percents. a survey asked students whether they had after-school jobs. write each ratio as a fraction...
TRANSCRIPT
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.