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  1. Adding and Subtracting with Unlike Denominators 3.5

  2. 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

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

  4. Vocabulary least common denominator (LCD)

  5. 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

  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. 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

  8. 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.

  9. 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.

  10. 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.

  11. 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.

  12. –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.

  13. 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.

  14. 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.

  15. 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

  16. 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