Subtraction of Unlike Fractions
2026-02-28 09:53 Diff
https://brightchamps.com/en-us/math/numbers/subtraction-of-unlike-fractions

132 Learners

Last updated on September 9, 2025

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

What is Subtraction of Unlike Fractions?

Subtracting unlike fractions involves finding a common denominator and converting the fractions to equivalent fractions with this common denominator. Once the fractions have the same denominator, the numerators can be subtracted directly. The process involves three main components: 

Numerators: These are the top numbers of fractions. 

Denominators: These are the bottom numbers of fractions. -

Operators: For subtraction, the operator is the minus (-) symbol.

How to do Subtraction of Unlike Fractions?

When subtracting unlike fractions, students should follow these steps:

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

2. Convert to equivalent fractions: Adjust the fractions so they have the same denominator.

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

4. Simplify the result: Reduce the fraction to its simplest form, if possible.

Methods to do Subtraction of Unlike Fractions

The following are the methods for subtracting unlike fractions: -

Method 1: Common Denominator Method

Step 1: Identify the least common denominator (LCD) of the fractions.

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

Step 3: Subtract the numerators and retain the common denominator.

Example: Subtract 1/3 from 5/4

Step 1: LCD of 3 and 4 is 12.

Step 2: Convert 1/3 to 4/12 and 5/4 to 15/12.

Step 3: Subtract: 15/12 - 4/12 = 11/12.

Answer: 11/12 

Method 2: Cross Multiplication Method

This method involves using cross multiplication to find a common denominator and directly computing the difference.

Example: Subtract 2/5 from 3/7

Solution: Cross multiply: (3 * 5) - (2 * 7) = 15 - 14 = 1.

Common denominator: 5 * 7 = 35.

Result: 1/35.

Therefore, the result of the subtraction is 1/35.

Explore Our Programs

Properties of Subtraction of Unlike Fractions

In fraction subtraction, there are some characteristic properties. These properties are listed below: -

  • Subtraction is not commutative: Changing the order of the fractions changes the result, i.e., A/B - C/D ≠ C/D - A/B. 
  • Subtraction is not associative: Unlike addition, regrouping terms in subtraction changes the result. 
  • Subtraction involves finding a common denominator: To make subtraction easier, fractions are converted to have a common denominator. 
  • Subtracting zero leaves the fraction unchanged: Subtracting zero from a fraction gives the same fraction: A/B - 0 = A/B.

Tips and Tricks for Subtraction of Unlike Fractions

Tips and tricks are useful for students to efficiently handle the subtraction of unlike fractions. Some helpful tips are listed below: 

Tip 1: Always find the least common denominator to make calculations simpler. 

Tip 2: Simplify fractions whenever possible to make subtraction easier. 

Tip 3: Using visual aids like fraction strips can help beginners understand the subtraction process better.

Ignoring the need for a common denominator

Students often try to subtract fractions directly without finding a common denominator. Always ensure that fractions have the same denominator before subtracting.

Problem 1

Find the least common denominator (LCD) which is 10. Convert: 1/2 = 5/10 and 3/5 = 6/10. Subtract: 6/10 - 5/10 = 1/10.

Okay, lets begin

Subtract 4/9 from 7/12

Well explained 👍

Problem 2

Find the LCD of 9 and 12, which is 36. Convert: 4/9 = 16/36 and 7/12 = 21/36. Subtract: 21/36 - 16/36 = 5/36.

Okay, lets begin

Subtract 2/7 from 5/6

Well explained 👍

Problem 3

Find the LCD of 7 and 6, which is 42. Convert: 2/7 = 12/42 and 5/6 = 35/42. Subtract: 35/42 - 12/42 = 23/42.

Okay, lets begin

Subtract 3/8 from 7/10

Well explained 👍

Problem 4

Find the LCD of 8 and 10, which is 40. Convert: 3/8 = 15/40 and 7/10 = 28/40. Subtract: 28/40 - 15/40 = 13/40.

Okay, lets begin

Subtract 5/11 from 13/15

Well explained 👍

Yes, but you need to convert the fractions to have a common denominator first.

1.Is subtraction commutative for fractions?

No, changing the order of fractions changes the result.

2.What are like fractions?

Like fractions have the same denominator, making them easier to add or subtract directly.

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

The first step is to find a common denominator for the fractions.

4.What methods are used for subtracting unlike fractions?

The common denominator method and cross multiplication method are commonly used.

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

Subtraction of unlike fractions can be challenging, often leading to common mistakes. However, being aware of these errors can help students avoid them.

What Are Numbers? 🔢 | Fun Explanation with 🎯 Real-Life Examples for Kids | ✨BrightCHAMPS Math

▶

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.