How do you subtract fractions with different denominators?

Problem: Subtract fractions with different denominators

3 | - | 3 |
---|---|---|

4 | 5 |

The denominators are 4 and 5.

1. Find the lowest common denominator of the fractions.

The least common multiple of 5 and 4:

lcm(5, 4) = 20

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

So, the lowest common denominator of the fractions is 20.

2. Change both fractions to the lowest common denominator.

Divide 20 by 4:

20 ÷ 4 = 5

The 5 is the factor that we use to change the first fraction to the lowest common denominator 20.

We multiply the numerator and denominator of the first fraction by 5

3 * 5 | = | 15 |
---|---|---|

4 * 5 | 20 |

Divide 20 by 5:

20 ÷ 5 = 4

The 4 is the factor that we use to change the second fraction to the lowest common denominator 20.

We multiply the numerator and denominator of the second fraction by 4

3 * 4 | = | 12 |
---|---|---|

5 * 4 | 20 |

3. Subtract the fractions.

Subtract the fractions with the common denominator:

15 | - | 12 | = | 3 |
---|---|---|---|---|

20 | 20 | 20 |

The answer:

3 | - | 3 | = | 3 |
---|---|---|---|---|

4 | 5 | 20 |