Adding and Subtracting Rational Numbers 3.2

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

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

Example: 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 Align the decimals. 0.73 She ran 0.73 second faster in June.

Example 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 2 zeros so the decimals align. –0.568 10.932 Tom ran the 100-meter dash in 10.932 seconds this year.

Example: 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: 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

Try This A. 1.5 + (–1.8) Move right 1.5 units. 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.

Try This 3 8 1 8 B. + Move right units. From , move right units. 1 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

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS Key Concept 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 – –2 7 2 7 4 7 + – = 2+(–4) 7

ADDING AND SUBTRACTING WITH LIKE DENOMINATORS Key Concept 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

Example: Adding and Subtracting Fractions with Like Denominators Add or subtract. 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

Try This A. B. 1 5 – 3 5 Subtract numerators. Keep the denominator. Add or subtract. 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

Example: 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: 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.

Try This A. 52.3 – y for y = –7.8 52.3 – (–7.8) Substitute –7.8 for y. 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

Try This B. + m for m = 5 5 8 7 8 + 5 5 8 7 8 Substitute 5 for m. + 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 = = 31 8 7 8 5 + 47 8 52 8 = Add numerators, keep the denominator. 1 2 = 6 Simplify.

Lesson Quiz: Part 1 1. –1.2 + 8.4 2. 2.5 + (–2.8) –0.3 – 3. + – Simplify. 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? 0.13m