Subtracting Fractions (common or uncommon denominators)

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.

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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.

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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?

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Summary

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

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