Fraction Table for Fast Calculations and Conversions

Fraction Table for Fast Calculations gives common fractions in decimal and percentage forms for quick arithmetic. This page covers standard values such as 1/2, 1/3, 1/4 and 1/8, conversion formulas, simplification rules, multiplication and division methods, and solved aptitude examples.

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What Is a Fraction Table for Fast Calculations?

A fraction table lists frequently used fractions along with their decimal and percentage equivalents. Memorising these equivalent forms reduces repeated division during aptitude calculations.

For a fraction a/b, decimal form is obtained by dividing a by b, while percentage form is (a/b) × 100%. For example, 3/8 = 0.375 = 37.5%. Equivalent fractions have the same value, so 1/2, 2/4 and 50/100 represent the same quantity.

Fraction Table for Fast Calculations Video Lessons

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Fraction Tables, Division and Estimation Tricks

Learn how to use fraction tables for faster calculations, apply division tricks, and estimate results efficiently in quantitative aptitude problems.

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Fraction Table for Fast Calculations Formula & Tricks

Important Formulas

Fraction to decimal
a/b = a ÷ b

Divide the numerator by the denominator to obtain the decimal value.

Fraction to percentage
a/b × 100%

Multiply the fraction by 100 to convert it into a percentage.

Percentage to fraction
p% = p/100

Write the percentage over 100 and reduce the fraction to lowest terms.

Fraction multiplication
a/b × c/d = ac/bd

Cancel common factors before multiplying the remaining numerators and denominators.

Fraction division
a/b ÷ c/d = a/b × d/c

Keep the first fraction, change division to multiplication, and invert the second fraction.

Quick Tricks

Use denominator factors of 10 or 100

Convert the denominator to 10, 100 or 1000 by multiplying the numerator and denominator by the same number.

Example: 3/25 = 12/100 = 12%, and 7/8 = 875/1000 = 0.875.
Cancel before multiplying

Reduce a numerator with a denominator from another fraction before carrying out multiplication.

Example: 8/15 × 25/16 = (8 ÷ 8)/(16 ÷ 8) × 25/15 = 25/30 = 5/6.
Use complements near one

For a fraction close to 1, subtract its missing part from 1.

Example: 19/20 = 1 - 1/20 = 1 - 0.05 = 0.95.

Fraction Table for Fast Calculations Concepts

Common Fraction Equivalents

Common fractions can be written directly as decimals and percentages using their standard equivalents.

Values such as 1/2, 1/4, 3/4, 1/5, 1/8 and 1/10 occur frequently in ratios, percentages and data calculations. For fractions with recurring decimals, use the exact fraction or a suitable decimal approximation.

Example: 5/8 = 0.625 = 62.5%, while 1/3 = 0.333... = 33 1/3%.

Simplifying Fractions

A fraction is in lowest terms when its numerator and denominator have no common factor other than 1.

Divide both terms by their greatest common divisor. Simplification does not change the value of the fraction and makes multiplication, comparison and conversion easier.

Example: 18/24 becomes 3/4 after dividing both numerator and denominator by 6.

Comparing Fractions

Fractions with the same denominator are compared through their numerators; other fractions can be compared by cross-multiplication.

For positive fractions a/b and c/d, compare ad and bc. If ad > bc, then a/b > c/d. Cross-products avoid converting both fractions into decimals.

Example: Compare 5/8 and 3/5: 5 × 5 = 25 and 3 × 8 = 24, so 5/8 > 3/5.

Applying Fractions in Aptitude Calculations

To find a fraction of a quantity, multiply the quantity by the fraction and cancel factors before multiplying.

The expression a/b of N means (a/b) × N. If N is divisible by b, divide N first and then multiply by a.

Example: 3/8 of 240 = 240 ÷ 8 × 3 = 30 × 3 = 90.

Fraction Table for Fast Calculations Data Table

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Common Fractions in Decimal and Percentage Form

Standard fraction equivalents used in quick aptitude calculations.

