Warm Up Add or subtract. 1. 1 + – 1 1 2. 3 – 2 3. 6.5 + (–1.2) 5.3 3 5 1 + – 2 5 1 5 1 11 12 7 12 1 3 1 2. 3 – 2 3. 6.5 + (–1.2) 5.3 4. 3.4 – 0.9 2.5

 

To add or subtract fractions with unlike denominators: Change the fractions so they have common denominators. Add or subtract the numerators. Keep the denominators. Simplify.

Example 1: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 1: 1 8 2 7 Find a common denominator: 8(7)=56. A. + 2 7 + 1 8 7 7 8 8 Multiply by fractions equal to 1. 23 56 = 16 56 + 7 56 Rewrite with a common denominator. Simplify.

Example 1: Adding and Subtracting Fractions with Unlike Denominators Add or Subtract. Method 2: Write as improper fractions. 1 6 5 8 B. 1 – 1 List the multiples of each denominator and find the LCD – 7 6 13 8 Multiples of 6: 6; 12; 18; 24; 30 Multiples of 8: 8; 16; 24; 32 13 8 – 7 6 4 4 3 3 Multiply by fractions equal to 1. Rewrite with a common denominator. 39 24 – 28 24 11 24 = – Simplify.

Find a common denominator 3(8)=24. + Check It Out: Example 1 Add or Subtract. Method 1: 1 3 5 8 Find a common denominator 3(8)=24. A. + 5 8 + 1 3 8 8 3 3 Multiply by fractions equal to 1. = 15 24 + 8 24 23 24 Rewrite with a common denominator.

2 + + + + = = 2 Check It Out: Example 1 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 3 4 + 13 6 Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 3 4 + 13 6 2 2 3 3 Multiply by fractions equal to 1. Rewrite with a common denominator. 35 12 = 9 12 + 26 12 11 12 = 2 Simplify.

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

– + – + = + + Evaluate – h for h = . Check It Out: Example 2 5 9 –7 12 –7 12 – 5 9 Substitute for h. –7 12 7 12 + 5 9 –7 12 – 5 9 7 12 + = 7 12 + 5 9 4 4 3 3 Multiply by fractions equal to 1. Rewrite with lowest common denominator (36). 21 36 + 20 36 41 36 or 1 5 36 Simplify.

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? 3 4 7 8 Subtract both amounts from 36 to find the amount of ribbon left. 36 – 12 –13 7 8 3 4 Write as improper fractions. The LCD is 8. 103 8 55 4 288 8 – Rewrite with a common denominator. 103 8 288 8 – 110 8 Simplify. , or 9 3 8 75 8 There will be 9 inches left. 3 8

– – , or 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? 3 4 5 12 Subtract both amounts from 12 to find the amount of board left. 12 – 6 – 4 3 4 5 12 27 4 53 12 144 12 – Write as improper fractions. The LCD is 12. Rewrite with a common denominator. 81 12 144 12 – 53 12 Simplify. , or 5 6 10 12 There will be foot left. 5 6

Lesson Quiz Add or subtract. 1. 5 14 1 7 1 2 + 2 3 1 2 7 1 6 2. 8 – 1 –2 1 15 3. 3 5 2 3 + –2 3 8 9 16 13 16 4. Evaluate – n for n = . 1 1 2 5. Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 3 4 2 in. 3 4