**Adding /Subtracting 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/subtract two fractions with the same denominator, add/subtract the numerators and place that sum/difference over the common denominator.

**Add /Subtract Fractions with different denominators**:

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

- 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**consist of an integer followed by a fraction.

Example: 3 2/3 + 5 2/3 =

Add the fractional part of the mixed numbers 2/3 + 2/3 = 4/3 Convert 4/3 to a mixed number 4/3 = 1 1/3 Add the integer portions of the mixed numbers 3 + 5 = 8 Add the integer from the sum of the fractions 8 + 1 = 9 State the final answer: 9 1/3

**Subtract mixed numbers**having the same denominator:

- Make the first numerator larger than the second if it is not.
- Subtract the second numerator from the first
- Place that difference over the common denominator.
- Subtract the integer portions of the two mixed numbers
- State the answer

Example: 5 1/3 - 3 2/3 =

Make the first numerator larger than the second 5 1/3 = 4 4/3 Subtract the fractional parts of the mixed numbers 4/3 - 2/3 = 2/3 Subtract the integer portions of the mixed numbers 4 - 3 = 1 State the final answer: 1 2/3

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