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3. Student Learning Goal Chart Lesson Reflections

4. Pre-Algebra Learning Goal Student will understand rational and real numbers.

5. Students will understand rational and real numbers by being able to do the following: Learn to write rational numbers in equivalent forms (3.1) Learn to add and subtract decimals and rational numbers with like denominators (3.2)

6. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Today’s Learning Goal Assignment Learn to add and subtract decimals and rational numbers with like denominators.

7. Pre-Algebra 3-2 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 – –2 7 2727 4747 + – = 2+(–4) 7 2727

8. Pre-Algebra 3-2 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. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers

10. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Simplify. 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.

11. Pre-Algebra 3-2 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. 0.13m

12. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Are you ready for the FAST Track? If YES, prepare for Ch. 3 Section 5 YES, Ch. 3 Section FIVE! If NO, continue with the Ch. 3 Section 2 lesson!

13. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Pre-Algebra HW (3-1, 3-2) Page 119 #1-21 all

14. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers 3-2 Adding and Subtracting Rational Numbers Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

15. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Warm Up Divide. 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 Pre-Algebra 3-2 Adding and Subtracting Rational Numbers

16. Pre-Algebra 3-2 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

17. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Today’s Learning Goal Assignment Learn to add and subtract decimals and rational numbers with like denominators.

18. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers The 100-meter dash is measured in hundredths of a second, so runners must react quickly to the starter pistol. If you subtract a runner’s reaction time from the total race time, you can find the amount of time the runner took to run the actual 100-meter distance.

19. Pre-Algebra 3-2 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 Align the decimals. Additional Example 1: Sports Application

20. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers 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? Try This: Example 1 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 2 zeros so the decimals align. 00

21. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers A. 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.

22. Pre-Algebra 3-2 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 B. 4545 1 You finish at, so 1515 + 2525 3535 =. 3535 From, move right units. 1515 2525

23. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers A. 1.5 + (–1.8) Move right 1.5 units. 1.6–0.4 00.8 From 1.5, move left 1.8 units. – 1.8 1.5 Use a number line to find the sum. Try This: Example 2A You finish at – 0.3, so 1.5 + (–1.8) = –0.3. 0.4 1.4

24. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers 0 3838 + 1818 3838 1818 1818 3838 1414 1212 5858 B. Try This: Example 2B Use a number line to find the sum. Move right units. 3838 From, move right units. 3838 1818 You finish at, which simplifies to. 1212 4848

25. Pre-Algebra 3-2 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 – –2 7 2727 4747 + – = 2+(–4) 7 2727

26. Pre-Algebra 3-2 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

27. Pre-Algebra 3-2 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. 6767 + –3 7 A. B.

28. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers = 1919 5959 + – 4949 5 + (–4) 9 = 5959 + –4 9 Try This: Example 3 Subtract numerators. Keep the denominator. 1515 –– 3535 1515 –– 3535 = – 4545 –1 – 3 5 = Add or subtract. A. B. can be written as. – 4949 –4 9

29. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers A. 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

30. Pre-Algebra 3-2 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 B. Evaluate the expression for the given value of the variable. Additional Example 4B: Evaluating Expressions with Rational Numbers

31. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers 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 Try This: Example 4A A. Evaluate the expression for the given value of the variable.

32. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers + 5858 47 8 Add numerators, keep the denominator. 5 + 47 8 Simplify. + m for m = 5 5858 7878 52 8 = + 5 5858 7878 Substitute 5 for m. 7878 5(8) + 7 8 5 = = 31 8 7878 B. Try This: Example 4B Evaluate the expression for the given value of the variable. 1212 = 6

33. Pre-Algebra 3-2 Adding and Subtracting Rational Numbers Simplify. 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.

34. Pre-Algebra 3-2 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. 0.13m