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Warm Up Add or subtract.

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. Problem of the Day The least common multiple of 6 and a number is 24. What is the other number?. 8 or 24.

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Warm Up Add or subtract.

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  1. 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

  2. Problem of the Day The least common multiple of 6 and a number is 24. What is the other number? 8 or 24

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

  4. 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).

  5. 8 8 7 7 2 7 1 8 + 7 56 16 56 23 56 = + Additional Example 1A: 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.

  6. 13 8 7 6 – 88 13 8 66 7 6 – 22 48 56 48 78 48 = – – Additional Example 1B: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: Write as improper fractions. 1 6 5 8 – 1 1 B. Find a common denominator: 6(8)=48. Multiply by fractions equal to 1. Rewrite with a common denominator. Simplify.

  7. Check It Out: Example 1A Add or Subtract. Method 1: 5 8 1 3 + A.

  8. Check It Out: Example 1B Add or Subtract. Method 1: 1 6 3 4 2 + B.

  9. 4 5 5 6 5 6 – Substitute for t. 6 6 5 5 4 5 5 6 – 1 30 25 30 24 30 = – Additional Example 2: Evaluating Expressions with Rational Numbers 4 5 5 6 Evaluate t –for t = . Multiply by fractions equal to 1. Rewrite with a common denominator: 6(5) = 30.

  10. 5 9 –7 12 Evaluate – h for h = . Check It Out: Example 2

  11. 7 8 3 4 3 4 7 8 36 – 12 –13 Additional Example 3: Consumer Application 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?

  12. 3 4 5 12 3 4 5 12 12 – 6 – 4 53 12 144 12 27 4 – – 53 12 144 12 81 12 – – 5 6 10 12 5 6 , or There will be foot left. Check It Out: Example 3 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? 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.

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