Fractions, Decimals, and Percents

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Fractions, Decimals, and Percents
LESSON 5-1
Problem of the Day
Replace the question marks with the correct
digits. a. 8 9 6.
15.96 b. 13. 0 . 4 2
4.122
9, 9, 7
6, 4, 9, 8
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Fractions, Decimals, and Percents
LESSON 5-1
Check Skills Youll Need
(For help, go to Lesson 2-2.)

• 1. Vocabulary Review A rational number is a
  number that
• can be written in the form ? .
• Write each fraction in simplest form.
• 3.
• 4. 5.

Check Skills Youll Need
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Fractions, Decimals, and Percents
LESSON 5-1
Check Skills Youll Need
Solutions 1. , b 0 2.
3. 4.
5.
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Fractions, Decimals, and Percents
LESSON 5-1
Additional Examples
Use mental math to write as a percent.
Why it works
Quick Check
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Fractions, Decimals, and Percents
LESSON 5-1
Additional Examples
Write each decimal as a percent.
a. 2.5
b. 0.003
Quick Check
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Fractions, Decimals, and Percents
LESSON 5-1
Additional Examples
A brand of cereal supplied 7 of the RDA
of sodium. Write this portion of the RDA as a
fraction.
Quick Check
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Fractions, Decimals, and Percents
LESSON 5-1
Additional Examples
Order 27, 0.24, and from least to greatest.
Quick Check
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Fractions, Decimals, and Percents
LESSON 5-1
Lesson Quiz
1. A cereal supplies 1 of the RDA for
calcium. Write 1 as a fraction. 2. Write
as a percent. 3. Write 1.5 as a
percent. 4. Order 60, 0.58, and .
7 20
35
150
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Estimating With Percents
LESSON 5-2
Problem of the Day
The Jackson Country Bird Sanctuary has three
times as many owls as hawks. It has 40 hawks and
owls in all. How many of each are in the
sanctuary?
30 owls, 10 hawks
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Estimating With Percents
LESSON 5-2
Check Skills Youll Need
(For help, go to Lesson 2-5.)
1. Vocabulary Review The multiplicative inverse
of is Find each product. 2. 36
3. 12 4. 60 5. 81
Check Skills Youll Need
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Estimating With Percents
LESSON 5-2
Check Skills Youll Need
Solutions 1. 2.
27 3.
8 4.
54 5.
45
4
6
1
1
9
81 1
5 9
81 5 1 9
81 5 1 9
1
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Estimating With Percents
LESSON 5-2
Additional Examples
Estimate 74 of 158 using decimals.
Quick Check
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Estimating With Percents
LESSON 5-2
Additional Examples
A video store rented 297 videos. The customers
returned 19 of the videos late. Estimate, using
fractions, how many videos were returned late.
Quick Check
About 60 videos were returned late.
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Estimating With Percents
LESSON 5-2
Additional Examples
Dion is saving for a coat that costs 59.95. She
has saved 45 of the cost. Estimate how much she
has saved.
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Estimating With Percents
LESSON 5-2
Additional Examples
(continued)
Why it works
Quick Check
So, 45 of 59.95 is about 27.
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Estimating With Percents
LESSON 5-2
Lesson Quiz
Show the numbers you use to estimate. Numbers
used may vary, Samples are given. 1. Use
decimals to estimate 54 of 29. 2. Use fractions
to estimate 74 of 38. 3. Estimate a 15 tip on
8.15. 4. About 60 of 27 students are in the
play.
0.5 30 15
0.1(8) 0.1(4) 0.8 0.4 1.20
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Percents and Proportions
LESSON 5-3
Problem of the Day
Use graph paper. Design and draw a diagram to
determine which has the greater areaa square
with sides of 10 cm or a circle with a diameter
of 10 cm.
Draw a circle within the square to prove that the
square has the greater area.
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Percents and Proportions
LESSON 5-3
Check Skills Youll Need
(For help, go to Lesson 4-3.)
1. Vocabulary Review Two equal ratios form
a Solve each proportion. 2. 3.
4. 5. 6.
Check Skills Youll Need
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Percents and Proportions
LESSON 5-3
Check Skills Youll Need
