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##### Adding and Subtracting with Unlike Denominators

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**1 5**1 1 3 1 Warm Up Add or subtract. 3 5 2 5 1. 1 + – 11 12 7 12 2. 3 – 2 3. 6.5 + –1.2 5.3 4. 3.4 – 0.9 2.5**Learn to add and subtract fractions with unlike**denominators.**Vocabulary**least common denominator (LCD)**1 3**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? 2 5 1 2**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.**8 8**7 7 2 7 1 8 + 7 56 16 56 23 56 = + Example: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: 2 7 1 8 Find a common denominator: 8(7)=56. A. + Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify**7 6**5 8 + Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 4 4 5 8 3 3 7 6 + Remember! The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. 28 24 15 24 43 24 19 24 = = 1 + Example: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: Write as an improper fraction. 1 6 5 8 B. 1 + List the multiples of each denominator and find the LCD Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.**8 8**1 3 3 3 5 8 + 8 24 23 24 15 24 = + Try This Add or Subtract. Method 1: Find a common denominator 3(8)=24. 5 8 1 3 + A. Multiply by fractions equal to 1. Rewrite with a common denominator.**3 4**13 6 + Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 2 2 13 6 33 3 4 + 26 12 35 12 9 12 11 12 = 2 = + Try This Add or Subtract. Method 2: Write as an improper fraction. 1 6 3 4 B. 2 + List the multiples of each denominator and find the LCD Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.**4 5**5 6 5 6 – Substitute for n. 6 6 5 5 4 5 5 6 – 1 30 25 30 24 30 = – Example: Evaluating Expressions with Rational Numbers 4 5 5 6 Evaluatet –for t = . Multiply by fractions equal to 1. Rewrite with a common denominator: 6(5) = 30.**–7 12**5 9 –7 12 – Substitute for h. –7 12 5 9 5 9 5 9 7 12 7 12 + + = – 4 4 3 3 5 9 7 12 + 20 36 21 36 + 41 36 5 36 or 1 Try This 5 9 –7 12 Evaluate– h for h = . Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). Simplify.**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? 7 8 3 4 3 4 7 8 36 – 12 – 13 55 4 288 8 103 8 – – 110 8 288 8 103 8 – – 75 8 3 8 3 8 , or 9 There will be 9 inches left. Example: Consumer Application Subtract both amounts from 36 to find the amount of ribbon left. Write as improper fractions. The LCD is 8. Rewrite with a common denominator. Simplify.**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? 3 4 5 12 5 12 3 4 12 – 6 – 4 53 12 144 12 27 4 – – 53 12 144 12 81 4 – – 5 6 10 12 5 6 , or There will be inches left. Try This Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. Rewrite with a common denominator. Simplify.**12**1 6 7 1 15 –2 13 16 Lesson Quiz: Part 1 Add or subtract. 5 14 1 7 1. + 12 2 3 – 2. 1 8 3 5 2 3 3. –2 + 9 16 38 4.Evaluate – n for n = . 1**3 4**2 in. Lesson Quiz: Part 2 12 Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3 4