1. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Warm Up Warm Up California Standards California Standards Lesson Presentation Lesson PresentationPreview

2. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Warm Up Simplify. 1. 2. 3. Write each decimal as a fraction in simplest form. 4. 1.15 5. – 0.22 21 14 24 56 12 30 2525 1 1212 3737 1 3 20 – 11 50

3. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers NS1.2 Add, subtract, multiply, and divide rational numbers (integers, fractions, and terminating decimals) and take positive rational numbers to whole-number powers. California Standards

4. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers A. 0.3 + (–1.2) Think: Find the difference of |1.2| and |3|. 0.9 Add or subtract. Additional Example 1: Adding and Subtracting Decimals – 1.2 is greater than 0.3; use the sign of 1.2. B. 17.2 – 4.39 Line up the decimal points. Use a zero as a placeholder. – 4.39 17.20 12.81 Subtract.

5. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers A. 0.4 + 2.2 Line up the decimal points. + 2.2 Add or subtract. Check It Out! Example 1 0.4 2.6 Add. B. 12.4 – 3.29 Line up the decimal points. Use a zero as a placeholder. – 3.29 12.40 9.11 Subtract.

6. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers In August 2001, at the World University Games in Beijing, China, Jimyria Hicks ran the 200-meter dash in 24.08 seconds. Her best time at the U.S. Senior National Meet in June of the same year was 23.35 seconds. How much faster did she run in June? She ran 0.73 second faster in June. 24.08 –23.35 0.73 Line up the decimal points. Additional Example 2: Sports Application

7. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Tom ran the 100-meter dash in 11.5 seconds last year. This year he improved his time by 0.568 seconds. How fast did Tom run the 100-meter dash this year? Check It Out! Example 2 Tom ran the 100-meter dash in 10.932 seconds this year. Subtract 0.568 from 11.5 to determine the new time. 10.932 –0.568 11.5 Add two zeros so the decimals align. 00

8. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers

9. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Remember! Subtracting a number is the same as adding its opposite.

10. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Additional Example 3: Adding and Subtracting Fractions with Like Denominators Subtract numerators. Keep the denominator. 2929 –– 5959 2929 –– 5959 = – 7979 = 3737 6767 + – 3737 –2 – 5 9 = 6 + (–3) 7 = can be written as. – 3737 –3 7 Add or subtract. Write each answer in simplest form 6767 + –3 7 A. B.

11. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers = 1919 5959 + – 4949 5 + (–4) 9 = 5959 + –4 9 Check It Out! Example 3 Subtract numerators. Keep the denominator. 1515 –– 3535 1515 –– 3535 = – 4545 –1 – 3 5 = Add or subtract. Write each answer in simplest form A. B. can be written as. – 4949 –4 9

12. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 12.1 – x for x = –0.1 Substitute –0.1 for x. 12.1 – (–0.1) 12.2 Think: 12.1 – (–0.1) = 12.1 + 0.1 Evaluate the expression for the given value of the variable. Additional Example 4A: Evaluating Expressions with Rational Numbers

13. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 4545 = 3 + 7 10 31 10 Add numerators, keep the denominator. 7 + 31 10 Simplify. + m for m = 3 7 10 1 10 38 10 = + 3 7 10 1 10 Substitute 3 for m. 1 10 3(10) + 1 10 3 = = 31 10 1 10 Evaluate the expression for the given value of the variable. Additional Example 4B: Evaluating Expressions with Rational Numbers

14. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers 52.3 – y for y = –7.8 Substitute –7.8 for y. 52.3 – (–7.8) 60.1 Think: 52.3 – (–7.8) = 52.3 + 7.8 Check It Out! Example 4A Evaluate the expression for the given value of the variable.

15. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers + 5858 47 8 Add numerators, keep the denominator. 5 + 47 8 Simplify. + m for m = 5 5858 7878 52 8 = + 5 5858 7878 Substitute 5 for m. 7878 5(8) + 7 8 5 = = 47 8 7878 Check It Out! Example 4B Evaluate the expression for the given value of the variable. 1212 = 6

16. Evaluating Algebraic Expressions 2-3 Adding and Subtracting Rational Numbers Add or subtract. 1. –1.2 + 8.42. 2.5 + (–2.8) 7.2 – 0.3 3. 4. 62.1 + x for x = –127.0 1212 – – 64.9 Lesson Quiz Evaluate. 3434 + 5454 – Sarah’s best broad jump is 1.6 meters, and Jill’s best is 1.47 meters. How much farther can Sarah jump than Jill? 5.5. 0.13 m