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