Warm Up

2-5 Dividing Rational Numbers

Warm UpWarm Up

Lesson Presentation

Problem of the Day

Lesson Quizzes


Warm UpMultiply.

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


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


Learn to divide fractions and decimals.


reciprocal

Vocabulary


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. 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


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

=


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=


7 15

÷ 3 4

7 15

• 4 3

=7 15

÷ 3 4

28 45

=

Check It Out: Example1A


A.


No common factors.

Simplest form

7 • 415 • 3

=


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

Check It Out: Example1B


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.

13.24

=1.320.4

= 1.320.4

1 decimal place 1 zero

1010


= 1.6

38.424

=

Find 0.384 ÷ 0.24.

Additional Example 2: Dividing Decimals

0.3840.24

0.384 ÷ 0.24 = 100100

Divide.38.424

=


= 2.34

58.525

=

Find 0.585 ÷ 0.25.

Check It Out: Example 2

0.5850.25

0.585 ÷ 0.25 = 100100

Divide.58.525

=


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=

When n = 0.15, = 35.5.25

n


k ÷ for k = 54 5

5 ÷ 5 4

= 5 1

•4 5

1 46

5 • 51 • 4

= == 254

Additional Example 3B: Evaluating Expressions with Fractions and Decimals


Divide.


When k = 5, k ÷ = .4 5

1 46


2.55for b = 0.75

b

Divide.

= 3.4

Check It Out: Example 3A

2.550.75

2.550.75

= 100100

25575

=


100 100

0.75 has 2 decimal

places, so use .

When b = 0.75, = 3.4.2.55

b


u ÷ , for u = 9


9 • 71 • 4

= No common factors

4 7

= 9 19 ÷ 4

7

= 3 415

7 4

Check It Out: Example 3B


When u = 9, u ÷ = .3 4154

7


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?

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

3 4


Additional Example 4 Continued

Set up an equation.

22 Make a Plan


Let n = number of batches.

Solve33

12

34 = n÷

34

21

= n•

64 , or 1 batches of cookies.1

2



Look Back44

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

12



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?

1 6 5

8


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:

Check It Out: Example 4 Continued


Set up an equation.

22 Make a Plan

Amount of fuel on board

Amount of fuel for one trip

Number of trips

÷ =



Let t = number of trips.

Solve33

58

16

= t÷

61

= t•58

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

308

34



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



Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizDivide.

1.

2. –14 ÷ 1.25

4. Evaluate for x = 6.3.112 x

3. 3.9 ÷ 0.65 6

–11.2

–1 89

÷5 6

2 1 2

–1

17.7

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

5.

182


1. Divide.

3 ÷ –1

A. –1 C. –2

B. –2 D. –3


7 9

1 2

5 8

1 6

1 5

4 5


2. Divide.

–12 ÷ 2.5

A. –4.8

B. –4.3

C. 5.0

D. 5.2



3. Divide.

18 ÷ 2.4

A. 3

B. 5.5

C. 7.5

D. 10



4. Evaluate for p = 7.2.

A. 19.7

B. 19.72

C. 20.3

D. 20.72


142 p


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


Warm Up

Documents

Transcript of Warm Up