for each question.

Simplification forms the backbone of the Quantitative Ability section in HSSC CET. Almost every arithmetic problem—whether it involves percentages, profit-loss, or time-work—requires you to simplify expressions quickly and accurately. Examiners use simplification questions to test your command over basic operations, order of precedence, and mental math speed.

Key ideas

• BODMAS Rule: The golden rule for order of operations—Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Always work left to right within the same priority level.
• Brackets Hierarchy: Solve innermost brackets first. Order: Vinculum (bar) → Parentheses ( ) → Curly braces { } → Square brackets [ ].
• Fractions: A fraction a/b represents a parts out of b equal parts. To add/subtract fractions, make denominators equal (LCM). To multiply, multiply numerators and denominators directly. To divide, multiply by the reciprocal.
• Decimals: Decimals are base-10 fractions. Align decimal points for addition/subtraction. Count total decimal places for multiplication. Move decimal point for division.
• Mixed Numbers: Convert mixed numbers (like 3½) to improper fractions (7/2) before calculating. Convert back only at the end.

Watch out for

• Wrong BODMAS order: Students often add before multiplying. Fix: Remember "DM before AS"—division and multiplication come before addition and subtraction.
• Ignoring bracket hierarchy: Solving [ ] before ( ) leads to wrong answers. Fix: Always start from the innermost bracket and work outward.
• Forgetting to convert mixed numbers: Calculating 2½ + 1¼ directly without converting to improper fractions. Fix: Convert to 5/2 + 5/4 = 15/4 = 3¾.

Quick reference

• BODMAS: Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction (L→R)
• LCM trick: For 2–3 small denominators, multiply them and simplify at the end if time is short
• 0.5 = 1/2, 0.25 = 1/4, 0.125 = 1/8, 0.2 = 1/5 — memorize these conversions
• √2 ≈ 1.41, √3 ≈ 1.73, √5 ≈ 2.24 — useful for approximation questions
• To simplify √72: Factor as √(36 × 2) = 6√2

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.

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