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MAT081 :: Lecture Note :: Week 08
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The word percent means "per one hundred."
Percent values are suffixed by a
%
character.A percent is a fraction where the denominator is 100.
5% equals 5/100 15% equals 15/100 120% equals 120/100 37.5% equals 37.5/100Percent values can be written as a decimal number by multiplying the value by
0.01
.4% equals 4(.01) equals 0.04 11% equals 11(.01) equals 0.11 110% equals 110(.01) equals 1.10Decimal values can be written as percents by multiplying by 100%.
0.02 equals 0.02(100)% equals 2% 0.33 equals 0.33(100)% equals 33% 2.10 equals 2.10(100)% equals 210%Percents can be written as fractions by multiplying by
1/100
(or one onehundreth).5% equals 5(1/100) equals 5/100 25% equals 25(1/100) equals 25/100 110% equals 110(1/100) equals 110/100PurpleMath.com:: Converting Between Decimals, Fractions, and Percents [opens new window]
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The following algorithm converts a fraction into a percent.
a) divide the numerator by the denominator b) multiply the resulting decimal number by 100(%)Examples.
3/8 = 0.375; 0.375 * 100(%) = 37.5% 1/2 = 0.5; 0.5 * 100(%) = 50% 7/11 = 0.6364; 0.6364 * 100(%) = 63.64% 11/7 = 1.5714; 1.5714 * 100(%) = 157.14%The following algorithm converts a percent into a fraction.
a) write the percent as a fraction (n% = n/100) b) reduce the fraction, if possibleExamples.
25% = 25/100; 25/100 reduces to 1/4 62% = 62/100; 62/100 reduces to 31/50 202% = 202/100; 202/100 reduces to 2 1/50 1% = 1/100; 1/100 is reduced 0.2% = 0.2/100; 0.2/100 reduces to 0.1/50 or 1/500
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The percentage increase between two values is calculated as follows.
new value  original value  * 100 original valueThe percentage decrease between two values is calculated as follows.
original value  new value  * 100 original valueExamples
The Maricopa Community Colleges increased 200506 instate tuition rates by
$5
per credithour. The 200405 tuition rate was$55
.old rate: $55 [200405 rate] increase: $ 5 ["increase" implies addition] new rate: $60 [sum of $55 and $5] percentage increase: 60  55 5  =  = 0.0909 55 55 0.0909 * 100 = 9.09%The Maricopa Community Colleges increased 200607 instate tuition rates from
$60 per credithour
to$65 per credithour
.percentage increase: 65  60 5  =  = 0.0833 60 60 0.0833 * 100 = 8.33%
The Valley Metro Transit is considering decreasing bus fares by
$0.25
. Current bus rates are$1.25
per two hours of bus riding.current rate: $1.25 proposed decrease: $0.25 [the word "decrease" implies subtraction] new rate: $1.00 [difference of $1.25 and $1.00] percentage decrease: 1.25  1.00 0.25  =  = 0.2000 1.25 1.25 0.2000 * 100 = 20%PurpleMath.com:: "Percent of" Word Problems: General Increase and Decrease [opens new window]
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Percent problems come in many forms. Three popular forms are often worded as follows.
What is 'a' percent of 'b'? 'a' is what percent of 'b'? 'a' is 'b' percent of what?Here are some rules to map these type of percent word problems into equations.
"what" becomes a variable "is" becomes an equals operator "of" becomes a multiply operator1) What is
5%
of10
?n = 5% * 10 ...variable is named 'n' n = 5(.01) * 10 ...%5 converted to decimal n = 0.05 * 10 ...word "of" became times n = 0.5 ...decimal arithmetic 0.5 is 5% of 10 ...final answer2)
7
is what percent of49
?7 = n * 49 7 n * 49  =  49 49 1  = n 7 .143 = n .143 * 100 = 14.3 = n (final answer: 14.3%) 7 is 14.3% of 493)
4
is12%
of what?4 = 12% * n 4 = 12(.01) * n 4 .12 * n  =  .12 .12 33.3 = n 4 is 12% of 33.3External Hyperlinks
 PurpleMath.com:: Basic "Percent of" Word Problems [opens new window]
 WebMath.com:: Word Problems Involving Percents [opens new window]
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_______% of the five cells are red.
_______% of the five cells are green.
_______% of the ten cells are not white.
Shade 45% of the five cells.
Shade 0.5% of the five cells.
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