When dealing with percents on the SAT math section, it is crucial to have a good understanding of them. For simple fractions, a pizza divided into 8 pieces with 4 of them taken away would leave you with a fraction. In this case, you put the 4 over the 8 (which could be further reduced to ½.)
Percents work in a similar way, but instead of dividing a number into the eight slices or another number, it is divided into 100 pieces so that comparable numbers are used. Remembering that fractions are really a number over 100 is helpful when taking the math section of the SAT.
TIP: When answering questions, it will sometimes be necessary to change percents into fractions. While it is commonly taught to change percents into decimals, on the SAT, it is a good idea to change them into fractions to make the answer easier to get to and make sure it is the correct one.
A lot of the percent problems on the SAT are really just translation problems. Percents in translation problems work the same as in other translation problems, so it is simply a matter of moving from word to word and changing it to math. With percents, however, when the word percent is seen, the number goes in front of the word over the number 100. This turns the percent back into a fraction which means there is no need to worry about moving the decimal place and getting the answer wrong.
Percent Increase/Decrease
For Percent Increase/Decrease Problems, you only need to memorize one formula:
CHANGE
------------ X 100 = percent change
ORIGINAL
The change in value should be divided by the original value and multiplied by 100 to give you the percentage of change - positive or negative.
TIP: The numerator is the change in value - not the new value.
Percent More Than/Less Than:
More difficult problems on the SAT math section that deal with percents will be even more complex because of the extra steps necessary to get the final answer - which will be the correct answer.
Thomas spends $702 on general expenses, $204 for all utilities, and $1200 on rent every month. The total amount for these bills is 42 percent more than he spent 5 years ago. How much did he spend on necessities 5 years ago?
Problems like this are more difficult because it is not possible to simply add what he spends and subtract a percentage from that. There is one amount that is not known - the amount in the past.
The formulas -- x(1 + %) or x( 1 - %) = new amount for more than/less than problems respectively. In these, x represents the original amount.
