2-5

1. 2-5 Dividing Rational Numbers Course 3 Warm Up Problem of the Day Lesson Presentation

2. 1 2 –2 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

3. 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

4. Learn to divide fractions and decimals.

5. Vocabulary reciprocal

6. 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.

7. 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. = =

8. 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

9. 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 2 2 B. ÷ Write as an improper fraction. Multiply by the reciprocal. No common factors 19 ÷ 16 = 1 R 3

10. 3 4 7 15 4 3 7 15 ÷ = • 7 • 4 = 28 45 15 • 3 = Check It Out: Example1A Divide. Write the answer in simplest form. 3 4 7 15 A. ÷ Multiply by the reciprocal. No common factors. Simplest form

11. 22 5 3 1 2 5 4 ÷ 3 ÷ = 22 5 1 3 = 22 • 1 = 5 • 3 22 15 7 15 1 = or Check It Out: 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

12. 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 the 1. = 1 decimal place 1 zero

13. 38.4 38.4 = = 100 0.384 0.384 ÷ 0.24 = 24 24 100 0.24 1.6 = Additional Example 2: Dividing Decimals Find0.384 ÷ 0.24. Divide.

14. 58.5 58.5 = = 100 0.585 0.585 ÷ 0.25 = 25 25 100 0.25 2.34 = Check It Out: Example 2 Find0.585 ÷ 0.25. Divide.

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

16. 5 1 5 4 4 5 • = 1 4 1 4 254 = 5 • 5 6 6 = = 1 • 4 4 5 When k = 5, k ÷ = . Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. 4 5 k ÷ for k = 5 Multiply by the reciprocal. 5÷ Divide.

17. 0.75 has 2 decimal places, so use . 2.55 2.550.75 100100 = 100 100 0.75 25575 = 3.4 When b = 0.75, = 3.4. = 2.55 b Check It Out: Example 3A Evaluate the expression for the given value of the variable. 2.55 for b = 0.75 b Divide.

18. 9 1 7 4 4 7 = ÷ 9 9 • 7 = 1 • 4 3 4 = 15 When u = 9, u ÷ = . 3 4 4 7 15 Check It Out: Example 3B Evaluate the expression for the given value of the variable. 4 7 u ÷ , for u = 9 Multiply by the reciprocal. No common factors

19. 1 1 2 3 4 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 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? The number of batches of cookies you can bake is the number of batches using the oats that you have. List the important information:

20. 3-4 Dividing Rational Numbers Make a Plan 2 Course 3 Additional Example 4 Continued Set up an equation.

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

22. 3-4 Dividing Rational Numbers Look Back One cup of oats would make two batches so 1 is a reasonable answer. 12 4 Course 3 Additional Example 4 Continued

23. 1 6 5 8 Check It Out: 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?

24. 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. 58 Check It Out: 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:

25. Make a Plan 2 Check It Out: Example 4 Continued Set up an equation. Amount of fuel on board Amount of fuel for one trip Number of trips ÷ =

26. 3 Solve 58 16 = t ÷ 58 61 = t • 308 34 , or 3 round trips, or 3 complete round trips. Check It Out: Example 4 Continued Let t = number of trips.

27. 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 Check It Out: Example 4 Continued

28. 89 –1 17.7 Lesson Quiz 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. A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? 5. about 181