Fraction Decimal Percentage
1/2 0.5 50%
1/3 0.333... 33 1/3%
2/3 0.666... 66 2/3%
1/4 0.25 25%
3/4 0.75 75%
1/5 0.2 20%
2/5 0.4 40%
3/5 0.6 60%
4/5 0.8 80%
1/6 0.1666... 16 2/3%
5/6 0.8333... 83 1/3%
1/8 0.125 12.5%

Note: Ellipses indicate recurring decimals. Mixed-number percentages are exact values.

Additional Fractions for Quick Conversion

Useful denominator-based values for percentage and ratio questions.

Fraction Decimal Percentage
1/10 0.1 10%
3/10 0.3 30%
7/10 0.7 70%
9/10 0.9 90%
1/20 0.05 5%
3/20 0.15 15%
7/20 0.35 35%
9/20 0.45 45%
11/20 0.55 55%
13/20 0.65 65%
17/20 0.85 85%
19/20 0.95 95%

Note: For denominator 20, multiply the numerator by 5 to obtain the percentage.

Practice Fraction Table for Fast Calculations Questions

Practise published questions related to this topic.

1The price of petrol is increased by 28%. A person wants to increase his expenditure by 22% only. By approximately what percent should he decrease his consumption?→ 2An article is sold for Rs. 288 after successive discounts of 20% and 25%. What is the marked price of the article?→ 321.6 ÷ 3.6 × 2 + 0.25 × 16 ÷ 4 - 6 is equal to∶→ 4What is the value of x so that the seven digit number 55350x2 is divisible by 72?→ 5Two articles are sold for Rs. 4,752 each. On one, the seller gains 32% and on the other he loses 28%. What is his overall gain or loss percentage, correct to one decimal place?→ 6The price of sugar is increased by 17%. A person wants to increase his expenditure by 5% only. By approximately what percent should he decrease his consumption?→ 7The value of 15.2 + 5.8 ÷ 2.9 × 2 - 3.5 × 2 ÷ 0.5 is equal to:→ 8What is the value of x so that the seven digit number 8439x53 is divisible by 99?→ 9Two articles are sold for Rs. 962 each. On one, the seller gains 30% and on the other he loses 26%. What is his overall gain or loss percentage, nearest to one decimal place?→ 10An article is sold for Rs. 288 after successive discounts of 25% and x%. If the marked price of the article is Rs. 480, what is the value of x?→

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Quick Revision Notes

Fraction Table Revision Points

Recall these direct conversions and calculation rules.

  • a/b in decimal form is a ÷ b.
  • a/b in percentage form is (a/b) × 100%.
  • 1/2 = 50%, 1/4 = 25%, 1/5 = 20%, 1/8 = 12.5% and 1/10 = 10%.
  • To find a/b of N, calculate N ÷ b × a whenever cancellation is possible.
  • For division by a fraction, multiply by its reciprocal.
  • Compare a/b and c/d by comparing ad and bc.
  • Recurring values include 1/3 = 0.333... and 1/6 = 0.1666....

Related Topic Explainers

Vedic Maths → Multiplication Tricks → Squaring Tricks → Division Tricks → Percentage Tricks → Fraction Tricks → Square Root Tricks → Cube Root Tricks →

Fraction Table for Fast Calculations FAQs

What is the formula for converting a fraction into a percentage?

Multiply the fraction by 100: a/b × 100%. For example, 3/8 × 100% = 37.5%.

What is 3/8 in decimal and percentage form?

3/8 = 0.375 = 37.5%.

How do you find 5/12 of 288?

Divide 288 by 12 and multiply by 5: 288 ÷ 12 × 5 = 24 × 5 = 120.

How do you convert 62.5% into a fraction?

62.5% = 62.5/100 = 625/1000 = 5/8.

Which is greater: 7/12 or 5/8?

Cross-products are 7 × 8 = 56 and 5 × 12 = 60. Therefore, 5/8 is greater.

How is 1/3 represented in a fraction table?

1/3 = 0.333... = 33 1/3%. The decimal repeats indefinitely.

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