How do you add fractions with different denominators?

Problem: Add fractions with different denominators

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

4 | 8 |

The denominators are 4 and 8.

1. Find the lowest common denominator of the fractions.

8 is exactly divisible by 4. Hence we conclude that 8 is the least common multiple of 8 and 4:

lcm(8, 4) = 8

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

So, the lowest common denominator of the fractions is 8.

2. Change both fractions to the lowest common denominator.

Divide 8 by 4:

8 ÷ 4 = 2

The 2 is the factor that we use to change the first fraction to the lowest common denominator 8.

We multiply the numerator and denominator of the first fraction by 2

1 * 2 | = | 2 |
---|---|---|

4 * 2 | 8 |

3. Add the fractions.

Add the fractions with the common denominator:

2 | + | 3 | = | 5 |
---|---|---|---|---|

8 | 8 | 8 |

The answer:

1 | + | 3 | = | 5 |
---|---|---|---|---|

4 | 8 | 8 |