- 1). Identify the parts of the problem that will comprise your proportion. All proportion and percent problems contain three distinct pieces, two of which are given in the problem, and one which is the variable, or unknown. For instance, say that you are told that 36 is 80 percent of some number, and you are asked to find that number. The first part of the proportion is the "is." This is the number that is part of some larger number. In some problems, it is named, while in others, it is the unknown. In the example, 36 is the "is." The second part of the proportion is the "of." This is the number of which the percent is being taken. It may be named in some problems, and may be the variable in other problems. In the example, the "of" is the unknown. The third and most easily identifiable part of the proportion is the percent itself, which is always followed by a "%" symbol. In the example, the percent is 80.
- 2). Arrange the proportion using the formula "is divided by of" equals "percent divided by 100." Written as a fraction, this looks like "is/of = %/100." Replace the values you identified in Step 1 for the words "is" and "of," as well as the "%" symbol. Of course, one of these will be unknown, so replace the unknown with a variable such as "x." In the example, write 36/x = 80/100.
- 3). Perform cross-multiplication. Multiply the numerator of the first fraction by the denominator of the second, and the denominator of the first fraction by the numerator of the second. Place the results on opposite sides of the equal sign. The example becomes 80x = 3,600.
- 4). Divide both sides by the coefficient, which is the number to the left of the variable. In the example, divide 3,600 by 80, obtaining 45. This is your answer.
- 5). Interpret your answer to ensure that it makes sense by inserting it into the initial question. In the example, ask yourself whether it's possible that 36 could be 80 percent of 45. This indeed makes sense, because 36 almost as large as, but not larger than, 45.
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