RATIOS, PROPORTIONS, AND RATES
Setup: 1.05x = 59,346
31 . Combined Percent Increase and Decrease
To determine the combined effect of multiple percent increases and/or decreases, start with
100 and see what happens.
Example: A price went up 10 percent one year, and the new price went up 20 percent the
next year. What was the combined percent increase?
Setup: First year: 100 + (10 percent of 100) = 110. Second year: 110 + (20 percent of
110) = 132. That’s a combined 32 percent increase.
32 . Setting Up a Ratio
To find a ratio, put the number associated with the word of on top and the quantity associated
with the word to on the bottom and reduce. The ratio of 20 oranges to 12 apples is which
reduces to
33 . Part-to-Part Ratios and Part-to-Whole Ratios
If the parts add up to the whole, a part-to-part ratio can be turned into two part-to-whole ratios
by putting each number in the original ratio over the sum of the numbers. If the ratio of
males to females is 1 to 2, then the males-to-people ratio is and the females-to-
people ratio is In other words, of all the people are female.
34 . Solving a Proportion
To solve a proportion, cross multiply:
