2. Page 124 #33-64 ANSWERS

3. Student Learning Goal Chart Lesson Reflection

4. Pre-Algebra Learning Goal Students 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) 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)

6. Pre-Algebra 3-4 Dividing Rational Numbers Today’s Learning Goal Assignment Learn to divide fractions and decimals.

7. Pre-Algebra 3-4 Dividing Rational Numbers Pre-Algebra HW Page 129 #24-57 all

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

9. Pre-Algebra 3-4 Dividing Rational Numbers Warm Up Multiply. Pre-Algebra 3-4 Dividing Rational Numbers 1. 5656 –3 1212 –2 2. 2323 –15 – 3. 0.05(2.8) 4. –0.9(16.1) 10 0.14 –14.49

10. Pre-Algebra 3-4 Dividing Rational Numbers 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

11. Pre-Algebra 3-4 Dividing Rational Numbers Today’s Learning Goal Assignment Learn to divide fractions and decimals.

12. Pre-Algebra 3-4 Dividing Rational Numbers reciprocal Vocabulary

13. Pre-Algebra 3-4 Dividing Rational Numbers A number and its reciprocal have 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.

14. Pre-Algebra 3-4 Dividing Rational Numbers Multiplication and division are inverse operations. They undo each other. Notice that multiplying by the reciprocal gives the same result as dividing. 1313 2525 2 15 = 2525 = ÷ 1313 = 1313 = 2 5 15 2 5252 2 15

15. Pre-Algebra 3-4 Dividing Rational Numbers Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. Multiply by the reciprocal. 5 11 ÷ 1212 2121 = No common factors. 5 11 ÷ 1212 10 11 = A. Simplest form 5 11 2121 =

16. Pre-Algebra 3-4 Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. B. 3838 ÷ 22 3838 ÷ 22 = 19 8 2121 ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors = 19 8 1212 19 1 8 2 = 3 16 = 1 19 ÷ 16 = 1 R 3 19 16 =

17. Pre-Algebra 3-4 Dividing Rational Numbers 7 15 ÷ 3434 4343 = 7 15 ÷ 3434 28 45 = Try This: Example1A Divide. Write the answer in simplest form. A. Multiply by the reciprocal. No common factors. Simplest form 7 4 15 3 =

18. Pre-Algebra 3-4 Dividing Rational Numbers Write as an improper fraction. 2525 ÷ Multiply by the reciprocal. 34 22 1 5 3 = No common factors. 22 ÷ 15 = 1 R 7 2525 ÷ 3 4 = 22 5 3131 ÷ B. Divide. Write the answer in simplest form. = 22 5 1313 7 15 = or 1 22 15 Try This: Example1B

19. Pre-Algebra 3-4 Dividing Rational Numbers 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. 13.2 4 = 1.32 0.4 = 1.32 0.4 1 decimal place1 zero 10

20. Pre-Algebra 3-4 Dividing Rational Numbers = 1.6 38.4 24 = 0.384 ÷ 0.24 Additional Example 2: Dividing Decimals Divide. 0.384 0.24 0.384 ÷ 0.24 = 100 Divide. 38.4 24 =

21. Pre-Algebra 3-4 Dividing Rational Numbers = 2.34 58.5 25 = 0.585 ÷ 0.25 Try This: Example 2 0.585 0.25 0.585 ÷ 0.25 = 100 Divide. 58.5 25 =

22. Pre-Algebra 3-4 Dividing Rational Numbers 5.25 for n = 0.15 n Divide. = 35 Additional Example 3A: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 5.25 0.15 5.25 0.15 = 100 100 0.15 has 2 decimal places, so use. 525 15 = A.

23. Pre-Algebra 3-4 Dividing Rational Numbers k ÷ for k = 5 4545 5 ÷5 ÷ 5454 = 5151 4545 1414 6 B. 5 1 4 = = = 25 4 Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable.

24. Pre-Algebra 3-4 Dividing Rational Numbers 2.55 for b = 0.75 b Divide. = 3.4 Try This: Example 3A 2.55 0.75 2.55 0.75 = 100 255 75 = A. Evaluate the expression for the given value of the variable. 100 0.75 has 2 decimal places, so use.

25. Pre-Algebra 3-4 Dividing Rational Numbers u ÷, for u = 9 Write as in improper fraction and multiply by the reciprocal. 9 7 1 4 = No common factors. 4747 63 ÷ 4 = 15 R 3 = 9191 9 ÷ 4747 = 3434 15 7474 B. Try This: Example 3B Evaluate the expression for the given value of the variable.

26. Pre-Algebra 3-4 Dividing Rational Numbers Additional Example 4: Problem Solving Application 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? 3434 1212 1 Understand the Problem The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information: The amount of oats is cup. One batch of cookies calls for cup of oats. 1212 3434

27. Pre-Algebra 3-4 Dividing Rational Numbers Additional Example 4 Continued Set up an equation. 2 Make a Plan

28. Pre-Algebra 3-4 Dividing Rational Numbers Let n = number of batches. Solve 3 1212 3434 = n ÷ 3434 2121 6464, or 1 batches of the cookies. 1212 Additional Example 4 Continued

29. Pre-Algebra 3-4 Dividing Rational Numbers Look Back4 One cup of oats would make two batches so 1 is a reasonable answer. 1212 Additional Example 4 Continued

30. Pre-Algebra 3-4 Dividing Rational Numbers Try This: Example 4 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? 1616 7878

31. Pre-Algebra 3-4 Dividing Rational Numbers It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now. 7878 1616 1 Understand the Problem 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: Try This: Example 4 Continued

32. Pre-Algebra 3-4 Dividing Rational Numbers Set up an equation. 2 Make a Plan Amount of fuel on board Amount of fuel for one trip Number of trips ÷ = Try This: Example 4 Continued

33. Pre-Algebra 3-4 Dividing Rational Numbers Let t = number of trips. Solve 3 5858 1616 = t ÷ 6161 5858, or 3 round trips, or 3 complete round trips. 30 8 3434 Try This: Example 4 Continued

34. Pre-Algebra 3-4 Dividing Rational Numbers Look Back4 Try This: Example 4 Continued 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. 5858 1212

35. Pre-Algebra 3-4 Dividing Rational Numbers Lesson Quiz: Part 1 Divide. 1. 2. –14 ÷ 1.25 4. Evaluate for x = 6.3. 112 x 3. 3.9 ÷ 0.65 6 –11.2 –1 8989 ÷ 5656 2 1212 17.7

36. Pre-Algebra 3-4 Dividing Rational Numbers A penny weighs 2.51 grams. How many pennies would it take to equal one pound (453.6 grams)? Lesson Quiz: Part 2 5. 181