Subtraction of Dissimilar Fractions
2026-02-28 06:02 Diff
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Last updated on August 5, 2025

The mathematical operation of finding the difference between two fractions with different denominators is known as the subtraction of dissimilar fractions. It helps simplify expressions and solve problems involving fractions with unlike denominators.

What is Subtraction of Dissimilar Fractions?

Subtracting dissimilar fractions involves finding a common denominator so the fractions can be subtracted. It requires converting each fraction to an equivalent fraction with the same denominator.

There are three components of a fraction:

Numerator: The top part of a fraction, indicating how many parts are taken.

Denominator: The bottom part of a fraction, indicating the total number of equal parts.

Fraction bar: This separates the numerator and the denominator and denotes division.

How to do Subtraction of Dissimilar Fractions?

When subtracting dissimilar fractions, students should follow these steps:

Find a common denominator: Determine the least common multiple (LCM) of the denominators.

Convert fractions: Rewrite each fraction as an equivalent fraction with the common denominator.

Subtract the numerators: Subtract the numerators while keeping the common denominator.

Simplify the result: If possible, simplify the fraction to its lowest terms by dividing both the numerator and the denominator by their greatest common divisor (GCD).

Methods to do Subtraction of Dissimilar Fractions

The following are methods for subtracting dissimilar fractions:

Method 1: Least Common Denominator (LCD) Method

Step 1: Find the least common denominator of the fractions.

Step 2: Convert each fraction to an equivalent fraction with the LCD.

Step 3: Subtract the numerators and keep the LCD as the denominator.

Step 4: Simplify the resulting fraction if possible.

Example: Subtract 3/4 from 5/6.

Step 1: LCM of 4 and 6 is 12.

Step 2: Convert: 3/4 = 9/12, 5/6 = 10/12.

Step 3: Subtract: 10/12 - 9/12 = 1/12.

Method 2: Cross-Multiplication Method

Step 1: Cross-multiply the fractions.

Step 2: Subtract the cross products and write over the product of the denominators.

Step 3: Simplify the resulting fraction if possible.

Example: Subtract 2/3 from 4/5.

Step 1: Cross-multiply: (4×3) - (2×5) = 12 - 10 = 2.

Step 2: Denominator: 3×5 = 15.

Step 3: Result: 2/15.

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Properties of Subtraction of Dissimilar Fractions

In fraction subtraction, some characteristic properties are observed:

  1. Subtraction is not commutative In subtraction, changing the order of the fractions changes the result, i.e., A/B - C/D ≠ C/D - A/B.
  2. Subtraction is not associative Unlike addition, regrouping is not possible in subtraction. For three or more fractions, changing the grouping changes the result. ((A/B) - (C/D)) - (E/F) ≠ (A/B) - ((C/D) - (E/F)).
  3. Subtraction is the addition of the opposite Subtracting a fraction is the same as adding its opposite, so convert subtraction into addition by reversing the sign of the second fraction. A/B - C/D = A/B + (-C/D).
  4. Subtracting zero from a fraction leaves the fraction unchanged Subtracting zero from any fraction results in the same fraction: A/B - 0 = A/B.

Tips and Tricks for Subtraction of Dissimilar Fractions

Useful tips for students to efficiently handle subtraction of dissimilar fractions include:

Tip 1: Always determine the least common denominator to simplify calculations.

Tip 2: Simplify fractions at every step to manage smaller numbers and reduce errors.

Tip 3: Visual learners can use fraction strips or area models to understand subtraction better.

Ignoring common denominators

Students often forget to find a common denominator before subtracting. Always convert fractions to have the same denominator before proceeding.

Problem 1

Use the cross-multiplication method, (2×3) - (1×5) = 6 - 5 = 1 Denominator: 3×5 = 15 Result: 1/15

Okay, lets begin

Subtract 5/8 from 3/4

Well explained 👍

Problem 2

Use the LCD method, LCM of 8 and 4 is 8. Convert: 3/4 = 6/8 Subtract: 6/8 - 5/8 = 1/8

Okay, lets begin

Subtract 7/9 from 5/6

Well explained 👍

Problem 3

Use the cross-multiplication method, (5×9) - (7×6) = 45 - 42 = 3 Denominator: 9×6 = 54 Result: 3/54 = 1/18 Since the smaller fraction is subtracted from the larger, the result is -1/18.

Okay, lets begin

Subtract 2/7 from 3/5

Well explained 👍

Problem 4

Use the LCD method, LCM of 7 and 5 is 35. Convert: 2/7 = 10/35, 3/5 = 21/35 Subtract: 21/35 - 10/35 = 11/35

Okay, lets begin

Subtract 4/11 from 7/9

Well explained 👍

No, fractions with different denominators must first be converted to equivalent fractions with a common denominator before subtraction.

1.Is subtraction commutative for fractions?

No, the order of fractions matters in subtraction; changing them changes the outcome.

2.What is a common denominator?

A common denominator is a shared multiple of the denominators of two or more fractions, used to make the fractions comparable for operations like addition and subtraction.

3.What is the first step in subtracting dissimilar fractions?

The first step is to find a common denominator for the fractions so they can be written as equivalent fractions with the same denominator.

4.What methods are used for the subtraction of dissimilar fractions?

The least common denominator (LCD) method and the cross-multiplication method are used for subtracting dissimilar fractions.

Common Mistakes and How to Avoid Them in Subtraction of Dissimilar Fractions

Subtraction of dissimilar fractions can be challenging, leading to common mistakes. Awareness of these errors can help students avoid them.

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Hiralee Lalitkumar Makwana

About the Author

Hiralee Lalitkumar Makwana has almost two years of teaching experience. She is a number ninja as she loves numbers. Her interest in numbers can be seen in the way she cracks math puzzles and hidden patterns.

Fun Fact

: She loves to read number jokes and games.