Subtraction of Improper Fractions
2026-02-28 17:50 Diff
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Last updated on August 5, 2025

The mathematical operation of finding the difference between two improper fractions is known as the subtraction of improper fractions. It involves simplifying expressions and solving problems that include fractions where the numerator is greater than or equal to the denominator.

What is Subtraction of Improper Fractions?

Subtracting improper fractions involves finding a common denominator and then subtracting the numerators. It requires converting the fractions to like denominators before performing the subtraction.

There are three components to consider with improper fractions:

Numerator: The top number in a fraction, which is greater than or equal to the denominator in improper fractions.

Denominator: The bottom number in a fraction, which indicates the total number of equal parts.

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

How to Subtract Improper Fractions?

When subtracting improper fractions, students should follow these steps:

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

Adjust fractions: Convert each fraction to an equivalent fraction with the common denominator.

Subtract numerators: Subtract the numerators of the equivalent fractions.

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

Methods to Subtract Improper Fractions

The following are the methods for subtracting improper fractions:

Method 1: Same Denominator Method

If the fractions already have the same denominator, simply subtract the numerators and write the result over the common denominator.

Method 2: Different Denominator Method

If the fractions have different denominators, follow these steps:

Step 1: Determine the least common denominator (LCD) by finding the LCM of the denominators.

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

Step 3: Subtract the numerators of the equivalent fractions.

Step 4: Simplify the resulting fraction if necessary.

Example: Subtract 7/4 from 11/3.

Step 1: LCM of 4 and 3 is 12.

Step 2: Convert to equivalent fractions: 11/3 = 44/12, 7/4 = 21/12.

Step 3: 44/12 - 21/12 = 23/12.

Step 4: The result is 23/12.

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Properties of Subtraction of Improper Fractions

Subtraction of improper fractions has specific properties:

  • Subtraction is not commutative: In subtraction, changing the order of the fractions changes the result, i.e., A - B ≠ B - A.
  • Subtraction is not associative: Unlike addition, we cannot regroup in subtraction. For three or more fractions, changing the grouping alters the result. (A − B) − C ≠ A − (B − C).
  • Subtraction can be converted to addition of the opposite: Subtracting a fraction is equivalent to adding its opposite, thus making calculations easier. A − B = A + (−B).
  • Subtracting zero leaves the fraction unchanged: Subtracting zero from any fraction results in the same fraction: A - 0 = A.

Tips and Tricks for Subtraction of Improper Fractions

These tips can help students efficiently handle the subtraction of improper fractions:

Tip 1: Always find the least common denominator before subtracting.

Tip 2: If the numerators are the same, the result is zero; no further calculations are needed.

Tip 3: Simplify the resulting fraction to its lowest terms to make the answer clearer.

Ignoring the need for a common denominator

Students often attempt to subtract fractions without finding a common denominator. Always ensure the denominators are the same before subtracting.

Problem 1

Find a common denominator, which is 15. Convert: 14/3 = 70/15, 9/5 = 27/15. Subtract: 70/15 - 27/15 = 43/15.

Okay, lets begin

Subtract 5/2 from 11/4

Well explained 👍

Problem 2

Find a common denominator, which is 4. Convert: 11/4 = 11/4, 5/2 = 10/4. Subtract: 11/4 - 10/4 = 1/4.

Okay, lets begin

Subtract 13/6 from 7/2

Well explained 👍

Problem 3

Find a common denominator, which is 6. Convert: 7/2 = 21/6, 13/6 = 13/6. Subtract: 21/6 - 13/6 = 8/6, which simplifies to 4/3.

Okay, lets begin

Subtract 8/3 from 5/1

Well explained 👍

Problem 4

Find a common denominator, which is 3. Convert: 5/1 = 15/3, 8/3 = 8/3. Subtract: 15/3 - 8/3 = 7/3.

Okay, lets begin

Subtract 23/8 from 3/1

Well explained 👍

No, a common denominator is necessary to ensure the fractions are comparable before subtraction.

1.Is subtraction of fractions commutative?

No, the order of terms affects the result 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, allowing the fractions to be compared or combined.

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

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

4.What methods can be used for subtracting improper fractions?

The same denominator method and the different denominator method are used for subtracting improper fractions.

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

Subtracting improper fractions can be challenging and often leads to common mistakes. Being aware 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.