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How to Calculate a Missing Ratio in a Proportion

Writing out proportions is a useful way to visualize multiple ratios. A ratio describes the relationship between different values. For instance, if you had three oranges for every five apples then the numerical ratio of oranges to apples would be 3:5. A proportion is a mathematical expression that shows two different ratios as equal. For instance, 3:5 = 6:10 is a proportion expressing the same ratio in two different ways. Proportions can be used to determine a missing value in a ratio.

Instructions

    • 1

      Write out the proportion in fraction form. As an example, say you have a math problem stating that there are five apples for every two oranges. You are then asked, "How many apples do you have if you have 20 oranges?" Write out fractions in the following form, using "X" to represent the unknown value: 5:2 = X:20.

    • 2

      Cross multiply the two ratios. Multiply the numerator of the first ratio by the denominator of the second ratio, then multiply the denominator of the first ratio by the numerator of the second ratio. For this example, you would multiple 5 x 20 and 2X. This should now be expressed as 100 = 2X.

    • 3

      Simplify each side so that only the unknown integer remains. For this example, you would divide both sides by two to get the value of "X." Continuing with the example, 100/2 = 2X/2. When simplified, you end up with 50 = X.

    • 4

      Plug the integer value back into the original proportion. For example, the original proportion would be written as 5:2 = 50:20.

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