Preview Warm Up California Standards Lesson Presentation

Warm Up Simplify. 1. 2. 3. Write each decimal as a fraction in simplest form. 4. 1.15 5. –0.22 21 14 1 1 2 12 30 2 5 24 56 3 7 1 3 20 – 11 50

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

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

Line up the decimal points. Check It Out! Example 1 Add or subtract. A. 0.4 + 2.2 0.4 Line up the decimal points. + 2.2 2.6 Add. B. 12.4 – 3.29 12.40 Line up the decimal points. Use a zero as a placeholder. – 3.29 9.11 Subtract.

She ran 0.73 second faster in June. Additional Example 2: Sports Application 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? 24.08 –23.35 Line up the decimal points. 0.73 She ran 0.73 second faster in June.

Add two zeros so the decimals align. Check It Out! Example 2 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? Subtract 0.568 from 11.5 to determine the new time. 11.5 00 Add two zeros so the decimals align. –0.568 10.932 Tom ran the 100-meter dash in 10.932 seconds this year.

Remember! Subtracting a number is the same as adding its opposite.

Subtract numerators. Keep the denominator. Additional Example 3: Adding and Subtracting Fractions with Like Denominators Add or subtract. Write each answer in simplest form 2 9 – 5 9 Subtract numerators. Keep the denominator. A. 2 9 – 5 9 –2 – 5 9 = = – 7 9 6 7 3 7 can be written as . – 3 7 –3 7 B. + – 6 7 + –3 7 6 + (–3) 7 = = 3 7

Subtract numerators. Keep the denominator. Check It Out! Example 3 Add or subtract. Write each answer in simplest form 1 5 – 3 5 Subtract numerators. Keep the denominator. A. 1 5 – 3 5 –1 – 3 5 = = – 4 5 5 9 4 9 can be written as . – 4 9 –4 9 B. + – 5 9 + –4 9 5 + (–4) 9 = = 1 9

Additional Example 4A: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. 12.1 – x for x = –0.1 12.1 – (–0.1) Substitute –0.1 for x. 12.2 Think: 12.1 – (–0.1) = 12.1 + 0.1

Additional Example 4B: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. + m for m = 3 7 10 1 10 + 3 7 10 1 10 Substitute 3 for m. 1 10 + 7 10 31 10 3(10) + 1 10 3 = = 31 10 1 10 7 + 31 10 38 10 = Add numerators, keep the denominator. 4 5 = 3 Simplify.

52.3 – (–7.8) Substitute –7.8 for y. Think: 52.3 – (–7.8) = 52.3 + 7.8 Check It Out! Example 4A Evaluate the expression for the given value of the variable. 52.3 – y for y = –7.8 52.3 – (–7.8) Substitute –7.8 for y. Think: 52.3 – (–7.8) = 52.3 + 7.8 60.1

Add numerators, keep the denominator. Check It Out! Example 4B Evaluate the expression for the given value of the variable. + m for m = 5 5 8 7 8 + 5 5 8 7 8 Substitute 5 for m. 7 8 + 5 8 47 8 5(8) + 7 8 5 = = 47 8 7 8 5 + 47 8 52 8 = Add numerators, keep the denominator. 1 2 = 6 Simplify.

Lesson Quiz Add or subtract. 1. –1.2 + 8.4 7.2 2. 2.5 + (–2.8) –0.3 3 4 + 5 4 – 1 2 – 3. Evaluate. 4. 62.1 + x for x = –127.0 –64.9 5. 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? 0.13 m