Solutions 1. proportion 2. 20b 400 b
20 3. 12e 800 e 66 4. 12n 1,200 n
100 5. 100s 300 s 3 6. 24y 600
y 25
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Percents and Proportions
LESSON 5-3
Additional Examples
Find 32 of 240.
Quick Check
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Percents and Proportions
LESSON 5-3
Additional Examples
Brenda saw a blender for 24 in a bargain store.
In a second store, the same blender was 160 of
the cost of the blender in the bargain store.
Find 160 of 24.
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Percents and Proportions
LESSON 5-3
Additional Examples
(continued)
The price of the blender in the second store was
38.40.
Quick Check
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Percents and Proportions
LESSON 5-3
Additional Examples
Suppose 11,550 elementary students make up 14
of a citys population. What is the population of
the city?
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Percents and Proportions
LESSON 5-3
Additional Examples
(continued)
The population of the city is 82,500 people.
Quick Check
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Percents and Proportions
LESSON 5-3
Additional Examples
26 is what percent of 80?
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Percents and Proportions
LESSON 5-3
Lesson Quiz
1. Find 25 of 160. 2. The price of a music CD
is 12. If the store raises the price to 125 of
its current price, what will be the new price of
the CD? 3. So far, the sixth grade class has
sold 32 tickets to their play. The number
represents 20 of the tickets that are available.
How many tickets are available? 4. 98 is what
percent of 56?
40
15
160
175
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Percents and Equations
LESSON 5-4
Problem of the Day
Write the prime factorization of 364.
22 ? 7 ? 13
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Percents and Equations
LESSON 5-4
Check Skills Youll Need
(For help, go to Lesson 1-7.)
1. Vocabulary Review Is 2 8 16 an equation
or an expression? Explain. Solve each
equation. 2. 0.25p 10 3. 12.25 9.8x
4. 24 1.6s 5. 0.64k 0.02
Check Skills Youll Need
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Percents and Equations
LESSON 5-4
Check Skills Youll Need
Solutions 1. Equation it contains an
sign. 2. p 40 3.
x 1.25 4.
s 15 5. k
0.03125
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Percents and Equations
LESSON 5-4
Additional Examples
Quick Check
Misha got 84 correct on a 25 problem test. How
many did he answer correctly?
c 0.84 25
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Percents and Equations
LESSON 5-4
Additional Examples
Use an equation. 12 is 8 of what number?
Quick Check
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Percents and Equations
LESSON 5-4
1. Find 81 of 110. 2. You buy a book for
17.80. Sales tax is 8. What is the sales tax
cost of the book? 3. 45 is 75 of what
number? 4. Find what percent 68 is of 80.
Lesson Quiz
89.1
1.42
60
85
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Percent of Change
LESSON 5-5
Problem of the Day
Dan, Susan, Monica, and Jose want to talk on the
phone once to each of the others. How many
telephone calls will be made?
6 calls
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Percent of Change
LESSON 5-5
Check Skills Youll Need
(For help, go to Lesson 5-1.)
1. Vocabulary Review A is a ratio that
compares a number to 100. Write each fraction as
a percent. Round to the nearest tenth of a
percent. 2. 3. 4. 5.
Check Skills Youll Need
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Percent of Change
LESSON 5-5
Check Skills Youll Need
Solutions 1. percent 2. 1.125
112.5 3. 0.27 27.3 4. 0.26
26.7 5. 3.6 366.7
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Percent of Change
LESSON 5-5
Additional Examples
Ten years ago, Maxs comic book was worth 2.50.
Now it is worth 13. Find the percent of increase
in value.
amount of change 13 2.50 10.50
The percent of increase in value is 420.
Quick Check
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Percent of Change
LESSON 5-5
Additional Examples
Andre changed the height of his basketball hoop
from 8 ft 4 in. to 9 ft 2 in. Find the percent of
increase.
amount of change 110 100 10
Quick Check
The height of the basketball hoop increased by
10.
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Percent of Change
LESSON 5-5
Additional Examples
