2. 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 2 5 1 1 2 3 7 1 3 20 – 11 50
3. 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. 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 17.2 0 12.81 Subtract.
5. 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 12.4 0 9.11 Subtract.
6. 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. 0.73 Line up the decimal points. Additional Example 2: Sports Application 24.08 – 23.35
7. 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
10. Additional Example 3: Adding and Subtracting Fractions with Like Denominators Subtract numerators. Keep the denominator. 6 7 + – 3 7 Add or subtract. Write each answer in simplest form A. B. 2 9 – – 5 9 2 9 – – 5 9 = – 7 9 = 3 7 – 2 – 5 9 = 6 + (–3) 7 = can be written as . – 3 7 – 3 7 6 7 + – 3 7
11. 5 9 + – 4 9 Check It Out! Example 3 Subtract numerators. Keep the denominator. Add or subtract. Write each answer in simplest form A. B. = 1 9 5 + (–4) 9 = 5 9 + – 4 9 1 5 – – 3 5 1 5 – – 3 5 = – 4 5 – 1 – 3 5 = can be written as . – 4 9 – 4 9
12. 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. Add numerators, keep the denominator. Simplify. Evaluate the expression for the given value of the variable. Additional Example 4B: Evaluating Expressions with Rational Numbers 4 5 = 3 + 7 10 31 10 7 + 31 10 + 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
14. 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. Add numerators, keep the denominator. Simplify. Check It Out! Example 4B Evaluate the expression for the given value of the variable. + 5 8 47 8 5 + 47 8 + m for m = 5 5 8 7 8 52 8 = + 5 5 8 7 8 Substitute 5 for m. 7 8 5(8) + 7 8 5 = = 47 8 7 8 1 2 = 6
16. Add or subtract. 1. –1.2 + 8.4 2. 2.5 + (–2.8) 7.2 – 0.3 3. 4. 62.1 + x for x = –127.0 – 64.9 Lesson Quiz Evaluate. 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 . 0.13 m 1 2 – 3 4 + 5 4 –
