1. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators NS1.2 Add and subtract rational numbers (fractions) NS2.2 Add and subtract fractions by using factoring to find a common denominator. California Standards

2. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators 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). Notes

3. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Find a common denominator: 8(7)=56. 2727 + 1818 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: = 23 56 Add numerators. Keep the denominator. 2727 + 1818 78 = 16 56 + 7 56 = 7 + 16 56 = Notes

4. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators 1616 1 – 1 5858 List the multiples of each denominator and find the LCD. Write as improper fractions. Multiples of 6: 6, 12, 18, 24, 30 Multiples of 8: 8, 16, 24, 32 Rewrite with the LCD. 11 24 = – 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: – 7676 13 8 = – 767643 = 39 24 – 28 24 = 28 – 39 24 = Notes

5. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Find a common denominator: 3(8)=24. 5858 + 1313 Multiply by fractions equal to 1. Rewrite with the LCD. Check It Out! Example 1A Add or subtract. Method 1: 23 24 = 5858 + 131383 = 15 24 + 8 24 = = 8 + 15 24 Add numerators. Keep the denominator. Rally Coach B

6. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators 1616 2 + 3434 List the multiples of each denominator and find the LCD Write as an improper fraction. Multiples of 6: 6, 12, 18, 24, 30 Multiples of 4: 4, 8, 12, 16 Rewrite with the LCD. Multiply by fractions equal to 1. 11 12 = 2 35 12 = Check It Out! Example 1B Add or subtract. Method 2: 3434 + 13 6 = 3434 + 23 = 9 12 + 26 12 = 26 + 9 12 = Add numerators. Keep the denominator. Rally Coach A

7. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators 25 56 Write the prime factorization of each denominator. Circle the common factors. Factors of 56: 2 ∙ 2 ∙ 2 ∙ 7 Factors of 84: 2 ∙ 2 ∙ 3 ∙ 7 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.

8. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators 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 = + 25 56 37 8432 = + 75 168 74 168 = 149 168 Add numerators. Keep the denominator.

9. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Write the prime factorization of each denominator. Circle the common factors. Factors of 32: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 Factors of 80: 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 Multiply. Check It Out! Example 2 Find +. Write the answer in simplest form. 2 ∙ 2 ∙ 2 ∙ 2 ∙ 2 ∙ 5 = 160 The LCD is 160. 19 32 9 80 Elbow Partners

10. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Multiply by fractions that equal to 1 to get a common denominator. Rewrite using the LCD. 160 ÷ 32 = 5 160 ÷ 80 = 2 = + 19 32 9 8052 = + 95 160 18 160 = 113 160 Add numerators. Keep the denominator. Check It Out! Example 2 Continued Find +. Write the answer in simplest form. 19 32 9 80

11. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Example 3 Subtract both amounts from 12 to find the amount of board left. Write as improper fractions. 12 – 6 – 4 3434 5 12 The LCD is 12. Simplify. There will be foot left. 5656 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? 5 12 3434 27 4 53 12 12 1 –– = 81 12 144 12 –– 53 12 =, or 5656 10 12 = 4 Steps

12. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Evaluate t – for t =. Additional Example 4: Evaluating Expressions with Rational Numbers 4545 – 5656 24 30 – 25 30 = Multiply by fractions equal to 1. 4545 5656 Substitute for t. 5656 Rewrite with a common denominator: 6(5) = 30. t – = 4545 4545 – 5656 56 = 1 30 = Simplify. Notes

13. Evaluating Algebraic Expressions 2-6 Adding and Subtracting with Unlike Denominators Check It Out! Example 4 Multiply by fractions equal to 1. Evaluate – h for h =–. 5959 7 12 Substitute – for h. 7 12 Rewrite with the LCD. Simplify. Face Partners