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# Percentages, Ratio and Proportion Study Guide for McGraw-Hill's Firefighter Exams (page 3)

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### Ratio and Proportion

A ratio is a comparison of two numbers or objects. The symbol: is used to separate the values in the ratio. To compare ratios, convert them to fractions by placing the number to the left of the symbol used to separate the two numbers as the numerator and the number to the right of the symbol as the denominator. The order of values in the given expression is important when notating the ratio.

Example: In a group of 30, there are 24 men and 6 women. The ratio of men to women is 24:6 or

Therefore, the expressed ratio of men to women can be simplified to 4:1 (for every 4 men in the group, there is 1 woman). Equivalent (equal) ratios have the same proportion when both sides of the ratio are multiplied or divided by the same number.

Example: 1:6 and 5:30 and 20:120 are all equivalent ratios but 1:6 is the simplest form.

A proportion is an equation of two ratios that are equal to each other. A basic property of a proportion is that the product of the means is equal to the product of the extremes.

Example: a/b = c/d or ad = bc (b and c are the means and a and d the extremes)

Note: Two quantities are in direct proportion when they decrease or increase by the same factor.

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