MAT082::Lecture Note::Week 08

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Overview

Since last class period... math stuff.
Introduction to percents.
"Percent of" problems.
Percent change problems.

Assignment(s):

Quote of the Week {Furman.edu:: Mathematical Quotations Server}
Leave the beaten track occasionally and dive into the woods.
You will be certain to find something you have never seen before.
-- Alexander Graham Bell (01847-01922) { invented the telephone in 01875; more...; Mesa...} [adventure] [log]
BARS of the Week {NASA.gov:: Astronomy Picture of the Day}
Mesa AZ | Imperial Dam CA | San Diego CA [log]

Since Last Class Period of Last Week

[Sunday Arizona Republic] "According to the 'NO on Prop. Foo' campaign, which is being outspent by nearly a 95-to-1 ratio, [...]"

[October's Tempe Town News] "Monetary donations are always appreciated as the Tempe Community Action Agency's Food Pantry has a 10-to-1 purchasing power ratio making cash donations more efficient."

[Friday Arizona Republic "Thought of the Day"] "There are two kinds of statistics, the kind you look up and the kind you make up." -- Rex Stout, American writer, 01886-01975

[Sunday Arizona Republic] "Thunderbird Lodge in Canyon de Chelly National Monument is dropping rates [...] $63 for a single room [...] savings of up to 43 percent [...]."

[Monday Money.CNN.com] "Market breadth was positive. On the New York Stock Exchange, winners topped losers 14 to 1 on volume of 760 million shares. On the Nasdaq, advancers beat decliners 6 to 1 on volume of 1.1 billion shares."

[Monday Arizona Republic, opinion by a nationally syndicated columnist for the New York Times] "The Foos have alienated whole professions. Lawyers donate to the Goo Party over the Foo Party at a 4 to 1 rate. With doctors, it's 2 to 1. With tech executives, it's 5 to 1. With investment bankers, it's 2 to 1."

[Tuesday Arizona Republic "Thought of the Day"] "Ninety-nine percent of failures come from people who have the habit of making excuses." -- George Washington Carver, American botanist, 01864-01943

[Tuesday YouTube Square One TV finds] Common Multiple Man ... Oops! Adding Fractions

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Percents

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 37.5/100

Percent 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 1.10

Decimal 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 one-hundreth).
5% equals 5(1/100) equals 5/100 25% equals 25(1/100) equals 25/100 110% equals 110(1/100) equals 110/100

PurpleMath.com:: Converting Between Decimals, Fractions, and Percents [opens new window]

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Converting Fractions Into Percents and Vice Versa

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 possible

Examples.

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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"Percent of" Problems

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 operator
1) What is 5% of 10?
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 answer

2) 7 is what percent of 49?
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 49

3) 4 is 12% of what?
4 = 12% * n 4 = 12(.01) * n 4 .12 * n --- = ------- .12 .12 33.3 = n 4 is 12% of 33.3

External Hyperlinks

PurpleMath.com:: Basic "Percent of" Word Problems [opens new window]

WebMath.com:: Word Problems Involving Percents [opens new window]

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Percent Increase and Decrease

It is often useful to determine the percentage increase or percentage decrease between two values.

Percentage increase formula.
   new value - original value
   -------------------------- x 100
          original value

   "new" value is always larger than "orignal" value
Percentage decrease formula.
   original value - new value
   -------------------------- x 100
          original value

   "original" value is always larger than "new" value
PurpleMath.com:: "Percent of" Word Problems: General Increase and Decrease [opens new window]

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Square One TV: 8% Of My Love

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