Fraction Tricks: Shortcuts, Formulas and Quick Methods

Fraction Tricks help simplify and calculate fractions quickly using common factors, compatible denominators, cancellation, and reciprocal rules. This page covers fraction simplification tricks, addition and subtraction methods, multiplication and division shortcuts, decimal and percentage conversions, and examples for fast, accurate calculations.

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What Are Fraction Tricks?

Fraction tricks are short methods used to simplify, compare, add, subtract, multiply, divide, or convert fractions with fewer calculation steps. They are based on factors, equivalent fractions, cancellation, and the reciprocal property.

A fraction is written as a/b, where a is the numerator, b is the denominator, and b ≠ 0. An equivalent fraction is obtained by multiplying or dividing both terms by the same non-zero number. For example, 3/4 = 6/8 because both numerator and denominator are multiplied by 2. Simplification means dividing the numerator and denominator by their greatest common factor: 24/36 = 2/3.

Fraction Tricks Formula & Tricks

Important Formulas

Equivalent fractions
a/b = (a × k)/(b × k), k ≠ 0

Multiplying or dividing both numerator and denominator by the same non-zero number preserves the value of the fraction.

Addition or subtraction
a/b ± c/d = (ad ± bc)/(bd)

For unlike denominators, cross-multiply and combine the products. Simplify the result if possible.

Multiplication
a/b × c/d = ac/bd

Cancel common factors between any numerator and denominator before multiplying.

Division
a/b ÷ c/d = a/b × d/c = ad/bc, c ≠ 0

Change division into multiplication and invert the second fraction.

Fraction to percentage
a/b × 100%

Multiply a fraction by 100 to express it as a percentage. For example, 3/5 = 60%.

Quick Tricks

Cancel before multiplying

Reduce crosswise between a numerator and the other denominator before multiplying. This keeps the numbers smaller and gives the same result.

Example: 18/35 × 14/27: cancel 18 with 27 by 9 to get 2 and 3, and 14 with 35 by 7 to get 2 and 5. Result = (2 × 2)/(5 × 3) = 4/15.
Use the complement for fractions near 1

Write a fraction close to 1 as 1 minus its difference from 1. This makes comparison and some calculations faster.

Example: 47/50 = 1 − 3/50. Therefore, 47/50 = 0.94.
Find a common denominator using the LCM

For addition or subtraction, use the least common multiple of the denominators instead of multiplying them directly. This reduces the size of intermediate numbers.

Example: 5/12 + 7/18: LCM(12,18) = 36, so 5/12 = 15/36 and 7/18 = 14/36. Sum = 29/36.
Invert only the divisor

In fraction division, keep the first fraction unchanged and take the reciprocal of only the second fraction.

Example: 3/8 ÷ 9/16 = 3/8 × 16/9. Cancelling gives 2/3.

Fraction Tricks Concepts

Simplifying Fractions by Common Factors

A fraction is in simplest form when its numerator and denominator have no common factor greater than 1.

Find the greatest common factor of the numerator and denominator, then divide both by it. For 84/126, the greatest common factor is 42. Thus, 84/126 = (84 ÷ 42)/(126 ÷ 42) = 2/3.

Example: Simplify 45/75. Since GCF(45, 75) = 15, 45/75 = 3/5.

Adding and Subtracting Fractions

Fractions with the same denominator are combined by adding or subtracting their numerators while keeping the denominator unchanged.

For unlike denominators, convert the fractions to a common denominator, preferably their LCM. For 7/12 − 1/8, LCM(12, 8) = 24; therefore, 14/24 − 3/24 = 11/24.

Example: 2/9 + 5/6: LCM(9, 6) = 18, so 2/9 = 4/18 and 5/6 = 15/18. The sum is 19/18 = 1 1/18.

Multiplying Fractions with Cancellation

To multiply fractions, multiply the numerators and denominators, but cancel common factors before multiplication whenever possible.

Cancellation can be performed between a numerator of one fraction and a denominator of the other fraction. For 8/15 × 25/16, cancel 8 with 16 and 25 with 15 to obtain 1/2 × 5/3 = 5/6.

