How do you subtract fractions with uncommon denominators?

Problem: Subtract fractions with uncommon denominators

1 | - | 3 |
---|---|---|

11 | 17 |

The denominators are 11 and 17.

1. Find the lowest common denominator of the fractions.

The least common multiple of 11 and 17:

lcm(17, 11) = 187

See least common multiple 11 and 17.

The least common multiple is the lowest common denominator of the fractions.

So, the lowest common denominator of the fractions is 187.

2. Change both fractions to the lowest common denominator.

The first fraction.

Divide 187 by the denominator 11:

187 ÷ 11 = 17

The 17 is the factor that we use to change the first fraction to the lowest common denominator 187.

We multiply the numerator and denominator of the first fraction by 17

1 * 17 | = | 17 |
---|---|---|

9 * 17 | 187 |

The second fraction.

Divide 187 by the denominator 17:

187 ÷ 17 = 11

The 11 is the factor that we use to change the second fraction to the lowest common denominator 187.

We multiply the numerator and denominator of the second fraction by 11

3 * 11 | = | 33 |
---|---|---|

17 * 11 | 187 |

3. Subtract the fractions.

Subtract the fractions with the common denominator:

17 | - | 33 | = | -16 |
---|---|---|---|---|

187 | 187 | 187 |

The answer:

1 | - | 3 | = - | 16 |
---|---|---|---|---|

11 | 17 | 187 |