Subtracting Fractions (common or uncommon denominators)

Subtracting Fractions

Subtracting fractions can be done in a couple of ways, depending on whether the fractions have the same (common) denominator or different (uncommon) denominators

The following diagram shows how to subtract fraction with common denominators and uncommon denominators. Scroll down the page for more examples and solutions for subtracting fractions.


 

Fraction Worksheets
Practice with the following worksheets.
Printable & Online Fractions Worksheets

Free Fraction Games
Learning Fractions	Equivalent Fractions	Compare Fractions
Simplify Fractions	Greatest Common Factor	Least Common Multiple
Improper Fractions & Mixed Numbers	Add Fractions	Subtract Fractions
Subtract Fractions from Whole Numbers	Multiply Fractions	Divide Fractions
Multiply Fractions & Whole Numbers	Divide Fractions & Whole Numbers	Add Mixed Numbers
Subtract Mixed Numbers	Multiply Mixed Numbers	Divide Mixed Numbers

 

Subtracting Fractions with Common Denominators or Like Denominators

When we subtract fractions that have the same, or common denominators, we subtract only the numerators. The denominators stay the same.

1. Keep the denominator the same.
2. Subtract the numerators (the top numbers).
3. Simplify the result if possible.

Example:
\(\frac{3}{7}-\frac{2}{7}=\frac{3-2}{7}=\frac{1}{7}\)

How to subtract fractions with common denominators.

• Show Step-by-step Solutions

Subtracting Fractions With Uncommon Denominators or Unlike Denominators

To subtract fractions with uncommon denominators, we need to change the fractions to equivalent fractions with common denominators before we find the difference.

1. Find the least common denominator (LCD), which is the LCM of the denominators.
2. Convert each fraction to an equivalent fraction with the LCM as the new denominator.
   To do this, divide the LCM by the original denominator and multiply both the numerator and denominator by that result.
   
3. Subtract the numerators (keeping the common denominator).
   
4. Simplify the result if possible.
   

Example:
\(\frac{1}{2}-\frac{2}{5}\)

Solution:

Step 1: Find the LCD or LCM of 2 and 5
Multiples of 2: 2, 4, 6, 8, 10, 12
Multiples of 5: 5, 10, 15
The LCD or the Least Common Multiple of 2 and 5 is 10

Step 2: Write both fractions as equivalent fractions with a common denominator of 10.

\(\frac{1}{2}=\frac{1×5}{2×5}=\frac{5}{10}\)
\(\frac{2}{5}=\frac{2×2}{5×2}=\frac{4}{10}\)

Step 3: Subtract the 2 equivalent fractions.

\(\frac{1}{2}-\frac{2}{5}=\frac{5}{10}-\frac{4}{10}=\frac{1}{10}\)

How to subtract fractions with uncommon denominators?

• Show Step-by-step Solutions

Summary

1. Same denominator? Subtract numerators directly.
2. Different denominators? Find the LCD first.

Check out this lesson on types of fractions:
Types of Fractions
Check out this lesson on equivalent fractions:
Equivalent Fractions
Check out this lesson on how to convert between mixed numbers and improper fractions:
Mixed Numbers & Improper Fractions
Check out this lesson on how to convert between fractions and decimals:
Fractions & Decimals

Check out these lessons on adding, subtracting, multiplying, and dividing fractions:
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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