Transcript 1-4
1-4 Adding and Subtracting with Unlike Denominators Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 1-4 Adding and Subtracting with Unlike Denominators Warm Up Add or subtract. 1. 1 35 + – 25 115 7 2. 3 11 12 – 2 12 1 13 3. 6.5 + (–1.2) 5.3 4. 3.4 – 0.9 2.5 1-4 Adding and Subtracting with Unlike Denominators Problem of the Day The least common multiple of 6 and a number is 24. What is the other number? 8 or 24 1-4 Adding and Subtracting with Unlike Denominators Learn to add and subtract fractions with unlike denominators. 1-4 Adding and Subtracting with Unlike Denominators Two hikers on the Appalachian Trail are 3 5 4 Miles from the trail ahead. The hikers walk 2 1/2 miles before taking a break. They then hike another 1 1/2 miles before taking a second break. How many more miles do they have to hike before reaching the summit? 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). 1-4 Adding and Subtracting with Unlike Denominators Additional Example 1A: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: A. 1 + 2 7 8 2 8 1 7 + 7 8 8 7 7 16 23 = + 56 56 56 Find a common denominator: 8(7)=56. Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify. 1-4 Adding and Subtracting with Unlike Denominators Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: 1 5 B. 1 6 – 1 8 7 – 13 8 6 7 4 – 13 3 8 3 6 4 11 28 39 = – – 24 24 24 Write as improper fractions. List the multiples of each denominator and find the LCD Multiples of 6: 6; 12; 18; 24; 30 Multiples of 8: 8; 16; 24; 32 Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 1A Add or Subtract. Method 1: 5 1 A. + 8 3 1 8 5 3 + 3 8 8 3 8 23 15 = + 24 24 24 Find a common denominator 3(8)=24. Multiply by fractions equal to 1. Rewrite with a common denominator. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 1B Add or Subtract. Method 2: 1 B. 2 6 13 6 26 12 13 6 2 2 + 9 12 + 3 4 + 3 4 + 3 4 Write as an improper fraction. List the multiples of each denominator and find the LCD Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 3 3 Multiply by fractions equal to 1. Rewrite with a common 35 = 12 = 2 11 12 denominator. Simplify. 1-4 Adding and Subtracting with Unlike Denominators Additional Example 2: Evaluating Expressions with Rational Numbers 4 Evaluate t – 5 5 for t = . 6 4 5 – 5 6 Substitute 4 6 5 5 – 5 6 6 5 Multiply by fractions equal to 1. 1 25 24 = – 30 30 30 Rewrite with a common denominator: 6(5) = 30. 5 6 for t. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 2 Evaluate 5 9 5 9 – h for h = –7 . 12 – –7 12 Substitute + 7 12 5 9 5 4 9 4 20 36 5 9 + + 7 3 12 3 21 36 41 or 1 5 36 36 – –7 12 = –7 12 5 9 for h. 7 + 12 Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). Simplify. Adding and Subtracting with 1-4 Unlike Denominators Additional Example 3: Consumer Application Two dancers are making necklaces from ribbon for their costumes. They need pieces measuring 13 3 inches and 12 7 inches. How much ribbon 8 4 will be left over after the pieces are cut from a 36-inch length? Subtract both amounts 3 7 36 – 12 8 –13 4 from 36 to find the amount of ribbon left. Write as improper 288 103 55 – 8 –4 8 fractions. The LCD is 8. 288 103 – 8 8 75 , or 9 3 8 8 – 110 8 Rewrite with a common denominator. Simplify. 3 There will be 9 8 inches left. 1-4 Adding and Subtracting with Unlike Denominators Check It Out: Example 3 Fred and Jose are building a tree house. They need to cut a 6 3 foot piece of wood and a 4 5 4 12 foot piece of wood from a 12 foot board. How much of the board will be left? Subtract both amounts 3 5 12 – 6 4 – 4 12 from 12 to find the amount of board left. 144 12 – 27 4 144 81 – 12 12 10 , or 5 12 6 – 53 12 – 53 12 Write as improper fractions. The LCD is 12. Rewrite with a common denominator. Simplify. 5 There will be 6 foot left.