Pre-Algebra 8-1 Relating Decimals, Fractions, and Percents 8-1 Relating Decimals, Fractions, and...

Pre-Algebra

8-1 Relating Decimals, Fractions, and Percents8-1 Relating Decimals, Fractions, and

Percents

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

8-1 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

Pre-Algebra


45

2145

or

Pre-Algebra


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

Pre-Algebra


Learn to relate decimals, fractions, and percents.

Pre-Algebra


Vocabulary

percent

Pre-Algebra


Percents are ratios that compare a number to 100.

RatioEquivalent Ratio with Denominator of 100 Percent

310

1234

3010050

10075

100

30%

50%

75%

Pre-Algebra


Think of the % symbol as meaning /100.

0.75 = 75% = 75/100

Reading Math

Pre-Algebra


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%

Pre-Algebra


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

=

Pre-Algebra




b: 0.25 =14

= 25%

Pre-Algebra




c: 40% =40100

=2

5

4

10=

Pre-Algebra




d: 0.60 =35

= 60%

Pre-Algebra




e: 23

% =66 0.666 = 23

Pre-Algebra




f: 12

% =87 0.875 = 78

8751000

=

Pre-Algebra




g: 125% =125 100

=5

4=

1

41

Pre-Algebra


Try This: Example 1


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

a: 12

% =12 0.125 = 18

1251000

=

Pre-Algebra


Try This: Example 1 Continued

b: 25% =25100

=1

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra



c: 0.375 =38

= 37 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra



d: 50% =50100

=1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra



e: 0.625 =58

= 62 %1

2


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra



f: 75% =75100

=3

4


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra



g: 1 =100 100

= 100%


c

a b

e

d

50%12 %

f

g

38

25%12

58

75%

1

Pre-Algebra


Find the equivalent fraction, decimal, or percent for each value given on the circle graph.

Additional Example 2: Finding Equivalent Fractions, Decimals, and Percents

0.15(100) = 15%

720

= 0.35

Fraction Decimal Percent

0.15

35%

38%

320

15100

=

720

35100

=

1950

38100

= 1950 = 0.38

325 = 0.12 0.12(100) = 12%

325

Pre-Algebra


You can use information in each column to make three equivalent circle graphs. One shows the breakdown by fractions, one shows the breakdown by decimals, and one shows the breakdown by percents.

Additional Example 2 Continued

The sum of the fractions should be 1.

The sum of the decimals should be 1.

The sum of the percents should be 100%.

Pre-Algebra


Try This: Example 2

Fill in the missing pieces on the chart below.

Fraction Decimal Percent

0.1

45%

110 0.1(100) = 10%

0.2(100) = 20%

45100

=0.45

1 5

15

=0.2525100

1 4

45100

920=

0.25(100) = 25%

= 0.2

Pre-Algebra


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 3: 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.

Pre-Algebra


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. So, what percentage of the food the baker cooks is eaten without being sold?

Try This: Example 3

Set up a ratio and reduce. items eatentotal items

113

113

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

So the baker, eats 7.7% of the items they bake.

Pre-Algebra


Lesson Quiz

Find each equivalent value.

1. as a percent

2. 20% as a fraction

3. as a decimal

4. as a percent

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?

38

1425

58

Pre-Algebra 8-1 Relating Decimals, Fractions, and Percents 8-1 Relating Decimals, Fractions, and...

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