Percents. A survey asked students whether they had after-school jobs. Write each ratio as a fraction in simplest form. Ratios and Unit Rates a. all students.

Percents

A survey asked students whether they had after-school

jobs. Write each ratio as a fraction in simplest form.

Ratios and Unit Rates

a. all students surveyed to students

without jobs

b. all students surveyed to students

with jobsall students surveyed

students with jobs100

40=

= 5

2

After-School Jobs

Response Number

Have a Job 40

60

100

Don’t Have a Job

Total

all students surveyed

students without jobs100

60=

= 5

3

The table shows prices for different packages of index cards.

Which size has the lowest unit price?

Ratios and Unit Rates

Price

$2.70

$1.30

$.75

100

50

25

Size(cards)

100 cards:price

number of cards

$2.70

100 cards= $.027/card

25 cards:price

number of cards

$0.75

25 cards= $.03/card

The 50-card pack has the lowest unit price.

50 cards:price

number of cards

$1.30

50 cards= $.026/card Find the

unit prices.

Convert 30 gal/min to cups/second.

Ratios and Unit Rates

30 gal/min = • •30 gal

1 min

16 c

1 gal

1 min

60 s

Use conversion factors that convert gallons to cups and minutes to seconds.

1 min

1260 s

Divide the common factors and units.

= • •130 gal

1 min

816 c

1 gal

=8 c

sSimplify.

30 gal/min equals 8 c/s.

Solve = .

Proportions2

7

y

14

Method 1: Multiplication Property of Equality

=2

7

y

14

• 14 = • 142

7

y

14

= y28

7

4 = y

(continued)

Proportions

Method 2: Cross products

=2

7

y

14

2 • 14 = 7 • y

28 = 7y

4 = y

=28

7

7y

7

Do the ratios and form a proportion? Explain.

Proportions

105 = 105 Simplify.

Yes; the ratios do form a proportion. The cross

products are equal.

3

5

21

35

Test by writing as a proportion.3

5

21

35

3 • 35 5 • 21 Write cross products.

One hundred rods is about 275 fathoms. About how many

fathoms is 25 rods?

Proportions

Let d = distance in fathoms.

length in rods

length in fathoms

100

275=

25

d

distance in rods

distance in fathoms

100d = 275(25) Write cross products.

d = 68.75 Simplify.

d = Divide each side by 100.275(25)

100

25 rods is about 68.75 fathoms.

Trapezoid ABCD ~ trapezoid EFGH. Find the

value of k.

Similar Figures and Scale Drawings

Write a proportion for corresponding sides.6

kSide AB corresponds = Side CD corresponds

to side EF. to side GH.

3

2

6 • 2 = k • 3 Write cross products.

= Divide each side by 3.6 • 2

3

3k

3

4 = k Simplify.

A flagpole casts a shadow 5 ft long. At the same time, a yardstick

casts a shadow 1.5 ft long. The triangle shown for the flagpole and

its shadow is similar to the triangle shown for the yardstick and its

shadow. How tall is the flagpole?

Similar Figures and Scale Drawings

Corresponding sides of similar triangles are in proportion.

1.5

5= 3

x

1.5x = 5 • 3   Write cross products.

Divide each side by 1.5.

1.5x

1.5= 5 • 3

1.5

x = 10   Simplify.

The flagpole is 10 ft tall.

The scale of a map is 1 in. : 24 mi. About how far is it between two

cities that are 3 in. apart on the map?

Similar Figures and Scale Drawings

It is about 72 mi between the two cities.

map (in.)

actual (mi.)

1

24

3

d

map (in.)

actual (mi.)= Write a proportion.

1 • d = 24 • 3 Write cross products.

d = 72 Simplify.

Write each percent as a fraction or a mixed number.

Fractions, Decimals, and Percents

a. 30%

b. 175%

Write as a fraction with a denominator of 100.30

100

Simplify.3

10

Write as a fraction with a denominator of 100.175

100

1 Write as a mixed number.3

4

Simplify.7

4

Express 7.3% as a decimal.

Fractions, Decimals, and Percents

= 0.073

7.3% = Write as a fraction with a denominator of 100.7.3

100

= 007.3   Divide by moving the decimal point two places to

the left. You may need to write one or more zeros.

Express 0.412 as a percent.

Fractions, Decimals, and Percents

Method 1: Rewrite as a fraction.

= 41.2%

Method 2: Move the decimal point.

