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Percents

Page history last edited by Andrea Grieser 13 years, 8 months ago

Percents are ratios that compare parts to a whole, where the whole is divided into 100 parts.  The word "percent" means per cent - for every hundred.  We use the symbol "%" to denote percentages.  For example 15% is the same as the fraction 15/100.    

 

We can convert:

  • percents to fractions:  drop the percent sign, and put number over 100; put in simplest form
  • fractions to percents:  either set up a proportion (see below), or divide the numerator by denominator to conver the fraction to a decimal; then multiply the decimal by 100 to get the percent (same as moving the decimal two places to the right)
  • decimals to percents:  multiply the decimal by 100 (same as moving decimal two places to the right)
  • percents to decimals:  drop percent sign and divide by 100 (same as moving the decimal two places to the left) 

 

The percent proportion is used to convert a fraction to a percent.  The percent proportion looks like this:

For example, if we want to know:

5 is what percent of 8?

 

We could set up the percent proportion:

 

Once we have the proportion set up, we can use the cross product property to find the missing value (in this case, the percent):

5*100 = 8p  =>  500 = 8p  => p = 62.5

 

So, 5 is 62.5% of 8.

 

Another way to solve this problem is to translate the English words to math.  The word "is" represents the equals sign (=).  The word "of" means multiply.

 

5 is what percent of 8

 

translates to

5 = x * 8

 

Solve for x by dividing both sides by 8:  x = 0.625.  This gives us the percent in decimal form.  Multiply by 100 (move the decimal two places to the right) to convert it to a percent:  62.5%

 

These class notes provide further explanation and examples.

 

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