MPESB Group · Bite-size lessons

Simplification

About 6 min · Mathematics · English

Time worked out from the lesson's 328 words at 150 words a minute, plus a minute for each question.

Simplification is the backbone of quantitative aptitude in MPESB Group 1/2/3 exams. The skill underlies nearly all other arithmetic topics—from percentage to profit-loss to data interpretation. Mastering simplification means you solve faster and with fewer careless errors.

Key ideas

• BODMAS Rule: The universal order of operations—Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction. Division and Multiplication share equal priority (left to right), as do Addition and Subtraction.
• Bracket Hierarchy: Solve innermost brackets first. Order: Vinculum (bar) → Parentheses ( ) → Curly braces { } → Square brackets [ ].
• Fractions: A fraction a/b represents a parts of b equal divisions. Proper fractions have numerator < denominator; improper fractions have numerator ≥ denominator.
• Decimals: Positional representation where digits after the decimal point represent tenths, hundredths, thousandths, etc. Every fraction can be expressed as a terminating or recurring decimal.
• Surds: Irrational roots that cannot be simplified to rational numbers (e.g., √2, ³√5). Surds follow specific rules for multiplication, division, and rationalization.

Watch out for

• Ignoring left-to-right rule for D/M and A/S: Students think division always comes before multiplication. Correct approach: D and M have equal priority—solve whichever appears first from left to right.
• Adding surds incorrectly: Writing √2 + √3 = √5 is wrong. Correct approach: Unlike surds cannot be combined; √2 + √3 stays as √2 + √3.
• Forgetting to simplify final fractions: Leaving answer as 12/16 instead of 3/4. Correct approach: Always reduce to lowest terms by dividing numerator and denominator by their HCF.

Quick reference

• BODMAS order: Brackets → Orders → Division/Multiplication (L→R) → Addition/Subtraction (L→R)
• Fraction division: Flip the second fraction and multiply.
• Surd addition: Only like surds (same radicand) can be combined.
• Rationalize: Multiply by conjugate to remove surd from denominator.
• Recurring decimal to fraction: 0.abab... = ab/99; 0.aaa... = a/9

Check yourself: 3 questions

This lesson is cut from the topic's note, not rewritten. Fact-checked on 17 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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