Unit 29: Percentages

The SAT will expect you to be comfortable using percentages for tips, taxes, discounts, and all other sorts of manipulations.

Example:

Of the 400 pieces of produce Bob grew last month, 15 percent of them were tomatoes. How many tomatoes did Bob grow last month?

A) 15
B) 30
C) 60
D) 150

Strategy:

  1. When asked to calculate percent change (percent increase of percent decrease), have the formula memorized and use it!
  2. Be comfortable converting percentages into decimals and vice versa.
  3. Practice converting words into equations: reviewed on the very next page.
  4. With tips and taxes, don’t forget the 1! To find the total cost of a 40-dollar item with a 5 percent sales tax, it is (1.05(40)).

Percentages are fractions.  Fractions are decimals.  Decimals are percentages.

$$50%=frac12=.5=50%$$

Working with percentages is the same as working with fractions.  Any percent can be turned into a fraction.  Percent means “per 100”.  Per, in math terms, means a divisor line.  

So 45% = 45 per 100 =  (frac{45}{100})   = (frac9{20})

x percent is simply (frac x{100})

Percent to decimal: To change a percent to a decimal, all you have to do is move the decimal point two places to the left (same as dividing by 100).

(45%=.45)
(133%=1.33)
(9%=.09)
(.7%=.007)
(10%=.1)

Decimal to percent: To change a decimal to a percentage, we just move the decimal two places to the right (same as multiplying by 100)

(.50=50%)
(.72=72%)
(8.6=860%)
(.001=.1%)

Changing words into percentages

“is” means “equals”

“of” means multiply

“what” means a variable, such as x

Whatever comes right before the percent goes on the top of the fraction.  As noted above, you could also use decimals instead of the fractions here.

An example problem:

Michael found a used VW van that he could fix. He bought the car for 65% of the original price of $7200. What did he pay for the car? (Round to the nearest dollar)