1. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Warm Up A student incorrectly multiplied two mixed numbers in the following fashion: 4 7 2 1 4 3 = 4 28 6 What’s the error? What should the correct answer be?

2. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers multiplicative inverse reciprocal Vocabulary

3. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Two numbers whose product is 1 are multiplicative inverses, or reciprocals.

4. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers A division problem can always be rewritten as a multiplication problem by using the reciprocal of the divisor.

5. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1A: Dividing Fractions Divide. Write the answer in simplest form. Multiply by the reciprocal. 5 11 ÷ 1212 No common factors. 5 11 ÷ 1212 10 11 Simplest form 5 11 2121

6. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 1B: Dividing Fractions Divide. Write the answer in simplest form. 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 or 1 19 16

7. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 7 15 ÷ 3434 4343 28 45 = Partner Share! Example1A Divide. Write the answer in simplest form. Multiply by the reciprocal. No common factors Simplest form 7 4 15 3

8. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Write as an improper fraction. 2525 ÷ Multiply by the reciprocal. 34 22 1 5 3 No common factors 22 5 3131 ÷ Divide. Write the answer in simplest form. 22 5 1313 7 15 or 1 22 15 Partner Share! Example1B

9. Evaluating Algebraic Expressions 2-5Dividing 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 represents the number of zeros after the 1 in the power of 10. 13.2 4 = 1.32 0.4 = 1.32 0.4 1 decimal place1 zero 10

10. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find 0.384 ÷ 0.24 Estimate the reasonableness of your answer. Additional Example 2: Dividing Decimals 0.24 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 0.24 ) 0.384 24 ) 38.4 Then divide as a whole number. 1  24 144.6 0.384 ÷ 0.24 = 1.6 Estimate: 40 ÷ 20 = 2 The answer is reasonable. – 144 0

11. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Find 0.65 ÷ 0.25 Estimate the reasonableness of your answer. Partner Share ! Example 2 0.25 has two decimal places so multiple both numbers by 100 to make the divisor an integer. 0.25 ) 0.65 25 ) 65.0 Then divide as a whole number. 2  50 150.6 0.65 ÷ 0.25 = 2.6 Estimate: 60 ÷ 20 = 3 The answer is reasonable. –150 n 0

12. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 5.25 for n = 0.15 n Substitute 0.15 for n. Additional Example 3: Evaluating Expressions with Rational Numbers Evaluate the expression for the given value of the variable. 5.25 n 0.15 = When n = 0.15, = 35. 5.25 n 0.15 ) 5.25 0.15 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  525 0 15 ) 525 35

13. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers 3.60 for n = 0.12 n Substitute 0.12 for n. Partner Share! Example 3 Evaluate the expression for the given value of the variable. 3.60 n 0.12 = When n = 0.12, = 30. 3.60 n 0.12 ) 3.60 0.12 has two decimal places, so multiply both numbers by 100 to make the divisor an integer.  360 0 12 ) 360 30

14. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 4: Problem Solving Application A muffin recipe calls for cup of oats. You have cup of oats. How many batches of muffins can you bake using all of the oats you have? 1212 1 Understand the Problem The number of batches of muffins 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 muffins calls for cup of oats. 1212 3434 3434

15. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Additional Example 4 Continued Set up an equation. 2 Make a Plan

16. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Let n = number of batches. Solve 3 1212 3434 = n ÷ 3434 2121 6464, or 1 = n 1212 Additional Example 4 Continued You can bake 1 batches of the muffins. 1212

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

18. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Partner Share! 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

19. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now. 5858 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: Partner Share! Example 4 Continued

20. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Set up an equation. 2 Make a Plan Amount of fuel on board Amount of fuel for one trip Number of trips ÷ = Partner Share! Example 4 Continued

21. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Let t = number of trips. Solve 3 5858 1616 = t ÷ 6161 5858, or 3 = t You can complete 3¾ trips, or 3 complete trips. 30 8 3434 Partner Share! Example 4 Continued

22. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Look Back4 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 Partner Share! Example 4 Continued

23. Evaluating Algebraic Expressions 2-5Dividing Rational Numbers Lesson Review! 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. about 182