44: Percents

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4-4 Percents
OBJECTIVES You need to be able to solve percent
problems.
Two quick questions 1) What does per mean? 2)
What does cent mean?
When we say miles per gallon, we are actually
saying miles divided by gallons. Per is a math
word for divide. Cent comes from early Roman
times when there were centurions and times were
began to be measured in centuries. Cent was a
Roman word for 100. C was the Roman numeral for
100. C is also for cookie, and thats good enough
for me.
So, percent must mean divide by 100. If you
remember this, you will be fine in this section.
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4-4 Percents
The official book definition of percent

• percent - a ratio that compares a number to 100

We use the sign for percent. Percents can
also be expressed as fractions or
decimals. Examples of how we can write percents
METHOD 1
METHOD 2
Use a proportion.
Use a calculator.
Three-fourths is how many percents?
300 4x 75 x 75
This is seventy-five one-hundredths,
or seventy-five per hundred, which is the same as
3(100) 4x
75
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4-4 Percents
Remember these quick rules to help you out (1)
To turn a decimal into a percent, move the
decimal two places to the right and slap a -sign
on the number.
0.28
28.
28
.
(2) To turn a percent into a decimal, rip off
the -sign and move the decimal two places to the
left.
38.4
38.4
.384
.
(3) To turn a fraction into a decimal, divide
the numerator by the denominator.
3 ? 5
0.6
(4) To turn a fraction into a percent, do (3)
then (1).
3 ? 5
0.6
60.
60
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4-4 Percents
EXAMPLE 2 Solve. A. 30 is what percent of 50?
Turn this English expression into an algebraic
expression using some special variables.
30 is what percent of 50?
Notice that I used a as the variable in this
example. This is to remind me that at the end of
the problem, I need to turn my answer into a
percent.
30 (50)
0.6
60
30 is 60 of 50.
B. 20 is what percent of 30?
20 30
20 (30)
0.66666666667
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4-4 Percents
EXAMPLE 3 Solve. A. 60 of what number is 54?
For this one, I will again use my preferred
method. The books method does not even work for
this type of problem.
60 of what number is 54?
Notice I turned the into a decimal to work the
problem.
0.6n 54
n 90
60 of 90 is 54.
B. What number is 40 of 37.5?
n 0.4 37.5 n 0.4(37.5)
n 15
15 is 40 of 37.5.
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4-4 Percents
HOMEWORK
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