55 Warm Up Problem of the Day Lesson Presentation Adding and Subtracting Fractions with Unlike Denominators Warm Up Problem of the Day Lesson Presentation

55 Warm Up Add or subtract. 1. 1 + 2 1 2. 3 – 2 3. 6.5 x 1.2 7.8 Adding and Subtracting with Unlike Denominators Warm Up Add or subtract. 1. 3 5 1 + 4 5 2 5 2 11 12 7 12 1 3 1 2. 3 – 2 3. 6.5 x 1.2 7.8 4. .72 ÷ 0.09 8

Vocabulary Least common multiple: the least whole number that is a multiple of 2 or more given numbers Least common denominator (LCD): the least common multiple of two or more denominators.

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.

A. Add or Subtract. Method 1: 1 8 2 7 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

B. + + = + = 1 Add or Subtract. Method 2: 1 + Additional Example 1B: 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 5 8 + 7 6 Multiples of 6: 6; 12; 24; 30 Multiples of 8: 8; 16; 24; 32 5 8 + 7 6 4 4 3 3 The least common multiple of two numbers is the smallest number other than zero that is a multiple of the two numbers. Remember! Multiply by fractions equal to 1. Rewrite with a common denominator. 43 24 = 15 24 + 28 24 19 24 = 1 Simplify.

A. Add or Subtract. Method 1: 1 3 5 8 Try This: 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.

B. 2 + 2 + + = Add or Subtract. Method 2: Try This: Example 1B 1 6 3 4 B. 2 + List the multiples of each denominator and find the LCD 3 4 + 1 6 2 2 33 2 Multiples of 6: 6; 12; 24; 30 Multiples of 4: 4; 8; 12; 16 Multiply by fractions equal to 1. 11 12 = 9 12 + 2 12 Rewrite with a common denominator. Simplify.

Additional Example 2: Evaluating Expressions with Rational Numbers 4 5 5 6 Evaluate t – for t = . 4 5 – 5 6 Substitute for n. 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.

36 – 12 – 13 – 12 – 13 35 9 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? 7 8 3 4 Subtract both amounts from 36 to find the amount of ribbon left. 36 – 12 – 13 7 8 3 4 7 8 6 8 8 – 12 – 13 35 Write as improper fractions. The LCD is 8. Rewrite with a common denominator. 9 3 8 Simplify. There will be 9 inches left. 3 8

Add or subtract. 1. 2. – 3. 4. Evaluate – n for n = . + 7 8 1 –2 + –2 Lesson Quiz: Part 1 Add or subtract. 1. 5 14 1 7 12 + 2 3 12 7 1 6 2. 8 – 1 3 5 2 3 –2 1 15 3. + –2 38 9 16 13 16 4. Evaluate – n for n = . 1

Lesson Quiz: Part 2 12 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