Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

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

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

Learn to add and subtract fractions with unlike denominators.

Two hikers on the Appalachian Trail are 5 from the trail ahead Two hikers on the Appalachian Trail are 5 from the trail ahead. The hikers walk 2 miles before taking a break. They then hike another 1 miles before taking a second break. How many more miles do they have to hike before reaching the summit? 3 4 1 8 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).

Find a common denominator: 8(7)=56. + Additional Example 1A: 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.

Additional Example 1B: 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 1A 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 1B 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.

Additional 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.

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? 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 Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems

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

Lesson Quiz for Student Response Systems 1. Add. + A. C. 1 B. D. 1 7 12 1 6 1 2 1 3 3 4 1 2

Lesson Quiz for Student Response Systems 2. Subtract. 8 – 6 A. 2 C. 3 B. 2 D. 3 3 4 1 4 1 2 3 4 1 4

Lesson Quiz for Student Response Systems 3. Add or subtract. + –3 A. –2 C. 2 B. –2 D. 2 8 9 1 2 11 18 1 3 1 3 4 9

Lesson Quiz for Student Response Systems 1 7 5 14 4. Evaluate 1 – x for x = . A. 1 C. B. D. 11 14 13 14 9 14

Lesson Quiz for Student Response Systems 1 4 5. A pine tree is 20 feet 3 inches tall. Another pine tree is 20 feet 5 inches tall. How much taller is the second pine tree than the first? A. 2 in. C. 3 in. B. 2 in. D. 3 in. 3 4 1 4 1 4 1 2 1 2