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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