2-10 Equivalent Fractions and Decimals Warm Up Write each fraction in the simplest form. 1. 2. 3. 4. 6969 12 48 5 25 1212 1414 4848 2323 1515

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2-10 Equivalent Fractions and Decimals

Warm UpWrite each fraction in the simplest form.

1. 2.

3. 4.

69

1248

525

12

14

48

23

15


Simplest Form (Fractions) • A fraction is in simplest form when the top and

bottom cannot be any smaller (while still being whole numbers).

Example: 2/4 can be simplified to 1/2

To simplify a fraction, divide the top and bottom by the highest number that can divide into both numbers exactly.


Rational Number• A rational number is a number that can

be written as a fraction with integers as the numerator and denominator.

• This includes fractions, regular counting numbers, negative numbers, terminating decimals and repeating decimals.


In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat. The statistics on the next slide are for the 2006 Major League Baseball season.


Player HitsAt

BatsBatting Average (thousandths)

Miguel Cabrera

Ichiro Suzuki

Hitsat Bats

195 ÷ 576 ≈ 0.339

224 ÷ 695 ≈ 0.322

195 576195576

224 695 224695

To convert a fraction to a decimal, divide the numerator by the denominator.


Write each fraction as a decimal. Round to the nearest hundredth, if necessary.

Fractions as Decimals

A. 14

1.00 9.0 5.000

B. 95 C. 5

3

4 5 30.2

– 820

– 200

14 = 0.25

5 1

– 540

.8

– 400

95

= 1.8

1

– 3

20

.6

– 1820

– 18

6

20– 18

2

53 ≈ 1.67

6


Check It Out: Example 1

Write each fraction as a decimal. Round to the nearest hundredth, if necessary.

A. 34

3.00 6.0 7.000

B. 65 C. 7

3

4 5 30.7

– 2 820

– 200

34 = 0.75

5 1

– 510

.2

– 100

65

= 1.2

2

– 6

10

.3

– 910– 9

3

10– 9

1

73 ≈ 2.33

3


Write each fraction as a decimal.

Fractions as Decimals

A.

4 5

4 5

x 2 2

= 8 10

= 0.8

Multiply to get a power of ten in the denominator.

B.

37 50

37 50

x 2 2

= 74 100

= 0.74





A.

3 5

3 5

x 2 2

= 6 10

= 0.6


B.

18 25

18 25

x 4 4

= 72 100

= 0.72



The decimals 0.75 and 1.2 in Example 1 are terminating decimals because the decimals comes to an end.

The decimal 0.333…is a repeating decimal because the decimal repeats a pattern forever. You can also write a repeating decimal with a bar over the repeating part.

0.333… = 0.3

0.8333… = 0.83

0.727272… = 0.72


Write each decimal as a fraction in simplest form.

Decimals as Fractions

A. 0.018 B. 1.55

0.018 = 181,000 1.55 =

155100

=18 ÷ 2

1,000 ÷ 2=155 ÷ 5

100 ÷ 5

=3120

or 1 1120=

9500

You read the decimal 0.018 as “eighteen thousandths.”

Reading Math




A. 0.015 B. 1.30

0.015 = 151,000 1.30 =130

100

= 15 ÷ 51,000 ÷ 5

= 130 ÷ 10100 ÷ 10

= 1310

or 1 310

= 3200


Lesson Quiz


1.

3. 4.


5. 0.42

7. If your soccer team wins 21 out of 30 games,

what is your team’s winning rate?

2.6253.2

2150

69 8

165 2.

218

6. 8.625

0.70

710

1120 0.550.7

5 8

or 8


1. Which of the following represents the

fraction as a decimal?

A. 3.4

B. 3.5

C. 3.6

D. 3.7

Lesson Quiz for Student Response Systems

18 5


2. Which of the following represents the

fraction as a decimal?

A. 0.65

B. 0.75

C. 0.85

D. 0.95


13 20


3. Which of the following represents the decimal 0.32 as a fraction in simplest form?

A. C.

B. D.


8 25

7 25

6 25

1 5


4. Which of the following represents the decimal 6.125 as a fraction in simplest form?

A. or 8 C. or 6

B. or 6 D. or 6


49 6

49 8

37 6

31 5

1 6

1 8

1 6

1 5


5. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate?

A. 0.65

B. 0.66

C. 0.67

D. 0.68


Documents

2-10 Equivalent Fractions and Decimals Warm Up Write each fraction in the simplest form. 1. 2. 3. 4. 6969 12 48 5 25 1212 1414 4848 2323 1515