Warm Up Divide. 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

Example 1: 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 Write the numbers so that the decimals line up. 0.73 She ran 0.73 second faster in June.

Add two zeros so the decimals align. Check It Out: Example 1 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.

Example 2: Using a Number Line to Add Rational Decimals Use a number line to find the sum. A. 0.3 + (–1.2) Move right 0.3 units. From 0.3, move left 1.2 units. –1.2 0.3 –1.4 –1.0 –0.4 0.4 You finish at –0.9, so 0.3 + (–1.2) = –0.9.

Example 2: Using a Number Line to Add Rational Decimals Use a number line to find the sum. 1 5 2 5 B. + Move right units. 1 5 From , move right units. 1 5 2 5 1 5 2 5 You finish at , so 1 5 + 2 5 3 5 = . 1 5 2 5 3 5 4 5 1

A. 1.5 + (–1.8) Move right 1.5 units. From 1.5, move left 1.8 units. Check It Out: Example 2 Use a number line to find the sum. A. 1.5 + (–1.8) Move right 1.5 units. From 1.5, move left 1.8 units. –1.8 1.5 –0.4 0.4 0.8 1.4 1.6 You finish at –0.3, so 1.5 + (–1.8) = –0.3.

3 8 + 1 8 Move right units. From , move right units. 1 2 4 8 3 8 1 8 Check It Out: Example 2 Use a number line to find the sum. 3 8 + 1 8 B. Move right units. 3 8 From , move right units. 3 8 1 8 You finish at , which simplifies to . 1 2 4 8 3 8 1 8 1 8 1 4 3 8 1 2 5 8

Add or subtract the numerators. To add or subtract fractions with like denominators: Add or subtract the numerators. Keep the denominators. Simplify. Remember! Subtracting a number is the same as adding its opposite.

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 To add subtract the opposite . – 3 7 3 7 6 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 To add – subtract the opposite . 4 9 4 9 5 9 4 9 B. + – 5 9 – 4 9 5 – 4 9 = = 1 9

Example 4: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. A. 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

Example 4: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. + m for m = 3 7 10 1 10 B. + 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 4 Evaluate the expression for the given value of the variable. A. 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 B. + 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