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# Percentages, Ratio and Proportion Study Guide for McGraw-Hill's Firefighter Exams (page 2)

By McGraw-Hill Professional
Updated on Mar 16, 2011

A percent is defined as one part in a hundred. The whole amount can be defined as 100 percent (%) and can be divided into 100 equal portions.

#### Converting Decimals to Percent and Vice Versa

To convert a decimal to a percent, move the decimal point two places to the right and insert the % sign at the end of your answer.

Example: 0.567 = 56.7%.

To convert a percent to a decimal, move the decimal point two places to the left, and remove the % sign at the end of your answer.

Example: 56.7% = 0.567.

#### Converting Fractions and Mixed Numbers to Percent and Vice Versa

To convert a fraction to a percent, multiply the fraction by 100%. Express the whole number (100) as a fraction by placing it over 1.

To convert a percent to a fraction, remember that the definition of percent is one part in a hundred. Remove the % sign and multiply the percent value by 1/100 and then reduce the fraction to its lowest terms.

To convert a mixed number percent to a fraction, eliminate the % sign and convert the mixed number to an improper fraction. Then, multiply the improper fraction by 1/100 to obtain the fraction.

#### Percent Problems—Finding the Part, Whole, or Percent

To find the part when given the whole and the percent, use the formula: Part = % · Whole ÷ 100

Example: What is 54% of 50?

Part = % · Whole ÷ 100

Part = (54) (50) ÷ 100

Part = 2700 ÷ 100 = 27

To find the % when given the whole and the part, use the formula: % = Part ÷ Whole · 100.

Example: What percent of 60 is 12?

% = (12) ÷ (60) · 100

% = 0.2 · 100

% = 20

To find the whole when given the part and %, use the formula: Whole = Part ÷ % · 100.

Example: 6 is 15% of what number?

Whole = Part ÷ % · 100

Whole = (6) ÷ (15) · 100

Whole = 0.4 · 100 = 40

#### Percent Problems—Increase and Decrease

Example: What is 60 increased by 10%?

Part = % · Whole ÷ 100

Part = (10) (60) ÷ 100

Part = 600 ÷ 100 = 6 Add the percentage increase to the original number.

60 + 6 = 66

Example: What is 12 decreased by 25%?

Part = % · Whole ÷ 100

Part = (25) (12) ÷ 100

Part = 300 ÷ 100 = 3 Subtract the percentage decrease from the original.

12 – 3 = 9

### 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.