Summary: Simplification Approximation

Table of Contents
1. Introduction
2. Basic Rules of Simplification
3. To Solve Modulus of a Real Number
4. Tips to Crack Approximation
5. Conversion of decimal numbers to nearest number
6. Approximation of Square Roots
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Introduction

• The Quantitative Aptitude section of competitive examinations includes topics such as Simplification and Approximation, Number Series, Permutation & Combination, Quadratic Equations, Data Interpretation, Data Analysis and other miscellaneous questions.
• About 10-12 questions commonly cover Percentage and Average, Ratio & Proportion, Partnerships, Profit & Loss, and Simple & Compound Interest.

Basic Rules of Simplification

• The BODMAS rule defines the order of operations to find the correct value of an expression.
• B = Bracket; O = Order (powers, roots); D = Division; M = Multiplication; A = Addition; S = Subtraction.
• Apply operations in this order: brackets first (follow the bracket nesting order: (), {}, []), then exponents/orders, then division and multiplication from left to right, and finally addition and subtraction from left to right.

To Solve Modulus of a Real Number

• The Modulus (absolute value) of x, written |x|, is always ≥ 0.
• Definition: |x| = x if x ≥ 0; |x| = -x if x < 0.

Tips to Crack Approximation

• First convert decimals or percentages to their nearest convenient values, then simplify the expression using those rounded values.
• For percentages in calculations, round to the nearest whole percent when appropriate, then compute with the rounded rates.

Conversion of decimal numbers to nearest number

• Round each decimal to the nearest chosen value before performing the required arithmetic.
• Use the rounded values to simplify calculations quickly and get an approximate answer.

Approximation of Square Roots

• Factor the number under the square root.
• For any factor appearing twice (a pair), move one instance of that factor outside the root.
• If a factor appears three times, remove two as a pair (move one outside) and keep the third inside; for 4, 6, 8, etc. occurrences count them as 2, 3, 4 pairs respectively.
• Multiply the numbers outside the root together; multiply the leftover numbers inside the root together.
• To simplify the square root of a fraction, simplify numerator and denominator separately.
• Note: The outside number squared times the remaining inside number should equal the original radicand (check correctness).