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# Ratios, Proportions, and Percents for CBEST Exam Study Guide

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Updated on Mar 23, 2011

Ratios and proportions, along with their cousins, percents, are sure to appear on the CBEST. A good understanding of these topics can help you pick up valuable points on the math section of the test.

### The Three-Step Ratio

The three-step ratio asks for the ratio of one quantity to another.

#### Sample Three-Step Ratio Question

Use the three steps to help you work out the following problem.

1. Which of the following expresses the ratio of 2 yards to 6 inches?
1. 1:3
2. 3:1
3. 1:12
4. 9:1
5. 12:1

1. One yard is 36 inches, so 2 yards is 72 inches. Thus, the ratio becomes 72:6. (The quantities can also be put in yards.)
2. This ratio can be expressed as or 72:6. In this problem, 72:6 is the form that is used in the answers.
3. Since the answer is not there, reduce. 72 inches:6 inches = 12:1. The answer is choice e. Notice that choice c, 1:12, is backward, and therefore incorrect.

#### Three Success Steps for Three-Step Ratios

1. Put the quantities in the same units of measurement (inches, yards, seconds, etc.).
2. Put the quantities in order and in the form given by the answer choices.
3. If the answer you come up with isn't a choice, reduce.

#### Practice

Try the three steps on the following problems.

1. Find the ratio of 3 cups to 16 ounces.
1. 2:3
2. 3:16
3. 16:3
4. 3:1
5. 3:2
2. Find the ratio of 6 feet to 20 yards.
1. 10:1
2. 6:20
3. 3:10
4. 20:6
5. 1:10
3. Find the ratio of 2 pounds to 4 ounces.
1. 2:4
2. 2:1
3. 1:8
4. 8:1
5. 8:5
4. In a certain class, the ratio of children who preferred magenta to chartreuse was 3:4.What was the ratio of those who preferred magenta to the total students in the class? Hint: Add 3 and 4 to get the total.
1. 7:3
2. 3:4
3. 4:3
4. 3:7
5. 4:7
##### Hot Tip
• You can eliminate two of the choices for question 2 immediately. You know that 3:16 or 16:3 can't be right because the units haven't been converted yet.
• In question 3, choices b and c are the same ratios. There can't be two right answers, so they can be eliminated. Six feet is two yards. Reducing 2:20 makes 1:10.

#### Four Success Steps for Four-Step Ratios

1. Label the categories of quantities in the problem to illustrate exactly what you're working with.
2. Set up the complete set in ratio form.
3. Set up the incomplete set in ratio form.
4. Cross multiply to get the missing figure.
1. In a certain factory, employees were either foremen or assembly workers. The ratio of foremen to assembly workers was 1 to 7.What is the ratio of the assembly workers to the total number of employees?
1. 1:7
2. 7:1
3. 7:8
4. 8:7
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