**Adding Fractions with Denominator**

A fraction represents a part of a whole or, more generally, any number of equal parts. A common denominator must be found when adding fractions that have different denominators. This is the most important (and probably the hardest) step in adding or subtracting fractions. A common denominator can always be found by multiplying the denominators.

**Adding Fractions with the Same Denominator**

Fractions consist of two numbers. The top number is called the numerator. The bottom number is called the denominator.

*numerator / denominator*

To add two fractions with the same denominator, add the numerators and place that sum over the common denominator.

**Adding Fractions with Different Denominators**

How to Add Fractions with different denominators:

- Find the Least Common Denominator (LCD) of the fractions
- Rename the fractions to have the LCD
- Add the numerators of the fractions
- Simplify the Fraction

Example: Find the Sum of 2/9 and 3/12

- Determine the Greatest Common Factor of 9 and 12 which is 3
- Either multiply the denominators and divide by the GCF (9*12=108, 108/3=36)
- OR – Divide one of the denominators by the GCF and multiply the answer by the other denominator (9/3=3, 3*12=36)
- Rename the fractions to use the Least Common Denominator(2/9=8/36, 3/12=9/36)
- The result is 8/36 + 9/36
- Add the numerators and put the sum over the LCD = 17/36
- Simplify the fraction if possible. In this case, it is not possible

**Adding Mixed Numbers with the Same Denominator**

Mixed numbers consist of an integer followed by a fraction.

- How to add two mixed numbers whose fractions have the same denominator:
- Add the numerators of the two fractions
- Place that sum over the common denominator.
- If this fraction is improper (numerator larger than or equal to the denominator) then convert it to a mixed number
- Add the integer portions of the two mixed numbers
- If adding the fractional parts created a mixed number then add its integer portion to the sum.

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