1. Course 3 2-3 Adding and Subtracting Rational Numbers 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 2525 1 1212 3737 1 3 20 – 11 50

2. Course 3 2-3 Adding and Subtracting Rational Numbers 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

3. Course 3 2-3 Adding and Subtracting Rational Numbers Learn to add and subtract decimals and rational numbers with like denominators. TB P. 72-75

4. Course 3 2-3 Adding and Subtracting Rational Numbers 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. 24.08 –23.35 0.73 Write the numbers so that the decimals line up. Additional Example 1: Sports Application

5. Course 3 2-3 Adding and Subtracting Rational Numbers 0.3 + (–1.2) Move right 0.3 units. 0.4 –1.0 –0.40 From 0.3, move left 1.2 units. – 1.2 0.3 Use a number line to find the sum. Additional Example 2A: Using a Number Line to Add Rational Decimals –1.4 You finish at – 0.9, so 0.3 + (–1.2) = –0.9.

6. Course 3 2-3 Adding and Subtracting Rational Numbers 0 1515 + 2525 1515 2525 1515 3535 2525 Use a number line to find the sum. Additional Example 2B: Using a Number Line to Add Rational Decimals Move right units. 1515 4545 1 You finish at, so 1515 + 2525 3535 =. 3535 From, move right units. 1515 2525

7. Course 3 2-3 Adding and Subtracting Rational Numbers 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 3535 4545 + – = 1 + (–4) 5 1515

8. Course 3 2-3 Adding and Subtracting Rational Numbers 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. = + adad a + b d bdbd

9. Course 3 2-3 Adding and Subtracting Rational Numbers Remember! Subtracting a number is the same as adding its opposite. SMATO! Subtract Means Add The Opposite

10. Course 3 2-3 Adding and Subtracting Rational Numbers Additional Example 3: Adding and Subtracting Fractions with Like Denominators Subtract numerators. Keep the denominator. 2929 –– 5959 2929 –– 5959 = – 7979 = 3737 6767 + – 3737 –2 – 5 9 = 6 + (–3) 7 = can be written as. – 3737 –3 7 Add or subtract. Write each answer in simplest form 6767 + –3 7 A. B.

11. Course 3 2-3 Adding and Subtracting Rational Numbers 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

12. Course 3 2-3 Adding and Subtracting Rational Numbers 4545 = 3 + 7 10 31 10 Add numerators, keep the denominator. 7 + 31 10 Simplify. + 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 Evaluate the expression for the given value of the variable. Additional Example 4B: Evaluating Expressions with Rational Numbers

13. Course 3 2-3 Adding and Subtracting Rational Numbers 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 1212 – 3434 + 5454 – – 64.9 Lesson Quiz: Part 1 Evaluate.

14. Course 3 2-3 Adding and Subtracting Rational Numbers 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? Lesson Quiz: Part 2 5.5. 0.13 m