Percent

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Percent
Chapter Seven

• 7.1 Percents, Decimals, and Fractions
• 7.2 Solve Percent Problems with Equations
• 7.3 Solve Percent Problems with Proportions
• 7.4 Applications of Percent
• 7.5 Sales Tax, Commission, Discount
• 7.6 Simple Interest

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Section 7.1
Percents, Decimals, and Fractions
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Understanding Percent
The word percent comes from the Latin phrase per
centum, which means per 100.
Percent means per one hundred. The symbol is
used to denote percent.
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Writing a Percent as a Decimal
Replace the percent symbol with its decimal
equivalent, 0.01 then multiply.
43 43(0.01) 0.43
100 100(0.01) 1.00 or 1
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Writing a Decimal as a Percent
Multiply by 1 in the form of 100.
0.65 0.65(100) 65. or 65
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Writing a Percent as a Fraction
Replace the percent symbol with its fraction
equivalent, then multiply. Dont
forget to simplify the fraction, if possible.
43 43
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Writing a Fraction as a Percent
Multiply by 1 in the form of 100.
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Helpful Hint
We know that
100 1
Recall that when we multiply a number by 1, we
are not changing the value of that number.
Therefore, when we multiply a number by 100, we
are not changing its value but rather writing the
number as an equivalent percent.
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Summary of Converting Percents, Decimals, and
Fractions

• To write a percent as a decimal, replace the
  symbol with its decimal equivalent, 0.01 then
  multiply.

• To write a decimal or fraction as a percent,
  multiply by 100.

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Solving Percent Problems with Equations
Section 7.2
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Key Words
of means multiplication (?) is means equals
() what (or some equivalent) means the unknown
number Let x stand for the unknown number.
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Helpful Hint
Remember that an equation is simply a
mathematical statement that contains an equal
sign ().
6 18x
equal sign
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Solving Percent Problems
20 of 50 10
20

50

10
percent
base
amount
Percent Equation percent base amount
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Helpful Hint
When solving a percent equation, write the
percent as a decimal or fraction. If your unknown
in the percent equation is percent, dont forget
to convert your answer to a percent.
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Helpful Hint
Use the following to see if your answers are
reasonable.
100 of a number the number
a number larger than the original number

a number less than the original number

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Solving Percent Problems with Proportions
Section 7.3
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Writing Percent Problems as Proportions
To understand the proportion method, recall that
30 means the ratio of 30 to 100, or .
30
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Writing Percent Problems as Proportions . . .
Since the ratio is equal to the ratio
, we have the proportion
,
called the percent proportion.
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Percent Proportion
always 100
or
percent
amount
base
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When we translate percent problems to
proportions, the percent can be identified by
looking for the symbol or the word percent. The
base usually follows the word of. The amount is
the part compared to the whole.
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Helpful Hint
Part of Proportion
How Its Identified
Percent
or percent
Base
Appears after of
Amount
Part compared to whole
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Solving Percent Proportions for the Amount
What number is 20 of 8?
amount
percent
base
amount
percent
base
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Solving Percent Proportions for the Base
20 is 40 of what number?
amount
percent
base
amount
percent
base
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Solving Percent Proportions for the Percent
What percent of 40 is 8?
amount
percent
base
amount
percent
base
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Helpful Hint
A ratio in a proportion may be simplified before
solving the proportion. The unknown number in
both and
is 20.
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Applications of Percent
Section 7.4
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The freshman class of 450 students is 36 of all
students at State College. How many students go
to State College?
Equation Method
State the problem in words, then translate to an
equation.
In words 450 is 36 of what number?
Translate
450

36

x
Solve 450 0.36x
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The freshman class of 450 students is 36 of all
students at State College. How many students go
to State College?
Proportion Equation Method
State the problem in words, then translate to a
proportion.
In words 450 is 36 of what number?
amount
base
percent
Translate and Solve
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Percent Increase Percent Decrease
percent increase
percent decrease
In each case write the quotient as a percent.
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Section 7.5
Percent and Problem Solving Sales Tax,
Commission, and Discount
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Calculating Sales Tax and Total Price
Most states charge a tax on certain items when
purchased called a sales tax.
A 5 sales tax rate on a purchase of a 10.00
item gives a sales tax of
sales tax 5 of 10 0.05 10.00 0.50
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The total price to the customer would be
purchase price
sales tax
plus
10.00

0.50

10.50
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Sales Tax and Total Price

• sales tax tax rate purchase price
• total price purchase price sales tax

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Calculating Commissions

• A wage is payment for performing work.
• An employee who is paid a commission as a wage is
  paid a percent of his or her total sales.

Commission commission commission rate sales
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Discount and Sale Price
amount of discount discount rate original
price sale price original price - amount of
discount
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Percent and Problem Solving Simple Interest
Section 7.6
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Calculating Simple Interest

• Interest is money charged for using other
  peoples money.
• Money borrowed, loaned, or invested is called the
  principal amount, or simply principal.
• The interest rate is the percent used in
  computing the interest (usually per year).
• Simple interest is interest computed on the
  original principal.

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Simple Interest

• simple interest principal rate time
• or
• I P r t
• where the rate is understood to be per year and
  time is in years.

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Finding the Total Amount of a Loan or Investment

• total amount (paid or received) principal
  interest

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