Calculate with Confidence5th edition

Gray Morris

Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

Ratio and Proportion

Unit One: Chapter 4

Mosby items and derived items © 2010 by Mosby, Inc., an affiliate of Elsevier Inc.

Ratio and Proportion: Objectives

After reviewing this chapter, you should be able to:

1. Define ratio and proportion2. Define means and extremes3. Calculate problems for a missing

term x using ratio and proportion

Ratio and Proportion: Background

Can be used to calculate all types of med problems or nurse/client ratios Example: 4 nurses to 28 clients = 1:7 ratio

Some meds use ratio to express strength of solution Example: epinephrine 1:1,000

Ratios should be expressed in lowest terms

Ratios

Used to indicate relationship between two numbers

Numbers are separated by a colon (:)Colon indicates division

Numerator on left : Denominator on right Example: 1:3 is the same as 1/3

Ratios: Measures in Solutions

In medications Ratio of parts of drug to parts of solution =

strength

Safety Point The more solution in which a drug is dissolved,

the less potent it becomes Example: 1 part drug to 1,000 parts solution is

more potent (stronger) than 1 part drug in 10,000 parts solution

ProportionsAn equation of two ratios of equal valueWritten in any of following formats

Example: 3:4 = 6:8 (separated with equals)3:4 :: 6:8 (separated with double

colon)

(written as a fraction)

Read as “3 is to 4 equals 6 is to 8” or three fourths equals six eighths when expressed as a fraction

3 64 8

Proportions: Means and Extremes

Relationship between left and right terms is expressed by means and extremes

In a true proportion, product of means is equal to product of extremes

Means = middle Extremes = ends

5:25 = 10:50 so… 5(50) = 25(10) TRUE

5:25 = 10:505 10

= 25 50

(proportion written as fraction)5 (extreme) 10 (mean)

= 25 (mean) 50 (extreme)

Ratio and Proportion: Solving for x

If three numbers in a true proportion are known, the unknown fourth number—called x—can be found

x is usually placed on the left

12:9 = 8:12( ) = 9(8)

12 = 7212 72

= 12 12

72 =

12 = 6

x

x

x

x

x

x

Proportion: Proof

12:9 = 8:xPlace the value previously obtained in the

spot for x12:9 = 8:6

Multiply means by extremes—should be equal

9(8) = 12(6)72 = 72

Ratio: Dosage Calculation

Ratio is used to represent the weight of a drug in a tablet or capsule or in milliliters of solution Examples: 1 tab : 0.125 mg or

1 mL : 250 mg or

1 tab0.125 mg

1 mL250 mg

Proportion: Dosage Calculation

R and P to solve for x in medications Example: If there are 500 mg in 1 capsule, how

many milligrams are delivered in 2 capsules?

1 cap : 500 mg = 2 caps : x mg1(x) = 500(2)1(x) = 1,000x = 1,000 mg