Course 3 6-1 Relating Decimals, Fractions, and Percents 6-1 Relating Decimals, Fractions, and...

Course 3

6-1 Relating Decimals, Fractions, and Percents6-1 Relating Decimals, Fractions, and

Percents

Course 3

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Course 3

6-1 Relating Decimals, Fractions, and Percents

Warm UpEvaluate.

1. 2.

3. 4.

13

1

3+

14

215

315

–712

312

4 5

7 2

123

1 4

45

2145

or

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Problem of the Day

A fast-growing flower grows to a height of 12 inches in 12 weeks by doubling its height every week. If you want your flower to be only 6 inches tall, after how many weeks should you pick it?

11 weeks

Course 3


Learn to compare and order decimals, fractions, and percents.

Course 3


Vocabulary

percent

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Percents are ratios that compare a number to 100.

RatioEquivalent Ratio with Denominator of 100 Percent

310

1234

3010050

10075

100

30%

50%

75%

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Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75

Reading Math

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

18 = 1 ÷ 8 = 0.125

To convert a decimal to a percent, multiply by 100 and insert the percent symbol.

0.125 100 12.5%

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Find the missing ratio or percent equivalent for each letter a–g on the number line.

Additional Example 1: Finding Equivalent Ratios and Percents

1

10a: 10% =

10100

=

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Additional Example 1 Continued

b: 0.25 =14

= 25%

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c: 40% =40100

=2

5

4

10=

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d: 0.60 =35

= 60%

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e: 23

% =66 0.666 = 23

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f: 12

% =87 0.875 = 78

8751000

=

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g: 125% =125 100

=5

4=

1

41

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Check It Out: Example 1


a: 12

% =12 0.125 = 18

1251000

=

c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Course 3


Check It Out: Example 1 Continued

b: 25% =25100

=1

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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c: 0.375 =38

= 37 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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d: 50% =50100

=1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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e: 0.625 =58

= 62 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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f: 75% =75100

=3

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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g: 1 =100 100

= 100%


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

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Additional Example 2A: Comparing Fractions, Decimals, and Percents

Compare. Write <, >, or =.

40%14

14

= 0.25 = 25%

25% < 40%

Write as a percent.

Compare.

14

< 40%

When multiplying a decimal by 100, simply move the decimal point two spaces to the right.

Remember!

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Additional Example 2B: Comparing Fractions, Decimals, and Percents


0.893 50%

0.893 = 89.3%

89.3% > 50%

Write as a percent.

Compare.

0.893 > 50%

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Check It Out: Example 2A


65%34

34

= 0.75 = 75%

75% > 65%

Write as a percent.

Compare.

34

> 65%

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Check It Out: Example 2B


0.136 20%

0.136 = 13.6%

13.6% < 20%

Write as a percent.

Compare.

0.136 < 20%

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Additional Example 3: Ordering Fractions, Decimals, and Percents

Write 0.075%, , 0.41, and 100% in order

from least to greatest.

34

34

= 0.75 = 75%

0.41 = 41%

Write as percents.

Compare.

34

0.075% < 41% < 75% < 100%

0.075%, 0.41, , 100%

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Write 35%, 0.25, , and 200% in order


12

12

= 0.50 = 50%

0.25 = 25%

Write as percents.

Compare.

12

25% < 35% < 50% < 200%

0.25, 35%, , 200%

Course 3


Gold that is 24 karat is 100% pure gold. Gold that is 14 karat is 14 parts pure gold and 10 parts another metal, such as copper, zinc, silver, or nickel. What percent of 14 karat gold is pure gold?

Additional Example 4: Physical Science Application

Set up a ratio and reduce.

parts pure goldtotal parts

1424

712

=

712

= 7 12 = Find the percent.0.583 = 58.3%

13So 14-karat gold is 58.3%, or 58 % pure

gold.

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A baker’s dozen is 13. When a shopper purchases a dozen items at the bakery they get 12. It is said that the baker eats 1 item from every batch. What percent of the food does the baker eat?


Set up a ratio and reduce.

items eatentotal items

113

113

= 1 13 = Find the percent.0.077 = 7.7%

The baker eats 7.7% of the items they bake.

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Lesson Quiz: Part 1

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal


4. 30%

5. 0.650 97% <

37.5%

0.625

>

38

711

15

58

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Lesson Quiz: Part 2

6. Write 245%, , 0.133, and 66.6% in order


5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice?

16%

0.133, , 66.6%, 245%

15

15

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