In 1980, the population of a city was
557,927. In 1990, its population was 496,938.
Find the percent of decrease. Round to the
nearest tenth.
amount of change 557,927 496,938 60,989
Quick Check
The population decreased by about 11.
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Percent of Change
LESSON 5-5
Lesson Quiz
Round to the nearest whole percent. 1. 81 people
attended last years annual picnic, and 93 people
attended this years picnic. What is the percent
of increase? 2. The speed limit on a highway
was 55 miles per hour last year. This year the
speed limit was increased to 65 miles per hour.
What is the percent increase in the speed
limit? 3. The population in Arthur County,
Nebraska dropped from 462 in 1990 to 444 in 2000.
What was the percent of decrease?
about 15
about 18
about 4
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Markup and Discount
LESSON 5-6
Problem of the Day
Round to the underlined place. a. 0.09972 b. 0.
109 c. 17.51 d. 0.998
0.0997
0.1
18
1.00
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Markup and Discount
LESSON 5-6
Check Skills Youll Need
(For help, go to Lesson 5-4.)
1. Vocabulary Review A relates a part to
the whole. Use an equation to solve each
problem. 2. What number is 16 of 25? 3. Find
80 of 250. 4. 33 is 3 of what
number? 5. 0.55 of what number is 77?
Check Skills Youll Need
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Markup and Discount
LESSON 5-6
Check Skills Youll Need
Solutions 1. percent 2. 0.16 25 n n
4 3. 0.80 250 n n 200 4. 0.03 w 33
w 1,100 5. 0.0055 w 77 w 14,000
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Markup and Discount
LESSON 5-6
Additional Examples
Find the percent of markup for a stapler costing
the school store 2.10 and selling for 3.36.
markup selling price stores cost
Quick Check
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Markup and Discount
LESSON 5-6
Additional Examples
A store sells a skirt that costs the store 40
and marks up the price 25. What is the selling
price for this skirt?
Method 1 Find the markup first. Then find the
selling price.
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Markup and Discount
LESSON 5-6
Additional Examples
(continued)
Method 2 Find the selling price directly.
The selling price equals 100 of the stores cost
plus a markup of 25 of the stores cost.
So, the selling price of the skirt is 100 25,
or 125, of 40.
The store sells the skirt for 50.
Quick Check
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Markup and Discount
LESSON 5-6
Additional Examples
A shoe store advertises a 35-off sale. What is
the sale price of shoes that regularly cost
94.99?
Method 1 Find the discount first. Then find the
sale price.
35 of 94.99 equals the discount.
The sale price is 61.74.
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Markup and Discount
LESSON 5-6
Additional Examples
(continued)
Method 2 Find the sale price directly.
The sale price equals 100 of the regular price
minus a discount of 35 of the regular price.
The sale price is 100 35, or 65, of 94.99.
The sale price is 61.74.
Quick Check
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Markup and Discount
LESSON 5-6
Additional Examples
You buy a CD at the sale price of 6. This is
25 off the regular price. Find the regular price
of the CD.
regular price 25 of regular price sale price
Let r the regular price.
Quick Check
The regular price of the CD is 8.
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Markup and Discount
LESSON 5-6
Lesson Quiz
1. A pair of shoes costs the store 40. The store
sells them for 65. What is the percent markup?
62.5 2. A school service club sells
calendars. Each calendar costs the club
5.50. The club marks up the price 80. What
is the selling price of each calendar?
9.90 3. A sweater regularly sells for 49. It
is on sale for 20 off. What is the sale
price? 39.20 4. You buy a baseball cap for
13. This price is 35 off the regular price.
Find the regular price. 20.00
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Simple Interest
LESSON 5-7
Problem of the Day
Luiss mother has two older sisters who are twins
and 6 yr older than she is. She has a brother who
is half her age. The sum of all their combined
ages is 145 yr. How old is each?
mother 38, older twins 44, brother 19
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Simple Interest
LESSON 5-7
Check Skills Youll Need
(For help, go to Lesson 2-6.)

