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Rules for adding and subtracting fractions with unlike denominators

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).

Example of adding fractions with unlike denominators

Problem: Add fractions with unlike denominators

1 + 5
612

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 * 212

Now the denominator of the first fraction is 12.

3. Add the fractions.

Add fractions with the common denominator:

1 + 5 = 1 * 2 + 5 = 
6126 * 212
2 + 5 = 
1212
7
12

The answer:

1 + 5 = 7
61212