1. Example 1 Adding Fractions a. 6 1 + 3 2 To find the LCD of the fractions, write the prime factorization of each denominator. 3 = 3 6 = 3 2 So, the LCD is. 6 = 3 2 6 4 = 2 2 3 2 6 1 = 1 1 6 1 6 5 = 6 1 + 6 4 6 1+4 =

2. 5 – 1218 7 Example 1 Adding Fractions b. + 12 = 3 2 To find the LCD of the fractions, write the prime factorization of each denominator. 2 = 183232 18 7 So, the LCD is. 36 = 3 23 2 2 22 2 = 2 2 = 3 3 36 14 5 – 12 15 – 36 15 – 36 = + 14 1 – 36

3. 10 3 Example 2 Subtracting Fractions a. – 6 5 6 = 3 2 To find the LCD of the fractions, write the prime factorization of each denominator. 2 = 105 10 3 So, the LCD is. 30 = 3 2 = 3 3 = 5 5 30 9 25 30 5 6 5 25 30 = – 9 16 – 30 = 8 – 15

4. 4 Example 2 Subtracting Fractions b. – 8 7 To find the LCD, write the prime factorization of each denominator. 1 = 1 8 = 2 32 3 So, the LCD is. 2 32 3 = 8 8 = 1 1 8 32 7 8 8 7 8 = 1 4 7 8 = – 8 = 8 25 8 1 3

5. Example 3 Modeling with Mixed Numbers A board is inches long. You cut off a piece inches long. The saw blade destroys an additional inch of wood, which is equal to the blade’s width. What is the length of the remaining piece of wood? CARPENTRY 8 5 36 4 3 12 1 16

6. Example 3 Modeling with Mixed Numbers SOLUTION 8 5 36 =– 4 3 12 1 16 + Write an algebraic model. 16 10 36 =– 16 12 1 16 + Rewrite fractions using LCD of 16. 16 10 36 =– 16 13 12 Add inside parentheses.

7. Example 3 Modeling with Mixed Numbers 16 26 35 = – 16 13 12 ANSWER The remaining piece of wood is inches long. 16 13 23 =+ 13 16 – 26 16 () 12 – 35 Write mixed numbers in expanded form and use the commutative property. 16 13 23 = Subtract whole numbers and fractions. Rename as. 16 10 36 16 26 35

8. Guided Practice Find the sum or difference. Then simplify if possible. for Examples 1, 2, and 3 1. + 3 1 9 5 ANSWER 9 2 3. + 12 7 4 1 ANSWER 6 5 24 1 – – 2. 10 3 + 5 4 ANSWER 10 1 1 4. – 3 1 8 3

9. Guided Practice Find the sum or difference. Then simplify if possible. for Examples 1, 2, and 3 5. – 3 10 9 6. 12 5 – 9 7 ANSWER 36 13 – ANSWER 10 1 2

10. Guided Practice for Examples 1, 2, and 3 7. WHAT IF? In Example 3, suppose you cut inches off the original piece of wood. What is the length of the remaining piece of wood? 6 5 4 ANSWER 48 35 31 in.