Math Review &
Basic
Pharmacology
Math
Posology
 Purpose
One very important part of nursing practice
is the ability to calculate correct dosages
of drugs and solutions. Accurately
performing mathematical calculations is
essential to the nurse not only in the study
of pharmacology, but also in chemistry and
physiology.
The information required to correctly
calculate dosages and prepare
medications for administration is provided.
Self-assessment tests are included. The
self-assessment tests will identify
strengths and weaknesses, as well as
provide direction for areas that may need
additional help.
Objectives

Identify relative value, add, subtract, multiply,
divide and reduce to the lowest terms any type
of fractions, decimal or mixed number.
 Define the concept of ratio and proportion and
use to solve equations to calculate the value of
“x”.
 Explain the relationship between decimals,
common fractions, ratios and percents, and
express as equivalents of each other.
Objectives (cont.)
 Identify
specific measurements with the
Household and Apothecaries’ system and
convert to metric equivalents.
 Convert numbers from one unit of
measure to another unit, within the same
system or between two systems (ex.
Metric, apothecaries’).
Use of this material

This material will help to determine your level of
competency and what you may need to review
prior to beginning drug calculation problems.
 This review includes some basic instructions in
the math that you will use and some sample
problems for you to solve.
 The more use you make of the study guide, the
less problems you will have when you begin
drug calculations.
Introduction
 Serious
harm to a patient can result from
small mathematical errors when
calculating drug dosages. Therefore, the
ability to accurately calculate correct
dosages is of utmost importance. “This is
not an option.”
Intro (cont.)
 Learning
to calculate drug dosages need
not be a source of anxiety. Following a
step-by-step approach and using basic
mathematical skills, you will be able to
consistently calculate drug dosages
accurately and confidently.
Intro (cont.)

If you approach drug calculations in a logical
manner, many errors can be avoided. Often,
drug dosages can be calculated in your head (or
at least you can obtain a rough estimate of the
correct amount). Of course, you should always
double-check your thinking mathematically.
When calculating dosages, always consider the
reasonableness of the computation. If you have
a feeling that something is not right, it most likely
is NOT. Let common sense prevail!
Measurements in the Metric and
Apothecary Systems
Metric
Decimals
Grams (Gms)
Millograms (mg)
Liters (L)
Milliliters (ml)
Kilogram (Kg)
Minims (mx)
Microgram (mcg)
Apothecary
Fractions
Grains (gr)
Dram (℥)
Ounce (ℨ)
Pound (lb)
Teaspoon (tsp)
Tablespoon (Tbsp)
Drops (gtts)
Equivalents

1 Gm = 1000 mg
 0.5 Gm = 500 mg
 gr. l = 60-64 mg
 gr. 1 ½ = 90-100 mg
 gr. ½ = 30 mg
 gr. ¼ = 15 mg
 gr. 1/6 = 10 mg
 gr. 1/100 = 0.6 mg
 gr. 1/150 = 0.4 mg
 gr. 1/200 = 0.3 mg










1 L = 1000 ml
1 mg = 1000 mcg
1 ℨ = 30 ml
1 ℥ = 4 ml
1 Tbsp = 15 ml
1 Tsp = 4-5 ml
1 qt. = 1000 ml = 1 L
1 Kg = 2.2 lbs.
15-16 gtts = 1 ml
15-16 mx = 1 ml
Fractions
A fraction is a part of a whole number and
consists of two parts – a numerator and a
denominator.
Relative Value of Fractions
After understanding the significance of the two parts of a
fraction, one must then be able to identify the value of the
fraction. When two or more fractions have the same
denominator, the numerator determines the relative value
of the fraction.
Fractions (cont.)
Relative Value (cont.)
Example:
5/6 is greater than 2/6
2/8 is less than 7/8
If two or more fractions have the same numerator, the
denominator determines the relative value to the fraction.
Example:
4/16 is less than 4/6
1/5 is greater than 1/8
Fractions (cont.)

