Ratios Percent

Chapter 2

Ratios, Percents, Simple Equations, and Ratio-Proportion

Ratios

• Indicates relationship of one part of quantity to whole – May be in fraction or separated by colon –Example: 51 • Five nurses per 35 patients written as  35 7 • Or 5:35 or 1:7 ex. One nurse to seven patients

Note: The numerator is to the left of the colon, the denominator is to the right of the colon.

Percent • Type of ratio • Means per hundred parts • Latin phrase “per centum” • Percent (%) means “per 100”; • Think of century (100 years), or cents (100) in a dollar

1 Converting Percent to Fraction

• To change percent to fraction: – Drop percent sign – Write the remaining number as numerator – Write 100 as the denominator – Reduce fraction to lowest terms

– THINK: per (/) cent (100)

Converting Percent to Fraction

• Example: 75 3 75%   100 4 82 8%  100 25

105 21 1 105% or 1 100 20 20

Converting Percent to Ratio

• To change percent to ratio: – Drop percent sign – Write remaining number as numerator – Write 100 as denominator – Reduce result to lowest terms – Express fraction as a ratio – Place numerator to left of colon and denominator to right of colon

2 Converting Percent to Ratio

35 7 • Example: 35%    7 : 20 100 20

70 7 70% 7 :10 100 10

Converting Percent to Decimal • To change percent to decimal: – Drop percent sign – Divide by 100 (which is the same as moving the decimal two places to the left) • Example: 4% .04. 0.04

20% .20. 0.20  0.2

Converting Decimal to Percent • To change decimal to percent: – Multiply by 100 (which is the same as moving the decimal two places to the right) – Add percent sign • Example: 0.5 0.50. 50%

3 Converting Ratio to Percent

• To change ratio to percent: – Convert ratio to fraction – Convert the fraction to a decimal – Convert the decimal to a percent

Example: 1 1: 2 1 2 0.5  0.50.  50% 2

Comparing Percents and Ratios

• Concentration of solution can be expressed as percent or ratio – 5% solution • 5 parts of solid per 100 total parts – 1:1,000 solution • 1 part of solid per 1,000 total parts

Comparing Percents and Ratios

• Compare concentrations of solution by converting percent and ratio proportions to decimal 5 • The stronger concentration: 5% 0.05 100 1 1:1,000 0.001 1, 000

4 Comparing Percents and Ratios

Example: 1 11100111 %3 0.0033 3 100 3 1 3 100 300

In this example, the line over 3 means the number 3 repeats itself indefinitely.

Solving Simple Equations for X • One method for solving dosage calculation problems • Answers expressed as decimal • Unknown quantity represented by X

Math Tip: Round decimals to hundredths (two decimal places). For most drug calculations, you will round to no more than two decimal places.

Solving Simple Equations for X

3 • Example: 2X 5 32 – Express as fraction X 51 32 6 – Multiply X 51 5 61 – Convert to mixed number 1X 55 1 – Convert to decimal 11.2X 5

5 Ratio-Proportion

• Proportion _ An equation of two equal ratios. May be expressed as fractions. – Written as two ratios separated by equal sign or double colon 5 :10  10 : 20 5 :10 ::10 : 20 5 10  10 20

Ratio-Proportion

• Product of means (the two inside numbers) equals product of extremes (the two outside numbers). Extremes Means

5:10 10 : 20 5201010 100 100

Proportion Cross-Products

• If two fractions are equivalent or equal, cross- products are also equal 5 10  10 20 5 20  10 10 100  100

6 Ratio-Proportion: Cross-Multiplying to Solve for X • Simplify equation – Divide each side of equation by same number to produce equivalent equation

1X  Therefore, 4 X 1 8 48 4x 8 If 4X 8, then , and X 2 44

Percentage of a Quantity

• Percentage (part) equals percent multiplied by whole quantity • Change % to decimal • Multiply the decimal by the whole quantity • Example: What is 12% of 48? X  12% 48  0.12 48  5.76

Tip: “of” in math means multiply