Page 124 #33-64 ANSWERS

1. Page 124 #33-64 ANSWERS

2. Student Learning Goal Chart Lesson Reflection

3. Pre-Algebra Learning GoalStudents will understand rational and real numbers.

4. 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) • Learn to add and subtract fractions with unlike denominators (3.5) • Learn to multiply fractions, decimals, and mixed numbers (3.3) • Learn to divide fractions and decimals (3.4)

5. Today’s Learning Goal Assignment Learn to divide fractions and decimals.

6. Pre-Algebra HW Page 129 #24-57 all

7. 3-4 Dividing Rational Numbers Pre-Algebra Warm Up Problem of the Day Lesson Presentation

8. 3-4 Dividing Rational Numbers 1 2 –2 Pre-Algebra Warm Up Multiply. 5 6 1. –3 23 2. 10 –15 – 3. 0.05(2.8) 0.14 4. –0.9(16.1) –14.49

9. Problem of the Day Katie made a bookshelf that is 5 feet long. The first 6 books she put on it took up 8 inches of shelf space. About how many books should fit on the shelf? 45 books

10. Today’s Learning Goal Assignment Learn to divide fractions and decimals.

11. Vocabulary reciprocal

12. A number and its reciprocalhave a product of 1. To find the reciprocal of a fraction, exchange the numerator and the denominator. Remember that an integer can be written as a fraction with a denominator of 1.

13. 2 5 2 5 1 3 1 3 2 15 2 15 ÷ = = 5 2 1 3 2 15 2•515 •2 Multiplication and division are inverse operations. They undo each other. Notice that multiplying by the reciprocal gives the same result as dividing. = =

14. 1 2 2 1 5 11 5 11 = ÷ • 2 1 5 11 = • 10 11 = Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. 1 2 5 11 A. ÷ Multiply by the reciprocal. No common factors. Simplest form

15. 2 1 3 8 19 8 = ÷ ÷ 2 2 19 8 1 2 = 19 • 1 = 8 • 2 3 16 19 16 1 = = Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. 3 8 B. 2 2 ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors 19 ÷ 16 = 1 R 3

16. 3 4 7 15 4 3 7 15 ÷ = • 7 • 4 = 28 45 15 • 3 = Try This: Example1A Divide. Write the answer in simplest form. 3 4 7 15 A. ÷ Multiply by the reciprocal. No common factors. Simplest form

17. 22 5 3 1 2 5 4 ÷ 3 ÷ = 22 5 1 3 = 22 • 1 = 5 • 3 22 15 7 15 1 = or Try This: Example1B Divide. Write the answer in simplest form. 2 5 4 3 B. ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors. 22 ÷ 15 = 1 R 7

18. 10 1.32 1.32 13.2 = 10 4 0.4 0.4 When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places is the number of zeros to write after 1. = 1 decimal place 1 zero

19. 38.4 38.4 = = 100 0.384 0.384 ÷ 0.24 = 24 24 100 0.24 1.6 = Additional Example 2: Dividing Decimals Divide. 0.384 ÷ 0.24 Divide.

20. 58.5 58.5 = = 100 0.585 0.585 ÷ 0.25 = 25 25 100 0.25 2.34 = Try This: Example 2 Divide. 0.585 ÷ 0.25 Divide.

21. 0.15 has 2 decimal places, so use . 100 5.25 5.25 = 100 100 0.15 100 0.15 525 = 15 35 = Additional Example 3A: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 5.25 A. for n = 0.15 n Divide.

22. 5 1 5 4 4 5 • = 1 4 254 = 5 • 5 6 = = 1 • 4 Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 4 5 B. k ÷ for k = 5 5÷

23. 0.75 has 2 decimal places, so use . 2.55 2.550.75 100100 = 100 100 0.75 25575 = 3.4 = Try This: Example 3A Evaluate the expression for the given value of the variable. 2.55 A. for b = 0.75 b Divide.

24. 9 1 7 4 4 7 = ÷ 9 9 • 7 = 1 • 4 3 4 = 15 Try This: Example 3B Evaluate the expression for the given value of the variable. 4 7 B. u ÷ , for u = 9 Write as in improper fraction and multiply by the reciprocal. No common factors. 63 ÷ 4 = 15 R 3

25. 1 1 2 A cookie recipe calls for cup of oats. You have cup of oats. How many batches of cookies can you bake using all of the oats you have? 34 Understand the Problem 34 The amount of oats is cup. One batch of cookies calls for cup of oats. 12 Additional Example 4: Problem Solving Application The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information:

26. Make a Plan 2 Additional Example 4 Continued Set up an equation.

27. 3 Solve 34 12 = n ÷ 21 34 = n • 64 12 , or 1 batches of the cookies. Additional Example 4 Continued Let n = number of batches.

28. Look Back One cup of oats would make two batches so 1 is a reasonable answer. 12 4 Additional Example 4 Continued

29. 1 6 A ship will use of its total fuel load for a typical round trip. If there is of a total fuel load on board now, how many complete trips can be made? 7 8 Try This: Example 4

30. 1 Understand the Problem 1 6 It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now. 78 Try This: Example 4 Continued The number of complete trips the ship can make is the number of trips that the ship can make with the fuel on board. List the important information:

31. Make a Plan 2 Try This: Example 4 Continued Set up an equation. Amount of fuel on board Amount of fuel for one trip Number of trips ÷ =

32. 3 Solve 58 16 = t ÷ 58 61 = t • 308 34 , or 3 round trips, or 3 complete round trips. Try This: Example 4 Continued Let t = number of trips.

33. A full tank will make the round trip 6 times, and is a little more than , so half of 6, or 3, is a reasonable answer. Look Back 58 12 4 Try This: Example 4 Continued

34. 89 –1 17.7 Lesson Quiz: Part 1 Divide. 5 6 1 2 1. –1 2 ÷ 2. –14 ÷ 1.25 –11.2 3. 3.9÷ 0.65 6 112 x 4.Evaluate for x = 6.3.

35. Lesson Quiz: Part 2 5. A penny weighs 2.51 grams. How many pennies would it take to equal one pound (453.6 grams)? 181