Mathematics » Introducing Fractions » Add and Subtract Fractions with Common Denominators

# Subtracting Fractions with a Common Denominator

## Subtracting Fractions with a Common Denominator

We subtract fractions with a common denominator in much the same way as we add fractions with a common denominator.

### Fraction Subtraction

If $$a,b,\text{and}\phantom{\rule{0.2em}{0ex}}c$$ are numbers where $$c\ne 0,$$ then

$$\frac{a}{c}-\frac{b}{c}=\frac{a-b}{c}$$

To subtract fractions with a common denominators, we subtract the numerators and place the difference over the common denominator.

## Example

Find the difference: $$\frac{23}{24}-\frac{14}{24}.$$

### Solution

 $$\frac{23}{24}-\frac{14}{24}$$ Subtract the numerators and place the difference over the common denominator. $$\frac{23-14}{24}$$ Simplify the numerator. $$\frac{9}{24}$$ Simplify the fraction by removing common factors. $$\frac{3}{8}$$

## Example

Find the difference: $$\frac{y}{6}-\frac{1}{6}.$$

### Solution

 $$\frac{y}{6}-\frac{1}{6}$$ Subtract the numerators and place the difference over the common denominator. $$\frac{y-1}{6}$$

The fraction is simplified because we cannot combine the terms in the numerator.

## Example

Find the difference: $$-\frac{10}{x}-\frac{4}{x}.$$

### Solution

Remember, the fraction $$-\frac{10}{x}$$ can be written as $$\frac{-10}{x}.$$

 $$-\frac{10}{x}-\frac{4}{x}$$ Subtract the numerators. $$\frac{-10-4}{x}$$ Simplify. $$\frac{-14}{x}$$ Rewrite with the negative sign in front of the fraction. $$-\frac{14}{x}$$

Now let’s do an example that involves both addition and subtraction.

## Example

Simplify: $$\frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}.$$

### Solution

 $$\frac{3}{8}+\left(-\frac{5}{8}\right)-\frac{1}{8}$$ Combine the numerators over the common denominator. $$\frac{3+\left(-5\right)-1}{8}$$ Simplify the numerator, working left to right. $$\frac{-2-1}{8}$$ Subtract the terms in the numerator. $$\frac{-3}{8}$$ Rewrite with the negative sign in front of the fraction. $$-\frac{3}{8}$$

### Optional Video: Subtracting Fractions With Like Denominators

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