The document provides examples and instructions for adding and subtracting fractions with unlike denominators using two different methods: 1) Find a common denominator by multiplying the denominators or finding the least common denominator. Then add or subtract the numerators and keep the common denominator. 2) Write the prime factorization of each denominator, circle the common factors, and use those factors to find the lowest common denominator. Then multiply fractions to equivalent fractions with the common denominator before adding or subtracting. 3) An example problem walks through subtracting amounts of ribbon from a total length to find the amount left over.

1. Warm Up California Standards Lesson Presentation Preview

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

3. NS1.2 Add, subtract , multiply, and divide rational numbers (integers, fractions , and terminating decimals) and take positive rational numbers to whole-number powers. NS2.2 Add and subtract fractions by using factoring to find a common denominator. California Standards

4. To add and subtract fractions with unlike denominators, first find a common denominator using one of these methods: Method 1 Find a common denominator by multiplying the denominators. Method 2 Find the least common denominator (LCD).

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

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

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

8. 1 6 2 + 3 4 List the multiples of each denominator and find the LCD Write as an improper fraction. Rewrite with the LCD. Multiply by fractions equal to 1. Check It Out! Example 1B Add or subtract. Method 2: Add numerators. Keep the denominator. Multiples of 6: 6, 12, 18, 24, 30 Multiples of 4: 4, 8, 12, 16 11 12 = 2 35 12 = 3 4 + 13 6 = 3 4 + 13 6 2 2 33 = 9 12 + 26 12 = 26 + 9 12 =

9. 25 56 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. Multiply. Additional Example 2: Using Factoring to Find the LCD Find + . Write the answer in simplest form. 37 84 2, 2, 2, 7, 3 2 ∙ 2 ∙ 2 ∙ 7 ∙ 3 = 168 The LCD is 168. Factors of 56: 2 ∙ 2 ∙ 2 ∙ 7 Factors of 84: 2 ∙ 2 ∙ 3 ∙ 7

10. 25 56 Multiply by fractions equal to 1 to get a common denominator. Rewrite using the LCD. Additional Example 2 Continued Find + . Write the answer in simplest form. 37 84 168 ÷ 56 = 3 168 ÷ 84 = 2 Add numerators. Keep the denominator. = + 25 56 37 84 3 3 2 2 = + 75 168 74 168 = 149 168

11. 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. Multiply. Check It Out! Example 2 Find + . Write the answer in simplest form. 2, 2, 2, 2, 2, 5 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = 160 The LCD is 160. Factors of 32: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 Factors of 80: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 19 32 9 80

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

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

14. Check It Out! Example 3 Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. The LCD is 12. Simplify. 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? 12 – 6 – 4 3 4 5 12 There will be foot left. 5 6 5 12 3 4 27 4 53 12 12 1 – – = 81 12 144 12 – – 53 12 = , or 5 6 10 12 =

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

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

17. Add or subtract. 1. + 5 14 1 7 2. 12 2 3 8 1 – 3. – 2 + 3 5 2 3 4. Evaluate – n for n = . 1 38 9 16 Lesson Quiz Robert is 5 feet 6 inches tall. Judy is 5 feet 3 inches tall. How much taller is Robert than Judy? 5. 3 4 12 13 16 7 1 6 – 2 1 15 12 2 in. 3 4