• Vocabulary Review A is a rule that shows a
  relationship between
• quantities.
• Solve each formula for the underlined variable.
• 2. V lwh 3. d rt
• 4. y x b 5. V Bh

Check Skills Youll Need
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Simple Interest
LESSON 5-7
Check Skills Youll Need
Solutions 1. formula 2. w 3. r 4. b y
x 5. B
V lh
d t
3V h
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Simple Interest
LESSON 5-7
Additional Examples
A student deposits 150 into a bank that pays 6
simple interest. Find the interest earned in 4
years.
In 4 years, the interest earned is 36.
Quick Check
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Simple Interest
LESSON 5-7
Additional Examples
Use the information from Example 1. Find
the final balance in the account after 5 years.
First, find the interest earned.
In 5 years, the interest earned is 45.
Next, find the final balance in the account.
Quick Check
The final balance in the account is 195.
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Simple Interest
LESSON 5-7
Lesson Quiz
1. You deposit 80 into an account that earns 6
simple interest. Find the amount of interest
earned in 3 years. 2. You deposit 180 into
an account that earns 6 simple interest. How
much will be in the account after 3 years?
14.40
212.40
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Ratios and Probability
LESSON 5-8
Problem of the Day
Which of the following numbers would give the
smallest product? 4.9, 75.12, 15.02, 21.275,
8.61, 0.942, 47.38, 3.824
0.942, 3.824
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Ratios and Probability
LESSON 5-8
Check Skills Youll Need
(For help, go to Lesson 4-1.)
1. Vocabulary Review A is a comparison of
two quantities by division. Write each ratio in
simplest form. 2. 3 6 3. 4. 5. 6
. 17 to 68
Check Skills Youll Need
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Ratios and Probability
LESSON 5-8
Check Skills Youll Need
Solutions 1. ratio 2.
, or 12 3.
4.
5. 6.
, or 1 to 4
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Ratios and Probability
LESSON 5-8
Additional Examples
There are 3 red, 2 green, 5 yellow, and 1 blue
marker pens in a box. Suppose you choose one at
random. Find these probabilities.
a. P (yellow)
b. P (brown)
The probability of choosing a brown marker pen is
0.
Quick Check
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Ratios and Probability
LESSON 5-8
Additional Examples
Quick Check
In a survey of the class, 13 of the students
prefer vanilla, 27 prefer chocolate, 10 prefer
strawberry, and the rest chose other flavors of
ice cream. What is the probability that a student
randomly selected from the class chose vanilla or
chocolate?
13 of the students chose vanilla, and 27 of the
students chose chocolate.
P(vanilla or chocolate) P(vanilla)
P(chocolate)
The probability that the student chose vanilla or
chocolate is 40.
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Ratios and Probability
LESSON 5-8
Additional Examples
Express as a fraction the probability that the
outcome for rolling two number cubes has a sum
less than 7.
Make a table to find the sample space for rolling
two number cubes.
1 2 3 4 5 6 1 (1,1) (2,1) (3,1) (4,1
) (5,1) (6,1) 2 (1,2) (2,2) (3,2) (4,2) (5,2) (6,2
) 3 (1,3) (2,3) (3,3) (4,3) (5,3) (6,3) 4 (1,4) (2
,4) (3,4) (4,4) (5,4) (6,4) 5 (1,5) (2,5) (3,5) (4
,5) (5,5) (6,5) 6 (1,6) (2,6) (3,6) (4,6) (5,6) (6
,6)
Quick Check
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Ratios and Probability
LESSON 5-8
Additional Examples
What is the probability (as a fraction) of there
being at least 1 male kitten in a litter of 4
kittens? Draw the sample space. Express the
probability as a fraction.
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Ratios and Probability
LESSON 5-8
Additional Examples
(continued)
Quick Check
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Ratios and Probability
LESSON 5-8
Lesson Quiz

• 1. A 6-sided number cube has the numbers 1, 2, 3,
  4, 5, and 6 on its faces. What is the probability
  of rolling a number less than 5? Write your
  answer as a fraction.
• 2. A survey shows that 24 of people get their
  news from the internet, 48 percent from TV, 22
  from newspapers, and 6 from news magazines. If
  you interviewed at random one person who answered
  the survey, what is the probability that you
  would select someone who gets news from TV or the
  internet?
• 3. A spinner has two equal sections, one
  yellow and one green. You spin 3 times in a row.
  Make an organized list to show the sample space
  for spinning the spinner 3 times. What is the
  probability of spinning green at least twice in a
  row?

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