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

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

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

Learn to divide fractions and decimals.

Vocabulary reciprocal

A number and its reciprocal have a product of 1 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.

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

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

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

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

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

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. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero

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

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

A. 100 35 5.25 for n = 0.15 n 0.15 has 2 decimal places, so use . 5.25 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 100 100 0.15 has 2 decimal places, so use . 5.25 0.15 = 100 525 15 = Divide. = 35

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 4 = 5 1 • 4 5 5 ÷ 5 • 5 1 • 4 = 254 1 4 6

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

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

Understand the Problem 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? 34 1 2 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. 12 34

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

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

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

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? 1 6 5 8

Understand the Problem Try This: Example 4 Continued 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: It takes of the total fuel load for a complete trip. You have of a total fuel load on board right now. 58 1 6

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

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

Try This: Example 4 Continued Look Back 4 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. 58 12

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

Lesson Quiz: Part 2 5. A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)? 181