1. Adding and Subtracting with Unlike Denominators 3.5

2. Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1 Warm Up

3. Learn to add and subtract fractions with unlike denominators.

4. least common denominator (LCD) Vocabulary

5. A pattern for a double-circle skirt requires 9 yards of 45-inch-wide material. To add a ruffle takes another 2 yards. If the total amount of material for the skirt and ruffle are cut from a bolt of fabric 15 yards long, how much fabric is left? 1313 2525 1212

6. To solve this problem, add and subtract rational numbers with unlike denominators. First find a common denominator using one of the following methods: Method 1 Find a common denominator by multiplying one denominator by the other denominator. Method 2 Find the least common denominator (LCD); the least common multiple of the denominators.

7. Find a common denominator: 8(7)=56. 2727 + 1818 Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify 2727 + 1818 78 23 56 = 16 56 + 7 56 A. Add or Subtract. Method 1: Example: Adding and Subtracting Fractions with Unlike Denominators

8. The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. Remember! 1616 1 + 5858 List the multiples of each denominator and find the LCD Write as an improper fraction. Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 Rewrite with a common denominator. 5858 + 767643 43 24 = 15 24 + 28 24 19 24 = 1 Multiply by fractions equal to 1. Simplify. 5858 + 7676 B. Add or Subtract. Method 2: Example: Adding and Subtracting Fractions with Unlike Denominators

9. Find a common denominator 3(8)=24. 5858 + 1313 Multiply by fractions equal to 1. Rewrite with a common denominator. 23 24 Add or Subtract. Method 1: = 15 24 + 8 24 A. 5858 + 131383 Try This

10. 1616 2 + 3434 List the multiples of each denominator and find the LCD Write as an improper fraction. Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 Rewrite with a common denominator. Multiply by fractions equal to 1. Simplify. 3434 + 13 6 3434 + 23 B. 11 12 = 2 35 12 = 9 12 + 26 12 Add or Subtract. Method 2: Try This

11. Evaluate t – for t =. 4545 – 5656 24 30 – 25 30 1 30 = Multiply by fractions equal to 1. 4545 5656 Substitute for n. 5656 Rewrite with a common denominator: 6(5) = 30. 4545 – 5656 56 Example: Evaluating Expressions with Rational Numbers

12. Evaluate – h for h =. Multiply by fractions equal to 1. 5959 –7 12 Substitute for h. –7 12 Rewrite with lowest common denominator (36). –7 12 – 5959 7 12 + 5959 = Simplify. 41 36 or 1 5 36 21 36 + 20 36 –7 12 – 5959 7 12 + 5959 + 595943 Try This

13. Subtract both amounts from 36 to find the amount of ribbon left. Write as improper fractions. The LCD is 8. 36 – 12 – 13 7878 3434 Rewrite with a common denominator. Simplify., or 9 3838 75 8 There will be 9 inches left. 3838 103 8 288 8 –– 110 8 103 8 55 4 288 8 –– Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 inches and 12 inches. How much ribbon will be left over after the pieces are cut from a 36-inch length? 7878 3434 Example: Consumer Application

14. Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. 12 – 6 – 4 3434 5 12 Rewrite with a common denominator. Simplify., or 5656 10 12 There will be inches left. 5656 81 4 144 12 –– 53 12 27 4 53 12 144 12 –– Fred and Jose are building a tree house. They need to cut a 6 foot piece of wood and a 4 foot piece of wood from a 12 foot board. How much of the board will be left? 5 12 3434 Try This

15. Add or subtract. 1. + 5 14 1717 13 16 2. 1212 2323 8 1 – 7 1616 3. –2 + 3535 2323 4. Evaluate – n for n =. 1 3838 9 16 –2 1 15 1212 Lesson Quiz: Part 1

16. Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3434 1212 2 in. 3434 Lesson Quiz: Part 2