How Do You Make the Denominators the Same When Adding Fractions?

To add fractions with different denominators, you need to find a common denominator before you can perform the addition.

Here's how to make the denominators the same:

1. Find a Common Denominator: The most common approach is to find the least common multiple (LCM) of the denominators. The LCM is the smallest number that both denominators divide into evenly. Sometimes, one denominator is a multiple of the other. In this case, the larger denominator can be the common denominator.

2. Determine the Multiplying Factor: For each fraction, determine what number you need to multiply the original denominator by to get the common denominator.

3. Multiply Numerator and Denominator: Multiply both the numerator and the denominator of each fraction by its respective multiplying factor. This is crucial because multiplying both the top and bottom of a fraction by the same number is equivalent to multiplying by 1, and thus doesn't change the fraction's value. It only changes how it's represented.

4. Add the Fractions: Once the fractions have the same denominator, you can add the numerators and keep the common denominator.

Example:

Let's add 1/3 and 2/9.

1. Common Denominator: The least common multiple of 3 and 9 is 9.

2. Multiplying Factors:

   • For 1/3, we need to multiply the denominator (3) by 3 to get 9.
   • For 2/9, we already have a denominator of 9, so we multiply by 1.

3. Multiply Numerator and Denominator:

   • 1/3 becomes (1 3) / (3 3) = 3/9
   • 2/9 remains 2/9 (or (21)/(91) = 2/9)

4. Add Fractions: 3/9 + 2/9 = 5/9

Therefore, 1/3 + 2/9 = 5/9.