Ratios and Proportions Study Guide: GED Math
Practice problems for these concepts can be found at:
Ratios are numbers that are used to compare things. Ratios play an important role in mathematics because they quantify all of the items that you compare on a day-to-day basis. There are several different ways to write ratios. Here are some examples of ways to write ratios.
- with the word to: 1 to 2
- using a colon (:) to separate the numbers: 1:2
- using the phrase for every: 1 for every 2
- separated by a division sign or fraction bar: 1/2 or
Let's look at an example. In the community gardening group, there are 24 women and 16 men. If you want to compare the number of women to the number of men, you can show this comparison in several different ways:
24 to 16
Regardless of which form is used, the meaning is the same: "There were 24 women for every 16 men." Notice that is a fractional form of a ratio. The fractional form of a ratio is often a convenient way to represent a ratio when solving problems.
In addition to comparing women to men, a comparison could also be made between women and total members. The total membership is 24 + 16 = 40 people. This ratio is , or 24 to 40, or 24:40.
Ratios are usually shown in lowest terms and can be simplified in the same way that fractions are simplified. For example, in the gardening group, there are 24 women and 16 men. This ratio can be expressed as 3:2, because . In this group there are three women for every two men. You can also express the ratio of men to total group members. This ratio is 2:5, because .
Write the following ratio as a fraction: 10 wins to 5 losses.
This ratio is .
Even though looks like an improper fraction, it's not, here—it's a ratio comparing the number of wins to the number of losses. You can, however, reduce the ratio to lowest terms: .
Solving Ratio Problems
There are several kinds of ratio problems. The examples that follow show how to solve different kinds of ratio problems.
- A painter mixes two quarts of red paint to three quarts of white paint. What is the ratio of red paint to white paint?
There are several ways you could write this ratio:
- 2 quarts of red paint to 3 quarts of white paint, or 2 to 3
- 2 quarts red paint : 3 quarts white paint, or 2:3
- 2 quarts red paint/3 quarts white paint, or
What is the ratio of games won to games lost, and what is the ratio of games won to games played?
Write your answers as fractions.
The first part of the question asks for the ratio of games won to games lost. So, you would write . You could reduce the ratio to .
The second part of the question asks for the ratio of games won to games played. First, you need to calculate the total number of games played. Because the Tigers won 30 games, lost 6 games, and tied no games, they must have played a total of 36 games. The ratio of games won to games played is 30 games won to 36 total games, or . You could reduce to .
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