pre-algebra 3-4 dividing rational numbers 3-4 dividing rational numbers pre-algebra warm up warm up...

Pre-Algebra

3-4 Dividing Rational Numbers


Pre-Algebra

Warm Up

Problem of the Day

Lesson Presentation

Pre-Algebra


Warm UpMultiply.

Pre-Algebra


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


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


Learn to divide fractions and decimals.

Pre-Algebra


reciprocal

Vocabulary

Pre-Algebra


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


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


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


Additional Example 1B: Dividing Fractions


B. 3 8

÷ 22

3 8

÷ 22 = 19 8

2 1÷ Write as an improper fraction.


No common factors

= 19 8

1 2

19 • 18 • 2

=

3 16

=1 19 ÷ 16 = 1 R 319 16=

Pre-Algebra


7 15

÷ 3 4

7 15

• 4 3

=7 15

÷ 3 4

28 45

=

Try This: Example1A


A.


No common factors.

Simplest form

7 • 415 • 3

=

Pre-Algebra


Write as an improper fraction.

2 5 ÷


34

22 • 15 • 3

= No common factors.

22 ÷ 15 = 1 R 7

2 5 ÷ 34 = 22

53 1÷

B.


= 22 5

1 3

7 15= or 122

15

Try This: Example1B

Pre-Algebra


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


= 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


= 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


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


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


Pre-Algebra


2.55for b = 0.75

b

Divide.

= 3.4

Try This: Example 3A

2.550.75

2.550.75

= 100100

25575

=

A.


100 100

0.75 has 2 decimal

places, so use .

Pre-Algebra


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


Pre-Algebra


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


Additional Example 4 Continued

Set up an equation.

22 Make a Plan

Pre-Algebra


Let n = number of batches.

Solve33

12

34 = n÷

34

21

= n•

64 , or 1 batches of the cookies.1

2


Pre-Algebra


Look Back44

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

12


Pre-Algebra


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

Pre-Algebra


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

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


Set up an equation.

22 Make a Plan

Amount of fuel on board

Amount of fuel for one trip

Number of trips

÷ =


Pre-Algebra


Let t = number of trips.

Solve33

58

16

= t÷

61

= t•58

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

308

34


Pre-Algebra


Look Back44


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


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


A penny weighs 2.5 grams. How many pennies would it take to equal one pound (453.6 grams)?

Lesson Quiz: Part 2

5.

181

pre-algebra 3-4 dividing rational numbers 3-4 dividing rational numbers pre-algebra warm up warm up...

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