Summarize this article:
101 LearnersLast updated on September 8, 2025
Subtraction of Fractions with Different Denominators
The mathematical operation of finding the difference between two fractions is known as the subtraction of fractions with different denominators. It helps simplify fractions and solve problems that involve numbers in fractional form and arithmetic operations.
What is Subtraction of Fractions with Different Denominators?
Subtracting fractions with different denominators involves finding a common denominator before performing the subtraction. It requires converting the fractions to equivalent fractions with a common denominator, and then subtracting the numerators.
There are two main components of a fraction:
Numerator: This is the top number of a fraction representing the parts taken.
Denominator: This is the bottom number of a fraction representing the total number of equal parts.
How to Subtract Fractions with Different Denominators?
When subtracting fractions with different denominators, students should follow these steps:
Find a common denominator: Determine the least common multiple (LCM) of the denominators.
Convert fractions: Adjust each fraction to have the common denominator.
Subtract numerators: Subtract the numerators while keeping the common denominator.
Simplify the result: If possible, reduce the fraction to its simplest form.
Methods to Subtract Fractions with Different Denominators
The following are the methods for subtracting fractions with different denominators:
Method 1: Finding the Least Common Denominator
Step 1: Identify the least common multiple of the denominators.
Step 2: Convert each fraction to an equivalent fraction with the LCM as the new denominator.
Step 3: Subtract the numerators and keep the common denominator.
Example: Subtract 1/4 from 3/8 Step 1: LCM of 4 and 8 is 8.
Step 2: Convert 1/4 to 2/8 and 3/8 stays as is. Step 3: 3/8 - 2/8 = 1/8
Method 2: Cross-Multiplication Method
Step 1: Multiply the numerator of each fraction by the denominator of the other fraction.
Step 2: Subtract the results and write the new numerator over the product of the denominators.
Example: Subtract 2/3 from 5/6 Solution: (5×3)-(2×6)/(6×3)=15-12/18=3/18=1/6
Properties of Subtraction of Fractions with Different Denominators
When subtracting fractions, certain properties must be considered:
- 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
- Subtraction is not associative Unlike addition, fractions cannot be regrouped in subtraction, as it changes the result.
- Subtracting zero Subtracting zero from a fraction leaves the fraction unchanged: A/B - 0 = A/B
Tips and Tricks for Subtraction of Fractions with Different Denominators
Tips and tricks can help students efficiently deal with the subtraction of fractions:
Tip 1: Always find the least common denominator for a simple calculation.
Tip 2: After subtraction, check if the fraction can be simplified.
Tip 3: Use the cross-multiplication method for quick calculations when the denominators are large.
Forgetting to find a common denominator
Students often forget to find a common denominator, which is crucial for correct subtraction. Always determine the least common denominator before proceeding.
Mistake 1
Incorrect simplification
After obtaining the result, ensure the fraction is simplified properly. Incorrect simplification leads to inaccurate answers.
Mistake 2
Misalignment in fraction conversion
When converting fractions to a common denominator, ensure proper alignment and conversion of numerators.
Mistake 3
Leaving fractions without simplification
Always check if the resulting fraction can be simplified as the final step.
Mistake 4
Ignoring missing numerators
If a fraction lacks a term, consider it as zero, e.g., when subtracting from a whole number, use a fraction representing the whole.
Mistake 5
Examples of Subtraction of Fractions with Different Denominators
Subtract 1/3 from 3/4
5/12
Problem 1
Use the least common denominator, LCM of 3 and 4 is 12. Convert 1/3 to 4/12 and 3/4 to 9/12. Subtract: 9/12 - 4/12 = 5/12
Subtract 5/6 from 7/8
Explanation
1/24
Problem 2
Use the cross-multiplication method, (7×6)-(5×8)/(8×6)=42-40/48=2/48=1/24
Subtract 2/5 from 4/7
Explanation
6/35
Problem 3
LCM of 5 and 7 is 35. Convert 2/5 to 14/35 and 4/7 to 20/35. Subtract: 20/35 - 14/35 = 6/35
Subtract 3/10 from 9/20
Explanation
3/20
Problem 4
LCM of 10 and 20 is 20. Convert 3/10 to 6/20 and 9/20 stays as is. Subtract: 9/20 - 6/20 = 3/20
Subtract 2/9 from 5/12
Explanation
7/36
No, fractions with different denominators cannot be subtracted directly. They must be converted to have a common denominator first.
1.Is subtraction commutative with fractions?
2.What is the least common denominator?
3.What is the first step in subtracting fractions with different denominators?
4.What methods are used for subtracting fractions with different denominators?
Common Mistakes and How to Avoid Them in Subtraction of Fractions with Different Denominators
Subtraction of fractions with different denominators can be challenging. Being aware of common mistakes can help avoid them.
Explore More numbers
![Important Math Links Icon]()
Previous to Subtraction of Fractions with Different Denominators
![Important Math Links Icon]()
Next to Subtraction of Fractions with Different Denominators
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.
