Chapter 2 Ratios, Percents, Simple Equations, and Ratio-Proportion Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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. Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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) Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. Converting Percent to Fraction • Example: 75 3 75% 100 4 82 8% 100 25 105 21 1 105% or 1 100 20 20 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 2 Converting Percent to Ratio 35 7 • Example: 35% 7 : 20 100 20 70 7 70% 7 :10 100 10 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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% Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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. Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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. Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 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 Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. Copyright © 2016 Cengage Learning. ALL RIGHTS RESERVED. 7.