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

5 – Example 1 Adding Fractions b = 3 2 To find the LCD of the fractions, write the prime factorization of each denominator. 2 = So, the LCD is. 36 = = 2 2 = – – – 36 = – 36

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

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

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

Example 3 Modeling with Mixed Numbers SOLUTION =– Write an algebraic model =– Rewrite fractions using LCD of =– Add inside parentheses.

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

Guided Practice Find the sum or difference. Then simplify if possible. for Examples 1, 2, and ANSWER ANSWER – – ANSWER –

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

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? ANSWER in.