Example: 12/35 × 14/18 = 2/5 × 7/3 after cancellation, so the result is 14/15.

Dividing Fractions Using Reciprocals

To divide by a fraction, multiply by its reciprocal; the reciprocal of a/b is b/a when a and b are non-zero.

Keep the first fraction unchanged, change ÷ to ×, and invert the second fraction. For 5/6 ÷ 10/9, use 5/6 × 9/10. Cancelling gives 3/4.

Example: 7/15 ÷ 14/25 = 7/15 × 25/14 = 5/6.

Converting Fractions to Decimals and Percentages

A fraction can be converted to a decimal by dividing the numerator by the denominator and to a percentage by multiplying the fraction by 100.

Common equivalents include 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, and 3/5 = 0.6 = 60%. If the denominator is 10, 100, or 1000, shift the decimal point to obtain the decimal directly.

Example: 7/8 × 100% = 87.5%, and 7 ÷ 8 = 0.875.

Fraction Tricks Video Lessons

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Practice Fraction Tricks Questions

Practise published questions related to this topic.

1An officer simplifies 1/(√3 + √2) . The simplified form is:→ 2The value of (27^(2/3) × 9^(-1/2))/(3⁻¹ × 81^(1/4)) is→ 3What is the smallest natural number that should be added to 9054 such that a remainder of 6 is left when the resulting number is divided by each of the numbers 28, 24, 56 and 29?→ 4√(√400 + √25) = ?→ 5An article is sold for a loss Rs. 81. Loss percentage is 18 percent. What is the selling price of the article?→ 6There are 3 classes A, B and C. There are 36, 60 and 72 students in these classes respectively. Each class is to be divided into groups. Each group has same number of students. Each group should have students from only one class. Every student is a part of 1 group. What is the maximum number of students in each group?→ 7Which of the following numbers is divisible by 3?→ 8Some articles were bought at the rate of Rs 8 per 5 articles, and sold at the rate of Rs 9 per 4 articles. Profit percent is:→ 9An article is sold for 40 percent profit. The value of discount given is equal to (5/14) of the marked price. Cost price of the article is how much percent less than its marked price?→ 10If the marked price of a fan is ₹775 and a discount of 12% is given on it, then what is the selling price of the fan?→

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Quick Revision Notes

Fraction Tricks: Quick Revision Points

Use these rules for fast and accurate fraction calculations.

  • A fraction a/b requires b ≠ 0.
  • Divide the numerator and denominator by their GCF to simplify a fraction.
  • Use the LCM of denominators for addition and subtraction.
  • For multiplication, cancel common factors before multiplying.
  • To divide by a fraction, multiply by its reciprocal.
  • Multiply a fraction by 100 to convert it into a percentage.
  • A proper fraction is less than 1, an improper fraction is at least 1, and a mixed number contains a whole number and a proper fraction.
  • After calculation, check whether the final fraction can be simplified further.

Fraction Tricks FAQs

How do you simplify a fraction quickly?

Divide both the numerator and denominator by their greatest common factor. For example, 36/48 ÷ 12 = 3/4.

What is the fastest method for adding fractions with unlike denominators?

Use the LCM of the denominators. For 1/6 + 1/4, the LCM is 12, so the sum is 2/12 + 3/12 = 5/12.

Can fractions be cancelled during multiplication?

Yes. Cancel common factors between a numerator and the denominator of another factor before multiplying. For example, 6/25 × 15/18 = 1/5 × 5/3 = 1/3.

What is the rule for dividing two fractions?

Keep the first fraction, change division to multiplication, and invert the second fraction: a/b ÷ c/d = a/b × d/c.

How do you compare two fractions quickly?

Cross-multiply when denominators are positive. For a/b and c/d, compare ad and bc. Since 5 × 8 = 40 and 3 × 13 = 39, 5/13 > 3/8.

How do you convert 7/20 into a percentage?

Multiply by 100: 7/20 × 100% = 35%.

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