Summary
◦ A ratio can be expressed as a fraction, but ratios are not fractions. A ratio compares parts to parts; a
fraction compares a part to the whole.
◦ You can use a Ratio Box to solve most ratio questions.
◦ Direct proportion is . Indirect proportion is x 1 y 1 = x 2 y 2.
◦ A percentage is just a convenient way of expressing a fraction whose bottom is 100.
◦ To convert a percentage to a fraction, put the percentage over 100 and reduce.
◦ To convert a fraction to a percentage, use your calculator to divide the top of the fraction by the
bottom of the fraction. Then multiply the result by 100.
◦ To convert a percentage to a decimal, move the decimal point two places to the left. To convert a
decimal to a percentage, move the decimal point two places to the right.
◦ In problems that require you to find a series of percentage increases or decreases, remember that
each successive increase or decrease is performed on the result of the previous one.
◦ If you need to find the percent increase or decrease use % change = × 100.
◦ To find the average (arithmetic mean) of several values, add up the values and divide the total by
the number of values.
◦ Use the Average Pie to solve problems involving averages. The key to most average problems is
finding the total.
◦ The median of a group of numbers is the number that is exactly in the middle of the group when the
group is arranged from smallest to largest, as on a number line. If there is an even number of
numbers, the median is the average of the two middle numbers.
◦ The mode of a group of numbers is the number in the group that appears most often.
◦ The range of a group of numbers is the difference between the greatest number in the group and the
least number.
◦ On questions about rates, use the Rate, or Work, Pie. Be careful with the units’the SAT will often
require you to do a unit conversion such as minutes to hours or inches to feet.
