Percent to Fraction & Fraction to Percent

What is Percent?

Percent = Per + Cent = Per 100

The symbol % simply means × 1/100.

Example: Find the percent of 360/600.

• 600 → 360
• 1 → 360/600
• 100 → (360/600) × 100 = 60%

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Percentage → Fraction

Multiply the percentage by 1/100

Percentage	Calculation	Fraction
10%	10 × 1/100	1/10
5%	5 × 1/100	1/20
20%	20 × 1/100	1/5
25%	25 × 1/100	1/4
16⅔% (= 50/3%)	50/3 × 1/100	1/6
40%	40 × 1/100	2/5

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Fraction → Percentage

Multiply the fraction by 100

Fraction	Calculation	Percentage
1/10	1/10 × 100	10%
1/20	1/20 × 100	5%
1/5	1/5 × 100	20%
1/6	1/6 × 100	16⅔% or 16.67%

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The Master Conversion Table (1/n)

Memorize these — they appear in almost every quant problem:

Fraction	Percentage		Fraction	Percentage		Fraction	Percentage
1/1	100%		1/10	10%		1/19	5.26%
1/2	50%		1/11	9.09%		1/20	5%
1/3	33.33%		1/12	8.33%		1/24	4.17%
1/4	25%		1/13	7.69%		1/25	4%
1/5	20%		1/14	7.14%		1/30	3.33%
1/6	16.67%		1/15	6.66%		1/40	2.5%
1/7	14.28%		1/16	6.25%		1/50	2%
1/8	12.5%		1/17	5.88%		1/100	1%
1/9	11.11%		1/18	5.55%

Exam tip: Recognizing 11.11% as 1/9, or 14.28% as 1/7 instantly saves 30+ seconds per question. These appear constantly in ratio, percentage, profit/loss, and SI/CI problems.

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The Multiplier Trick

Once you know 1/n as a percentage, any multiple k/n = k × (1/n)%.

Examples with 1/2 = 50%:

Fraction	= Multiplier × 50%	Percentage
3/2	3 × 50%	150%
4/2	4 × 50%	200%
5/2	5 × 50%	250%
9/2	9 × 50%	450%

This works for ANY denominator — just multiply the numerator by the base percentage.

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Practice: Quick-Fire Conversions

#	Convert	Answer
1	12.5% → fraction	1/8
2	1/7 → percentage	14.28%
3	33.33% → fraction	1/3
4	1/16 → percentage	6.25%
5	7.14% → fraction	1/14
6	1/25 → percentage	4%
7	9.09% → fraction	1/11
8	1/40 → percentage	2.5%