Ratios, Proportions, and Percents for CBEST Exam Study Guide (page 2)
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.
- Which of the following expresses the ratio of 2 yards to 6 inches?
- 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.)
- This ratio can be expressed as or 72:6. In this problem, 72:6 is the form that is used in the answers.
- 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
- Put the quantities in the same units of measurement (inches, yards, seconds, etc.).
- Put the quantities in order and in the form given by the answer choices.
- If the answer you come up with isn't a choice, reduce.
Try the three steps on the following problems.
- Find the ratio of 3 cups to 16 ounces.
- Find the ratio of 6 feet to 20 yards.
- Find the ratio of 2 pounds to 4 ounces.
- 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.
- 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
- Label the categories of quantities in the problem to illustrate exactly what you're working with.
- Set up the complete set in ratio form.
- Set up the incomplete set in ratio form.
- Cross multiply to get the missing figure.
- 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?
The Four-Step Ratio
The four-step ratio solution is used when there are two groups of numbers: the ratio set, or the small numbers; and the actual, real-life set, or the larger numbers. One of the sets will have both numbers given, and you will be asked to find one of the numbers from the other set.
Sample Four-Step Ratio Question
- The ratio of home games won to total games played was 13 to 20. If home teams won 78 games, how many games were played?
This problem can be solved in four steps.
- Notice the two categories: home team wins and total games played. Place one category over the other in writing.
- In the previous problem, the small ratio set is complete (13 to 20), and you're being asked to find the larger, real-life set. Work with the complete set first. Decide which numbers from the complete set go with each written category. Be careful; if you set up the ratio wrong, you will most probably get an answer that is one of the answer choices, but it will be the wrong answer.
- Determine whether the remaining number in the problem best fits home wins or total games. "If home teams won 78 games" indicates that the 78 goes in the home-team row. The number of total games played isn't given, so that spot is filled with an x.
- Now cross multiply. Multiply the two numbers on opposite corners: 20 × 78. Then divide by the number that is left (13).
Note: This step is frequently omitted by test takers in order to save time, but the omission of this step causes most of the mistakes made on ratio problems.
Notice which category is mentioned first: "The number of HOME games won to TOTAL games played …" Then check to see what number is first: "… was 13 to 20." Thirteen is first, so 13 goes with home games; 20 goes with the total games.
After you cross multiply and wind up with one fraction, you can divide a top number and the denominator by the same factor to avoid long computations. In the previous example, 13 ÷ 13 = 1 and 78 ÷ 13 = 6.
The problem would then be much simpler: 20 × 6 = 120.
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