1. 1-4 Adding and Subtracting with Unlike Denominators Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes

2. 1-4 Adding and Subtracting with Unlike Denominators Warm Up 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

3. 1-4 Adding and Subtracting with Unlike Denominators Learn to add and subtract fractions with unlike denominators.

4. 1-4 Adding and Subtracting with Unlike Denominators Two hikers on the Appalachian Trail are 5 from the trail ahead. The hikers walk 2 miles before taking a break. They then hike another 1 miles before taking a second break. How many more miles do they have to hike before reaching the summit? 3434 1212 1818

5. 1-4 Adding and Subtracting with Unlike Denominators 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).

6. 1-4 Adding and Subtracting with Unlike Denominators Find a common denominator: 8(7)=56. 2727 + 1818 Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify. Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators 2727 + 1818 78 23 56 = 16 56 + 7 56 A. Add or Subtract. Method 1:

7. 1-4 Adding and Subtracting with Unlike Denominators 1616 1 – 1 5858 List the multiples of each denominator and find the LCD Write as improper fractions. Multiples of 6: 6; 12; 18; 24; 30 Multiples of 8: 8; 16; 24; 32 Rewrite with a common denominator. 13 8 – 767643 11 24 = – 39 24 – 28 24 Multiply by fractions equal to 1. Simplify. – 7676 13 8 B. Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2:

8. 1-4 Adding and Subtracting with Unlike Denominators You may also use prime factorization to find the LCD. Helpful Hint

9. 1-4 Adding and Subtracting with Unlike Denominators Find a common denominator 3(8)=24. 5858 + 1313 Multiply by fractions equal to 1. Rewrite with a common denominator. 23 24 Check It Out: Example 1A Add or Subtract. Method 1: = 15 24 + 8 24 A. 5858 + 131383

10. 1-4 Adding and Subtracting with Unlike Denominators 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 Check It Out: Example 1B Add or Subtract. Method 2:

11. 1-4 Adding and Subtracting with Unlike Denominators Evaluate t – for t =. Additional Example 2: Evaluating Expressions with Rational Numbers 4545 – 5656 24 30 – 25 30 1 30 = Multiply by fractions equal to 1. 4545 5656 Substitute for t. 5656 Rewrite with a common denominator: 6(5) = 30. 4545 – 5656 56

12. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 2 Multiply by fractions equal to 1. Evaluate – h for h =. 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

13. 1-4 Adding and Subtracting with Unlike Denominators Additional Example 3: Consumer Application 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

14. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 3 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 foot left. 5656 81 12 144 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