how do you add a fraction with a different denominator

All fractions to be added have to be converted to a common denominator. Then you add the numerators.

Multiply the each fraction by the denominator of the other so that they will equal each other.

To add fractions with different denominators, you need to find a common denominator, which is a number that both denominators can divide evenly into.

Here's a step-by-step process to add fractions with different denominators:

1. Find the least common multiple (LCM) of the denominators. This is the smallest number that both denominators divide evenly into. For example, if the denominators are 3 and 4, the LCM is 12.

2. Rewrite each fraction so that they both have the common denominator. To do this, multiply the numerator and denominator of each fraction by the same value that would make the denominator equal to the LCM. For example, if you have 1/3 and 2/4, multiply 1/3 by 4/4 and 2/4 by 3/3.

3. Once you have both fractions with the same denominator, add the numerators together.

4. Simplify the fraction, if necessary, by reducing it to lowest terms. If the numerator and denominator have a common factor, divide both by that factor.

Let's take an example to illustrate the steps:
1/3 + 2/4

Step 1: The LCM of 3 and 4 is 12.

Step 2: Multiply 1/3 by 4/4, and multiply 2/4 by 3/3:
(1/3) * (4/4) + (2/4) * (3/3) = 4/12 + 6/12

Step 3: Now, add the numerators:
4/12 + 6/12 = 10/12

Step 4: Simplify the fraction if possible. The greatest common divisor of 10 and 12 is 2. Divide both numerator and denominator by 2:
10/12 ÷ 2/2 = 5/6

So, 1/3 + 2/4 = 5/6.