1 4 Adding and Subtracting with Unlike Denominators
1 -4 Adding and Subtracting with Unlike Denominators Warm Up Problem of the Day Lesson Presentation Lesson Quizzes 12/17/2021
1 -4 Adding and Subtracting with Unlike Denominators Warm Up Add or subtract. 1. 1 35 + – 25 11 12 1 13 2. 3 – 7 2 12 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 1 5 4 from the trail ahead. The hikers walk 2 8 miles before taking a break. They then hike 1 another 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 1 A: 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 1 B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: B. 1 16 7 6 5 – 18 – 13 8 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 7 4 6 4 28 24 – 39 24 – 13 3 8 3 =– 11 24 Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.
1 -4 Adding and Subtracting with Unlike Denominators Check It Out: Example 1 A 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 1 B Add or Subtract. Method 2: B. 1 26 13 6 26 12 13 6 2 2 + 9 12 + 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 41 36 – h for h = – 7. 12 – – 7 12 Substitute + 7 12 5 9 5 4 9 4 20 36 5 9 + + 7 3 12 3 – – 7 12 = – 7 12 5 9 for h. 7 + 12 Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). 21 36 or 1 5 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 fractions. 288 103 55 – 8 – 4 8 The LCD is 8. 288 103 – 8 8 75 , 8 or 9 3 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– 53 12 144 81 – 12 12 10 , 12 or 5 6 – 53 12 Write as improper fractions. The LCD is 12. Rewrite with a common denominator. Simplify. There will be 5 6 foot left.
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quizzes Standard Lesson Quiz for Student Response Systems
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz Add or subtract. 1. 5 1 + 14 7 2. 2 83 3. 3 5 1 2 12 1 6 – 1 7 + – 2 23 – 2 15 1 9 4. Evaluate 1 38 – n for n = 16. 1 62 13 16 inches tall. Judy is 5 5. Robert is 5 feet 3 34 inches tall. How much taller is 3 Robert than Judy? 2 4 in.
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz for Student Response Systems 1. Add. 7 + 1 6 12 1 1 A. C. 2 1 3 3 1 B. D. 4 1 2
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz for Student Response Systems 2. Subtract. 83 – 61 4 4 A. 2 1 2 C. 3 B. 2 3 4 D. 3 1 4
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz for Student Response Systems 3. Add or subtract. 8 + – 3 1 2 9 A. – 2 11 18 C. 2 1 3 B. – 2 1 3 D. 2 4 9
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz for Student Response Systems 4. Evaluate 1 A. 1 B. 13 D. 14 5 1 – x for x =. 14 7 C. 11 14 9 14
1 -4 Adding and Subtracting with Unlike Denominators Lesson Quiz for Student Response Systems 1 5. A pine tree is 20 feet 3 inches tall. 4 3 Another pine tree is 20 feet 5 4 inches tall. How much taller is the second pine tree than the first? A. 2 1 in. C. 3 1 in. 4 4 B. 2 1 in. 2 D. 3 1 in. 2
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