1. 3.1-Addition and Subtraction with Fractions Catherine Conway Math 081 Catherine Conway Math 081

2. RULE #1  To add two fractions that have the same denominator, we add their numerators to get the numerator of the answer. The denominator in the answer is the same as in the original fractions.

3. Addition and Subtraction of Fractions Practice: pg 193 #6, 10, 16

4. Examples: pg 193 #6, 10, 16

5. Definition  The least common denominator (LCD) for a set of denominators is the smallest number that is exactly divisible by each denominator.  (some other books call it the least common multiple (LCM)  The least common denominator (LCD) for a set of denominators is the smallest number that is exactly divisible by each denominator.  (some other books call it the least common multiple (LCM)

6. Find the LCM or LCD for the following 12: 2 x 2 x 3 18: 2 x 3 x 3 x 3 x 2 LCD: 2 x 2 x 3 x 3 = 36 40: 2 x 2 x 2 x 5 30: 2 x 3 x 5 x 3 x 2 LCD: 2 x 2 x 2 x 3 x 5 = 120

7. Find the LCM or LCD for the following 12 : 12, 24, 36, 48, 18 : 18, 36, 54 LCD: 12 x 3 = 36 18 x 2 = 36 40 : 40, 80, 120, 160 30 : 30, 60, 90, 120, 150 LCD: 40 x 3 = 120 30 x 4 = 120

8. To add or subtract any two fractions  Step 1 – Factor each denominator completely, and use the factors to determine the LCD  Step 2 – Rewrite each fraction as an equivalent fraction with the LCD.  Step 3 – Add or subtract the numerators of the fractions. Leave the denominator the same.  Step 4 – Reduce the fraction to lowest terms if it is not already in lowest terms.  Step 1 – Factor each denominator completely, and use the factors to determine the LCD  Step 2 – Rewrite each fraction as an equivalent fraction with the LCD.  Step 3 – Add or subtract the numerators of the fractions. Leave the denominator the same.  Step 4 – Reduce the fraction to lowest terms if it is not already in lowest terms.

9. Examples: pg 194 #34, 42, 44

10. Examples: pg 194 #48, 52

11. Examples: pg 194 #58, 66