Chapter 3.1

PercentProportion

2

a. If 52 out of 100 chickens are hens, then 52 per 100 or , or 52% of the chickens are hens.

b. If a person pays a tax of $9 on every $100 of purchases, then the tax rate is $9 per $100. The ratio is and the percent of tax is 9%.

ParallelExample 1

Understanding Percent

3

52

100

9

100

Write each percent as a decimal.

ParallelExample 2

Writing Percents as Decimals

4

a. 32% p% = p ÷ 10032% = 32 ÷ 100 = 0.32

b. 78% 78% = 78 ÷ 100 = 0.78

c. 93.4% 93.4% = 93.4 ÷ 100 = 0.934

d. 200% 200% = 200 ÷ 100 = 2.00

Write each percent as a decimal by moving the decimal point two places to the left.

a. 23%

23.%

0.23

23% = 0.23

b. 180%

180.% =

ParallelExample 3

Writing Percents as Decimals by Moving the Decimal Point

5

180.% = 1.80 or 1.8

Decimal point starts at far right side

Percent sign is dropped (Step 1)

Decimal point is moved two places to the left. (Step 2)

Write each percent as a decimal by moving the decimal point two places to the left.

c. 3.2%

.032 0 is attached so the decimal point can be moved two places to the left.

d. 0.7%

0.7% =

ParallelExample 3

Writing Percents as Decimals by Moving the Decimal Point

6

0.007 Two zeros are attached so the decimal point can be moved two places to the left.

Write each decimal as a percent by moving the decimal point two places to the right.

a. 0.26

0.26 Decimal point is moved two places to the right.

0.26 = 26%

b. 0.376

ParallelExample 4

Writing Decimals as Percents by Moving the Decimal Point

7

= 37.6%

Percent sign is attached and decimal point is not written with whole number percents.

= 3.40

Write each decimal as a percent by moving the decimal point two places to the right.

c. 1.83

d. 3.4

3.4 = 340%

e. 5

5. = 5.00

so 5 = 500%

ParallelExample 4

Writing Decimals as Percents by Moving the Decimal Point

8

Attach % sign.

0 is attached so the decimal point can be moved two places to the right.

= 183%

Two zeros are attached so the decimal point can be moved two places to the right.

Attach % sign.

Write each fraction as a percent. Round to the nearest tenth if necessary.

ParallelExample 3continued

Writing Fractions as Percents

9

b. Write as a percent by solving a proportion.5

8 5

8 100

p

Find cross products and show that they are equivalent.

8 5 100p 8 500p 8 500

8 8

p

1

1

62.5p

So, 562.5%.

8

Write each fraction as a percent. Round to the nearest tenth if necessary.

ParallelExample 3continued

Writing Fractions as Percents

10

c. Start with a proportion.5

12 5

12 100

p

Find cross products and show that they are equivalent.

12 5 100p 12 500p 12 500

12 12

p

1

1

41.6p

So, 5

41.612

41.7p

41.7%

11

The percent proportion can be used to solve problems.

Use the percent proportion and solve for the unknown value. Let x represent the unknown.

a. part = 20, percent = 80; find the whole.

Find the cross products.

Show that the cross products are equivalent.

ParallelExample 1

Using the Percent Proportion

12

part percent

whole 100

20 80

100x

20 80

100x

x • 80

20 • 100

80 20 100x

80 2000x

25x

part

whole

percent

100

Use the percent proportion and solve for the unknown value. Let x represent the unknown.

b. part = 12, whole = 40; find the percent.

The percent is written as 30%.

ParallelExample 1

Using the Percent Proportion

13

part percent

whole 100

12

40 100

x

3

10 100

x

10 3 100x

10 300x

30x

Write the fraction in lowest terms.

Find the cross products.

Divide both sides by 10.

part

whole

percent

100

Use the percent proportion and solve for the unknown value. Let x represent the unknown.

c. whole = 120, percent = 90; find the part.

The part is 108.

ParallelExample 1

Using the Percent Proportion

14

part percent

whole 100

90

120 100

x

9

120 10

x

10 9 120x

10 1080x

108x

Write the fraction in lowest terms.

Find the cross products.

Divide both sides by 10.

part

whole

percent

100

Solve each problem.

What is 6% of 80?

16% of what number is 12?

What percent of 75 is 90?

Solution:

1.2 or 120%x

Slide 2.6-19

Solving Percent Equations

75x

4.8x

CLASSROOM EXAMPLE 8

Solution:

Let x = the number of possible points on the test.

85

34 0

5

0 85

8

x

34 8

00

5

1x

40x

There were 40 possible points on the test.

Mark scored 34 points on a test, which was 85% of the possible points. How many possible points were on the test?

Slide 2.6-20

Solving Applied Percent ProblemsCLASSROOM EXAMPLE 9

ParallelExample 1

Solving for Sales Tax

Slide 6.6- 17

Sam’s Sporting Goods sells a tent for $189. If the sales tax is 5%, how much tax is paid? What is the total cost of the tent?

This is the tax amount.

The total amount for the tent is $198.45

ParallelExample 2

Finding the Sales Tax Rate

Slide 6.6- 18

The sales tax on a $580 recliner is $46.40. Find the rate of the sales tax.

46.4580

=𝑥

100𝑥=8 %

ParallelExample 3

Determining the Amount of Commission

Slide 6.6- 19

Caleb Martinez had exercise equipment sales of $12,700 while working part-time last month. If his commission rate is 9%, find the amount of his commission.

𝑥12700

=9

100𝑥=1143

Caleb earned $1143.

ParallelExample 5

Finding a Sale Price

Slide 6.6- 20

Art Designs has a painting with an original price of $620 on sale for 15% off. Find the sale price of the painting.

$93 was slashed from the original amount. 620-93=527The final sale price is $527

𝑥620

=15

100𝑥=93

Slide 6.6- 21

We are often interested in looking at increases or decreases in sales, production, population, and many other items. Use the following steps to find the percent of increase.

Finding the Percent of Increase

Step 1 Use subtraction to find the amount of increase.

Step 2 Use the percent proportion to find the percent of increase.

amount of increase (part) percent

original value (whole) 100

ParallelExample 6

Finding the Percent of Increase

Slide 6.6- 22

A budget had an increase from $19,600 last year to $40,060 this year. Find the percent of increase.

The percent of increase is 104.4%.

2046019600

=𝑥

100𝑥=104.38 %

Slide 6.6- 23

Finding the Percent of Decrease

Step 1 Use subtraction to find the amount of decrease.

Step 2 Use the percent proportion to find the percent of decrease.

amount of decrease (part) percent

original value (whole) 100

ParallelExample 7

Finding the Percent of Decrease

Slide 6.6- 24

The number of minutes Rita used on her cell phone dropped this month to 798 from 840 last month. Find the percent of decease.

42840

=𝑥

1004200840

=𝑥

𝑥=5

The percent of decrease is 5%.

HW 3.1

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