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

2. 2-5 Dividing Rational Numbers Warm Up Multiply. 1. 5656 –3 1212 –2 2. 2323 –15 – 3. 0.05(2.8) 4. –0.9(16.1) ‏ 10 0.14 –14.49

3. 2-5 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

4. 2-5 Dividing Rational Numbers MA.8.A.6.4 Perform operations on real numbers (including…rational numbers…)…using real-world problems… Sunshine State Standards

5. 2-5 Dividing Rational Numbers reciprocal Vocabulary

6. 2-5 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.

7. 2-5 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 10 30 =

8. 2-5 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 =

9. 2-5 Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. B. 5858 ÷ 32 5858 ÷ 32 = 21 8 3131 ÷ Write as an improper fraction. Multiply by the reciprocal. Divide out common factors. = 21 8 1313 21 1 8 3 = Simplest form. 7878 = 7 1

10. 2-5 Dividing Rational Numbers 9595 ÷ 3 10 Check It Out: Example1A Divide. Write each answer in simplest form. – – 3 2 = – 9595 ÷ 3 10 9595 10 3 – 9595 10 3 – 2 3 – 6 =

11. 2-5 Dividing Rational Numbers 2525 ÷ 34 Divide. Write each answer in simplest form. 2525 ÷ 3 4 22 5 1313 7 15, or 1 22 5 Check It Out: Example1B

12. 2-5 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 the 1. 13.2 4 = 1.32 0.4 = 1.32 0.4 1 decimal place1 zero 10

13. 2-5 Dividing Rational Numbers = 1.6 38.4 24 = Find 0.384 ÷ 0.24. Additional Example 2: Dividing Decimals 0.384 0.24 0.384 ÷ 0.24 = 100 Divide. 38.4 24 = 0.24 has 2 decimal places, so use. 100

14. 2-5 Dividing Rational Numbers 0.585 ÷ 0.25 Check It Out: Example 2A Find each quotient. = 2.34 585 250 = 0.585 ÷ 0.25 1000 0.585 0.25

15. 2-5 Dividing Rational Numbers 1.76 ÷ 0.8 Check It Out: Example 2B Find each quotient. = 2.2 176 80 = 1.76 ÷ 0.8 100 1.76 0.8

16. 2-5 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 = When n = 0.15, = 35. 5.25 n

17. 2-5 Dividing Rational Numbers k ÷ for k = 5 4545 5 ÷5 ÷ 5454 = 5151 4545 1414 6 5 1 4 = = = 25 4 Additional Example 3B: Evaluating Expressions with Fractions and Decimals Evaluate the expression for the given value of the variable. Divide. Multiply by the reciprocal. When k = 5, k ÷ =. 4545 1414 6

18. 2-5 Dividing Rational Numbers 2.55, for b = 0.75 b Check It Out: Example 3A Evaluate each expression for the given value of the variable. = 3.4 2.55 0.75 2.55 0.75 = 100 255 75 =

19. 2-5 Dividing Rational Numbers x ÷, for x = 1313 Check It Out: Example 3B Evaluate each expression for the given value of the variable. 3434 –2–2 3434 = 3131 ÷ 1313 –2–2 11 4 – 33 4 =, or 1414 8 – –

20. 2-5 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? 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 3434

21. 2-5 Dividing Rational Numbers Additional Example 4 Continued Set up an equation. 2 Make a Plan

22. 2-5 Dividing Rational Numbers Let n = number of batches. Solve 3 1212 3434 = n ÷ 3434 2121 6464, or 1 batches of cookies. 1212 Additional Example 4 Continued

23. 2-5 Dividing Rational Numbers Look Back4 One cup of oats would make two batches so 1 is a reasonable answer. 1212 Additional Example 4 Continued

24. 2-5 Dividing Rational Numbers 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? 1616 5858 1616 5858 = c ÷ 5858 6161 15 4, or 3 3434 30 8 = So, 3 complete round trips can be made.

25. 2-5 Dividing Rational Numbers Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

26. 2-5 Dividing Rational Numbers Lesson Quiz 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 A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? 5.  182

27. 2-5 Dividing Rational Numbers 1. Divide. 3 ÷ –1 A. –1C. –2 B. –2D. –3 Lesson Quiz for Student Response Systems 7979 1212 5858 1616 1515 4545

28. 2-5 Dividing Rational Numbers 2. Divide. –12 ÷ 2.5 A. –4.8 B. –4.3 C. 5.0 D. 5.2 Lesson Quiz for Student Response Systems

29. 2-5 Dividing Rational Numbers 3. Divide. 18 ÷ 2.4 A. 3 B. 5.5 C. 7.5 D. 10 Lesson Quiz for Student Response Systems

30. 2-5 Dividing Rational Numbers 4. Evaluate for p = 7.2. A. 19.7 B. 19.72 C. 20.3 D. 20.72 Lesson Quiz for Student Response Systems 142 p

31. 2-5 Dividing Rational Numbers 5. A piece of cake weighs 46 grams. How many pieces of cake would it take to equal 1 kg (1000 grams)? A. 20 pieces B. 21 pieces C. 22 pieces D. 23 pieces Lesson Quiz for Student Response Systems