0.412 = 41.2%

0.412 = 412

1,000

= 412 ÷ 10

1,000 ÷ 10

= 41.2

100

Four out of seven members of the chess club are boys. What

percent of the chess club members are boys?

Fractions, Decimals, and Percents

0.5714 Divide the numerator by the denominator.

57.14%   Write as a percent.

About 57% of the chess club members are boys.

Write a fraction.4

7

Find 23% of 158.

Proportions and Percents

23(158) = 100n Write cross products.

36.34 = n Simplify.

23% of 158 is 36.34.

= Write a proportion.23

100

n

158

=    Divide each side by 100.23(158)

100

100n

100

What percent of 34 is 28? Round to the nearest tenth

of a percent.

Proportions and Percents

34n = 100(28) Write cross products.

n = 82.35... Simplify.

= Write a proportion.n

100

28

34

=    Divide each side by 34.100(28)

34

34n

34

28 is approximately 82.4% of 34.

82.4 Round.

216 is 72% of what number?

Proportions and Percents

72n = 100(216) Write cross products.

n = 300 Simplify.

=    Divide each side by 72.100(216)

72

72n

72

= Write a proportion.72

100

216

n

216 is 72% of 300.

A tile floor has 90 blue tiles, which is 15% of all the tiles in the

floor. How many tiles are in the floor in all?

Proportions and Percents

15x = 100(90) Write cross products.

x = 600 Simplify.

The floor has 600 tiles in all.

Check: Is the answer reasonable? The problem says the number of

blue tiles is 15%. 10% of 600 is 60, so 5% of 600 is 30, and

15% is 60 + 30 = 90. The answer is reasonable.

= Write a proportion.15

100

90

x

=    Divide each side by 15.100(90)

15

15x

15

What is 35% of 84?

Percents and Equations

n = 0.35 • 84   Write an equation. Write the percent as a decimal.

n = 29.4 Simplify.

35% of 84 is 29.4.

What percent of 26 is 65?

Percents and Equations

n • 26 = 65 Write an equation.

n = 2.5 Simplify.

= 250%   Change the decimal to a percent.

65 is 250% of 26.

= Divide each side by 26.26n

26

65

26

A car salesman makes a 6.5% commission on each car he

sells. How much does he make on the sale of a car for

$35,000?

Percents and Equations

c = 0.065 • 35,000

= 2,275

The salesman’s commission is $2,275.

Words amount of commission is 6.5% of$35,000

Let c = amount of commission.

Equation c = 0.065 • $35,000

During a telephone survey, 414 people, or 46% of those called,

said that they were watching station RFGT at the time of the

call. How many people were called?

Percents and Equations

0.46n = 414

n = 900

900 people were called.

=0.46n

0.46

414

0.46

Words 414 is 46% of people called

Let n = number of people called.

Equation 414 = 0.46 • n

Find the percent of increase from 8 to 9.6.

Percent of Change

amount of increase = 9.6 – 8 = 1.6

= 0.2 = 20%

The percent of increase from 8 to 9.6 is 20%.

percent of increase = amount of increase

original amount

=1.6

8

In a given year, Hillsboro had a total of 7.5 in. of rain by March

1 and a total of 22.5 in. by July 1. Find the percent of increase

from 7.5 to 22.5.

Percent of Change

amount of increase = 22.5 – 7.5 = 15

= 2 = 200%

The percent of increase from March 1 to July 1 was 200%.

percent of increase = amount of increase

original amount

=15

7.5

Find the percent of decrease from 1,250 to 1,120.

Percent of Change

amount of decrease = 1,250 – 1,120 = 130

= 0.104 = 10.4%

percent of decrease = amount of decrease

original amount

= 130

1,250

A grocery store has a 20% markup on a can of soup.

The can of soup costs the store $1.25. Find the markup.

Markup and Discount

markup = percent of markup • store’s cost

= 0.2 • 1.25  

= 0.25        Simplify.

The markup is $.25.

A bookstore pays $4.50 for a novel. The percent of markup is

45%. Find the novel’s selling price.

Markup and Discount

0.45 • 4.50 = 2.03 Multiply to find the markup.

4.50 + 2.03 = 6.53   Store’s cost + markup = selling price.

The selling price is $6.53.

A camera that regularly sells for $210 is on sale for 30% off.

Find the discount.

Markup and Discount

discount = percent of discount • regular price

= 0.30 • 210

= 63

The discount is $63.