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What are the properties of proportions?

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wikiHow Staff Editor

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There are many properties of proportion, but here are the first 3: 1) If two ratios are equal, this is called a proportion. In other words, in a proportion, a/b = c/d. 2) The quantities a, b, c, and d are the “terms” of the proportion. The first and fourth terms (a and d) are the “extremes.” The second and third (b and c) are the “means.” 3) In a proportion, the product of the extremes equals the product of the means. In other words, if a/b = c/d, then a x d = b x c. This is the “cross product rule.”

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Question

What is the formula of a proportion?

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There are many formulae that can apply to proportions, but the basic starting point is a/b = c/d. Going from there, you can get a variety of other formulae, such as a x d = b x c and b^2 = a x c.

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What is a proportion example?

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Any 2 fractions with different terms that are equal is a proportion. For example, 1/2 = 3/6 or 2/3 = 6/9 are both examples of proportions.

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Question

What if there is a variable in both denominators?

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A proportion with a variable in each denominator cannot be solved. (It amounts to a single equation in two unknowns, which is not solvable.)

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If the food in a store can last 100 children 21 days, how long can the same food last 150 children eating at the same rate?

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This is merely a question of logic: 100 children are 2/3 of 150 children. Therefore, the number of days you're looking for is 2/3 of 21 days. (2/3)(21) = 14 days.

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What does it mean when I isolate the variable?

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To "isolate the variable" really means to get a variable on one side, and get a constant on the other side.

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