To add and subtract fractions with unlike denominators, first find a ________ denominator, such as the Least Common Deno

1. To add and subtract fractions with unlike denominators, first find a ________ denominator, such as the Least Common Denominator (LCD). common

2. 8 8 7 7 2 7 1 8 + = 7 56 16 56 + = 7 + 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. + Multiply by fractions equal to 1. Rewrite with a common denominator. Add numerators. Keep the denominator.

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

4. Factors of 56: 2 ∙ 2 ∙ 2 ∙ 7 Factors of 84: 2 ∙ 2 ∙ 3 ∙ 7 Additional Example 2: Using Factoring to Find the LCD 25 56 37 84 Find + . Write the answer in simplest form. Write the prime factorization of each denominator. Circle the common factors. List all the prime factors of the denominators, using the circled factors only once. 2, 2, 2, 7, 3 Multiply. 2 ∙ 2 ∙ 2 ∙ 7 ∙ 3 = 168 The LCD is 168.

5. 37 84 25 56 = + 74 168 75 168 = + 149 168 = 3 3 2 2 Additional Example 2 Continued 25 56 37 84 Find + . Write the answer in simplest form. 168 ÷ 56 = 3 168 ÷ 84 = 2 Multiply by fractions equal to 1 to get a common denominator. Rewrite using the LCD. Add numerators. Keep the denominator.

6. 9 80 19 32 Factors of 32: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 Factors of 80: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Check It Out! Example 2 Find + . Write the answer in simplest form. Write the prime factorization of each denominator. Circle the common factors. List all the prime factors of the denominators, using the circled factors only once. 2, 2, 2, 2, 2, 5 Multiply. 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2∙ 5 = 160 The LCD is 160.

7. 9 80 19 32 9 80 19 32 = + 18 160 95 160 = + 113 160 = 5 5 2 2 Check It Out! Example 2 Continued Find + . Write the answer in simplest form. 160 ÷ 32 = 5 160 ÷ 80 = 2 Multiply by fractions that equal to 1 to get a common denominator. Rewrite using the LCD. Add numerators. Keep the denominator.

8. 4 5 4 5 5 6 t – = 5 6 – Substitute for t. 6 6 5 5 4 5 5 6 – = 25 30 24 30 – = 1 30 = Additional Example 4: 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. Simplify.

9. 7 12 7 12 Substitute – for h. Check It Out! Example 4 5 9 Evaluate – h for h =– . Multiply by fractions equal to 1. Rewrite with the LCD. Simplify.

10. 3 4 7 8 3 4 7 8 36 – 12 –13 55 4 36 1 103 8 – – = 110 8 288 8 103 8 – – = 3 8 There will be 9 inches left. 75 8 3 8 , or 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? Subtract both amounts from 36 to find the amount of ribbon left. Write as improper fractions. The LCD is 8. Simplify.

11. 3 4 5 12 5 12 3 4 12 – 6 – 4 = 53 12 12 1 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. Simplify.

12. 12 1 6 7 3 4 2 in. 1 15 –2 13 16 Lesson Quiz 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 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