Adding and subtracting fractions with unlike denominators explanation.

Rules for adding and subtracting fractions with different denominators:

1. Find the lowest common denominator of the fractions;

2. Change both fractions to the lowest common denominator;

3. Add the fractions;

4. Convert the result to a mixed fraction (if necessary).

2. Change both fractions to the lowest common denominator;

3. Add the fractions;

4. Convert the result to a mixed fraction (if necessary).

Problem: Add fractions with unlike denominators

1 | + | 5 |
---|---|---|

6 | 12 |

The denominators are 6 and 12.

1. Find the lowest common denominator of the fractions.

To solve this problem, we need to find the least common multiple of the 6 and 12.

12 is exactly divisible by 6. Hence we conclude that 12 is the least common multiple of 6 and 12:

lcm(6, 12) = 12

The least common multiple of 12 and 6 is the lowest common denominator of the fractions.

So, the lowest common denominator of the fractions is 12.

2. Change both fractions to the lowest common denominator.

Divide 12 by 6:

12 ÷ 6 = 2

The 2 is the factor that we use to change the first fraction to the lowest common denominator 12.

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

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

6 * 2 | 12 |

Now the denominator of the first fraction is 12.

3. Add the fractions.

Add fractions with the common denominator:

1 | + | 5 | = | 1 * 2 | + | 5 | = |
---|---|---|---|---|---|---|---|

6 | 12 | 6 * 2 | 12 | ||||

2 | + | 5 | = | ||||

12 | 12 | ||||||

7 | |||||||

12 |

The answer:

1 | + | 5 | = | 7 |
---|---|---|---|---|

6 | 12 | 12 |