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Simplification & Approximation

Quantitative Aptitude / DI · Speed Calculation

Useful for: SSC CGL, Railway RRB, IBPS Banking, CTET, OTET, OSSTET, UGC NET, OSSC RHT — Regular High School Teacher

and 21 more exams

CSIR NET, CTSA / STSS, Central Univ./IIT/NIT Faculty, Junior Teacher, OAVS, OPSC Assistant Professor, OPSC PGT, OSEPA Primary Teacher / JT Category-I, OSEPA Upper Primary — Science, OSSC Mathematics, OSSC Teacher Readiness, OSSSC Govt Physical Education Teacher (PET), OSSSC Govt TGT Arts, OSSSC Govt TGT Science — CBZ, OSSSC Govt TGT Science — PCM, Sainik Schools, Special OTET, SSB Lecturer / PGT, SSB Lecturer (Degree Colleges), SSB School Teachers, SSB TGT PCM

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Overview

Simplification rewards correct order of operations and recognising recurring decimals and surd forms.

Key points

BODMAS / PEMDAS order: brackets, orders, division and multiplication, addition and subtraction.
Recurring decimals: 0.333… = 1/3; 0.1666… = 1/6; 0.abab… = ab/99.
Compare fractions by cross-multiplication or by converting to decimals.
Surds: √a × √b = √(ab); like surds add: 5√2 + 3√2 = 8√2.
Rationalise 1/(√a + √b) by multiplying by (√a − √b).

Explanation

Mixed recurring: 0.1666… = (16 − 1)/90 = 1/6.
Division and multiplication are done left to right in the order they appear.
Approximate square roots: √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236.
Simplify surds before adding: √50 = 5√2, √18 = 3√2.

Step by step

Follow BODMAS.
Convert recurring decimals and simplify surds.
Compute and compare with options.

Examples

2 + 3 × 4 − 6 ÷ 2 = 2 + 12 − 3 = 11.
√50 + √18 = 5√2 + 3√2 = 8√2.
1/(√3 + √2) = (√3 − √2)/(3 − 2) = √3 − √2.

Traps and advanced points

Trap: Adding before multiplying.
Trap: Adding unlike surds (√2 + √3 ≠ √5).
Trap: Treating 0.333… as 0.33 in exact answers.

Quick revision

BODMAS left to right.
0.ab recurring = ab/99.
Simplify surds before adding.

Practice MCQs

Simplify: 17 + 11 × 8 = ?
1. 97
2. 121
3. 105
4. 113
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Answer: (c) 105. BODMAS: multiplication first.
Simplify: 23 + 14 × 5 = ?
1. 88
2. 103
3. 98
4. 93
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Answer: (d) 93. BODMAS: multiplication first.
Simplify: 26 + 14 × 5 = ?
1. 96
2. 91
3. 106
4. 101
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Answer: (a) 96. BODMAS: multiplication first.
Simplify: 29 + 10 × 8 = ?
1. 125
2. 117
3. 109
4. 101
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Answer: (c) 109. BODMAS: multiplication first.
Simplify: 33 + 15 × 9 = ?
1. 177
2. 159
3. 186
4. 168
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Answer: (d) 168. BODMAS: multiplication first.
Simplify: 17 + 14 × 8 = ?
1. 121
2. 137
3. 129
4. 145
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Answer: (c) 129. BODMAS: multiplication first.
Simplify: 32 + 10 × 8 = ?
1. 112
2. 128
3. 104
4. 120
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Answer: (a) 112. BODMAS: multiplication first.
Simplify: 29 + 11 × 11 = ?
1. 172
2. 161
3. 150
4. 139
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Answer: (c) 150. BODMAS: multiplication first.
Simplify: 23 + 12 × 7 = ?
1. 114
2. 121
3. 100
4. 107
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Answer: (d) 107. BODMAS: multiplication first.
Simplify: 25 + 7 × 10 = ?
1. 105
2. 95
3. 85
4. 115
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Answer: (b) 95. BODMAS: multiplication first.
Simplify: 28 + 6 × 9 = ?
1. 82
2. 100
3. 73
4. 91
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Answer: (a) 82. BODMAS: multiplication first.
Simplify: 32 + 7 × 9 = ?
1. 104
2. 113
3. 86
4. 95
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Answer: (d) 95. BODMAS: multiplication first.
Simplify: 35 + 8 × 4 = ?
1. 71
2. 63
3. 67
4. 75
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Answer: (c) 67. BODMAS: multiplication first.
Simplify: 32 + 4 × 5 = ?
1. 62
2. 57
3. 52
4. 47
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Answer: (c) 52. BODMAS: multiplication first.
Simplify: 34 + 6 × 12 = ?
1. 106
2. 118
3. 130
4. 94
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Answer: (a) 106. BODMAS: multiplication first.