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Student Learning Goal Chart

Lesson Reflection

Pre-Algebra Learning Goal

Students will understand rational and real numbers.

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)

Pre-Algebra

3-4 Dividing Rational Numbers

Today’s Learning Goal Assignment

Learn to divide fractions and decimals.

Pre-Algebra

3-4 Dividing Rational Numbers

Pre-Algebra HW

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Pre-Algebra

3-4 Dividing Rational Numbers3-4 Dividing Rational Numbers

Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra

3-4 Dividing Rational Numbers

Warm UpMultiply.

Pre-Algebra

3-4 Dividing Rational Numbers

1. 5 6–3 1

2–2

2. 23–15 –

3. 0.05(2.8)

4. –0.9(16.1)

10

0.14

–14.49

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

Pre-Algebra

3-4 Dividing Rational Numbers

Today’s Learning Goal Assignment

Learn to divide fractions and decimals.

Pre-Algebra

3-4 Dividing Rational Numbers

reciprocal

Vocabulary

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.

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.

1 3

2 5

2 15

= 2 5

=÷2 15

1 3

= 1 3=

2 • 5 15 • 2

5 2

2 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

÷ 1 2

5 11

•2 1

=

No common factors.

5 11

÷ 1 2

10 11=

A.

Simplest form

5 11

•2 1

=

Pre-Algebra

3-4 Dividing Rational Numbers

Additional Example 1B: Dividing Fractions

Divide. Write the answer in simplest form.

B. 3 8

÷ 22

3 8

÷ 22 = 19 8

2 1÷ Write as an improper fraction.

Multiply by the reciprocal.

No common factors

= 19 8

1 2

19 • 18 • 2

=

3 16

=1 19 ÷ 16 = 1 R 319 16=

Pre-Algebra

3-4 Dividing Rational Numbers

7 15

÷ 3 4

7 15

• 4 3

=7 15

÷ 3 4

28 45

=

Try This: Example1A

Divide. Write the answer in simplest form.

A.

Multiply by the reciprocal.

No common factors.

Simplest form

7 • 415 • 3

=

Pre-Algebra

3-4 Dividing Rational Numbers

Write as an improper fraction.

2 5 ÷

Multiply by the reciprocal.

34

22 • 15 • 3

= No common factors.

22 ÷ 15 = 1 R 7

2 5 ÷ 34 = 22

53 1÷

B.

Divide. Write the answer in simplest form.

= 22 5

1 3

7 15= or 122

15

Try This: Example1B

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.

13.24

=1.320.4

= 1.320.4

1 decimal place 1 zero

1010

Pre-Algebra

3-4 Dividing Rational Numbers

= 1.6

38.424

=

0.384 ÷ 0.24

Additional Example 2: Dividing Decimals

Divide.

0.3840.24

0.384 ÷ 0.24 = 100100

Divide.38.424

=

Pre-Algebra

3-4 Dividing Rational Numbers

= 2.34

58.525

=

0.585 ÷ 0.25

Try This: Example 2

0.5850.25

0.585 ÷ 0.25 = 100100

Divide.

Divide.58.525

=

Pre-Algebra

3-4 Dividing Rational Numbers

5.25 for n = 0.15n

Divide.

= 35

Additional Example 3A: Evaluating Expressions with Fractions and Decimals

Evaluate the expression for the given value of the variable.

5.250.15

5.250.15

=100100 100

100

0.15 has 2 decimal

places, so use .

52515=

A.

Pre-Algebra

3-4 Dividing Rational Numbers

k ÷ for k = 54 5

5 ÷ 5 4

= 5 1

•4 5

1 46

B.

5 • 51 • 4

= == 254

Additional Example 3B: Evaluating Expressions with Fractions and Decimals

Evaluate the expression for the given value of the variable.

Pre-Algebra

3-4 Dividing Rational Numbers

2.55for b = 0.75

b

Divide.

= 3.4

Try This: Example 3A

2.550.75

2.550.75

= 100100

25575

=

A.

Evaluate the expression for the given value of the variable.

100 100

0.75 has 2 decimal

places, so use .

Pre-Algebra

3-4 Dividing Rational Numbers

u ÷ , for u = 9

Write as in improper fraction and multiply by the reciprocal.

9 • 71 • 4

= No common factors.

4 7

63 ÷ 4 = 15 R 3

= 9 19 ÷ 4

7

= 3 415

7 4

B.

Try This: Example 3B

Evaluate the expression for the given value of the variable.

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?

34

1 2

11 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

Pre-Algebra

3-4 Dividing Rational Numbers

Additional Example 4 Continued

Set up an equation.

22 Make a Plan

Pre-Algebra

3-4 Dividing Rational Numbers

Let n = number of batches.

Solve33

12

34 = n÷

34

21

= n•

64 , or 1 batches of the cookies.1

2

Additional Example 4 Continued

Pre-Algebra

3-4 Dividing Rational Numbers

Look Back44

One cup of oats would make two batches so 1 is a reasonable answer.

12

Additional Example 4 Continued

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?

1 6 7

8

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.

78

1 6

11 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

Pre-Algebra

3-4 Dividing Rational Numbers

Set up an equation.

22 Make a Plan

Amount of fuel on board

Amount of fuel for one trip

Number of trips

÷ =

Try This: Example 4 Continued

Pre-Algebra

3-4 Dividing Rational Numbers

Let t = number of trips.

Solve33

58

16

= t÷

61

= t•58

, or 3 round trips, or 3 complete round trips.

308

34

Try This: Example 4 Continued

Pre-Algebra

3-4 Dividing Rational Numbers

Look Back44

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.

58

12

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 89

÷5 62 1

2–1

17.7

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