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# Ratios, Proportions, and Percents for CBEST Exam Study Guide (page 2)

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Updated on Mar 23, 2011

1. e.
2. e.
3. d.
4. d.
5. c.

### 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

1. 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.

1. Notice the two categories: home team wins and total games played. Place one category over the other in writing.
2. 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.

3. 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.
4. 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.

5. 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.
6. Now cross multiply. Multiply the two numbers on opposite corners: 20 × 78. Then divide by the number that is left (13).
##### Hot Tip

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.