## Subtracting Fractions with a Common Denominator

Contents

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

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. | \(-\frac{3}{8}\) |