Percent

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Percent
PERCENTS AND PERCENT PROBLEMS - 7.5 7.6
Objectives Students will explain how ratios,
fractions, decimals, and percents are related,
how to convert between them, and how to use
percent. Students will perform calculations
involving profit, sale price, and tax as an
exercise.
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Percent Defined
The word per means for every.
Cent means hundred.
Example
Concert tickets are 12 per person.
Example
A century is 100 years.
Percent means for every hundred.
The symbol means percent.
Example
5 out of 100 people agree.
5 percent agree.
Example
5 percent of people agree.
5 agree.
Since means for every hundred, percent
represents a ratio.
Example
25 out of 500 people agree.
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Why Per Hundred?
The short answer is convenience.
Example
"5" is simpler to say than "twenty-five 500th's".
Percent is also a standard.
Converting fractions to hundredths
expresses different values relative to a common
denominator
and makes them easy to compare.
Hundredths are an especially convenient standard
for expressing fractions in the decimal place
system we use to represent numbers.
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The Long Answer
Any fraction can be converted to a percent.
Convert to a decimal first.
Example
Convert to decimal
How many 100th's does 0.75 represent?
Since 0.75 75 hundredths, 0.75 75 .
Thus
Percent Decimal 100
Example
Convert to decimal form.
0.625 100
62.5
Multiply by 100.
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Percent as a Decimal
We have seen that
Percent Decimal 100.
Dividing both sides by 100 gives
Decimal Percent 100
Since every decimal represents a fraction,
multiply
to find a percent of a number.
by percent as a decimal
Example
What is 10 of 103?
10 10 100 0.1
0.1 103 10.3
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Ratio, Fraction, Decimal, Percent
3 representations of 1 ratio and how they are
related
Fraction
Decimal
Percent
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Percent Difference
We frequently want to know the percent difference
between two numbers,
how much bigger or smaller one is than the other.
The
formula is exactly the same, once we know the
difference.
Difference 150 - 90 60 lbs
1. What is Ann's weight as a percent of Tom's?
Ann's Tom's 100
2. How much more does Tom weigh as a percent of
Ann's weight?
(60 90) 100 67
Difference Ann's 100
3. How much less does Ann weigh as a percent of
Tom's weight?
(60 150) 100 40
Difference Tom's 100
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Profit
Profit and loss are almost always treated as
percents.
Example
A clothing store's cost per T-shirt is 7.05.
1. What should they charge per shirt to a make a
profit of 30 ?
Markup (M) is how much a seller adds to their
cost (C).
Profit is markup as a percent of cost.
If profit is 30, then
Unknown
Known
Known
(M) (C) 100 30
M 30 100 (7.05)
Substitute Rearrange
Price
C M
7.05 2.12
9.17
2. What is their profit if they sell their shirts
for 11.00 each ?
Markup (M) equals selling price minus cost (C).
(M) 11.00 - 7.05 3.95 .
Profit M C 100
Profit 3.95 7.05 100
Substituting
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Discount
Discount is similar to profit.
, which is not a consideration when calculating
profit.
Example
A 339 stereo is 20 off.
Sales tax is 8.5 .
You have 295.
Can you afford it?
1. 20 of 339 is 0.2 339 67.80 .
This is by how much the sticker price is reduced.
Sale price is 339 - 67.80 271.20.
2. Sales tax is a percent of cash register price
, which in this case
is 271.20, the price after discount.
8.5 of 271.20
0.085 271.20
23.52
3. Total out-of-pocket cost to you, including
tax, is
271.20 23.52
294.41 .
You have enough money to purchase this item.
Can you afford it?