2-3 Adding and Subtracting Rational Numbers Warm Up Problem of the Day Course 3 Warm Up Problem of the Day Lesson Presentation

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

Problem of the Day Four sprinters run a race. In how many different ways can they arrive at the finish line, assuming there are no ties? 24

Learn to add and subtract decimals and rational numbers with like denominators.

She ran 0.73 second faster in June. Additional 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.

Additional Example 2A: Using a Number Line to Add Rational Decimals Use a number line to find the sum. 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.

Additional Example 2B: Using a Number Line to Add Rational Decimals Use a number line to find the sum. 1 5 2 5 + 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

1.5 + (–1.8) Move right 1.5 units. From 1.5, move left 1.8 units. –1.8 Check It Out: Example 2A Use a number line to find the sum. 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 2B Use a number line to find the sum. 3 8 + 1 8 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

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS Words Numbers To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the denominator. = , or – –3 5 3 5 4 5 + – = 1 + (–4) 5 1 5

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS Words Algebra To add or subtract rational numbers with the same denominator, add or subtract the numerators and keep the denominator. = + a d a + b d b d

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: Part 1 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

Lesson Quiz: Part 2 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