Type of Fractions


Proper fractions – fractions that have
numerators smaller than their denominator
Example: ¼, 6/8, 1/150
Improper fractions – fractions that have
numerators larger than or equal to their
denominators. Example: 8/3, 12/4, 200/150
Fractions (cont.)
Improper fractions can be changed to mixed
numbers by dividing the denominator into the
numerator.
Example: 12/4 = 12  4 = 3
8/3 = 8  3 = 2 2/3

Mixed numbers – Numbers that have a whole
number and a fraction part.
Example: 4 ½, 6 4/5, 7 1/8
Fractions (cont.)
 Reduction
of Fraction and Equivalent
Fractions
The purpose of changing the terms of a fraction without
changing its value is called reduction. This may be done
by dividing both terms of a fraction by the same number.
Example: 4/16
44=1
16  4 = 4
4/16 = 1/4
Fractions (cont.)
 Addition
and subtraction of fractions
Fractions may only be added to or subtracted from each
other when they have the same denominator.
Example: 1/3 + 2/4 + 5/6
12 is the lowest number into which each of these denominators can be
divided (least common denominator or LCD).
1/3 3 into 12 = 4 4x1 = 4
3/4 4 into 12 = 3 3x3 = 9
5/6 6 into 12 = 2 2x5 = 10
Therefore 1/3 = 4/12
Therefore 3/4 = 9/12
Therefore 5/6 = 10/12
Fractions (cont.)
After determining the LCD, the numerators of the
individual fractions are added together. The
denominator will remain unchanged.
4/12 + 9/12 + 10/12 = 23/12
This improper fraction can then be changed to a mixed
number.
23  12 = 1 11/12
The steps for subtraction of fractions are the same. First
obtain the LCD, then subtract the numerators.
11/12 – 6/12 = 5/12
Fractions (cont.)
 Multiplication

and Division of Fractions
Multiplication
To multiply a fraction by a whole number,
simply multiply the numerator by the whole
number. The denominator will remain
unchanged.
Example: 2/3 x 4 = 2 x 4 = 8 = 2 2/3
3
3
Fractions (cont.)

If the whole number and the denominator have
a common divisor, cancellation may be used to
shorten multiplication.
2 x 9 = 18 = 6
3
3
or
3
2 x 9 = 6=6
3
1
1
Fractions (cont.)
To multiply a fraction by a fraction, multiply the numerator of
each fraction for the numerator of the product. Multiply the
denominator of each fraction for the denominator of the product.
Example --
2 x 3 = 2 x 3 = 6
3
5
3 x 5 15
(6/15 can be reduced to 2/5)
Again, when the denominator of one fraction and the numerator
of another have a common divisor, cross cancellation can be
used.
1
2 x 3 = 2
3
5
5
1
Fractions (cont.)

Division
To divide a whole number by a fraction, invert the terms in the
divisor and multiply
Example:
8 ÷ 3 = 8 x 4 = 32 = 10 2
4
3
3
3
To divide a fraction by a whole number, make the whole number
an improper fraction (set the number over 1). For example, 4 =
4/1. Then invert the divisor and multiply.
Example:
2 ÷ 4 = 2 ÷ 4 = 2 x 1 = 2 = 1
3
3
1
3
4 12 6
Decimals
 Decimal
fractions
Decimal fractions are special fractions that are
often more easy to use than ordinary fractions.
A decimal fraction is special because it always
has 10 or some multiple of 10 as its
denominator. The most commonly used
measuring system for medications, the metric
system, uses decimal numbers.
Decimals (cont.)

To the right of the decimal point, each place represents a fraction
whose denominator is 10. Each place has a name. One place to
the right of the decimal point represents a denominator of 10. Two
places to the right represents a denominator of 100. Three places to
the right represents a denominator of 1000 and so forth. From the
decimal point to the left each place has a name. Moving to the left,
the places include ones, tens, hundreds, thousands and so forth.
D
E
C
I
M
A
L
HUNDREDS
TENS
ONES
Example:
.
TENTHS HUNDREDTHS THOUSANDTHS
155.205
Decimals (cont.)
 Addition
of Decimals
When adding decimals, arrange the numbers to be
added so that the decimal points line up in a column.
NEXT, add the numbers as if they are whole numbers.
Keep the decimal point at the same place in the answer
(sum) as it is in the problem.
Example:
7.439
+ 32.460
(answer) 39.899
Decimals (cont.)
 Subtraction
of Decimals
When subtracting decimals, again arrange the
numbers so that the decimal points line up in a
column. Then subtract the numbers as if they
are whole numbers. Remember to keep the
decimal point at the same place in the answer as
it is in the problem.
235.76
- 34.61
(answer) 201.15
Decimals (cont.)
 Multiplication
of Decimals
When multiplying decimal numbers, the
numbers are multiplied in the same manner as
whole numbers. The total number of places to
the right of the decimals in the problem is then
used to determine the decimal place in the
answer.
114.2
x 2.81
(answer) 320.902
Decimals (cont.)

Division of Decimals
To divide one decimal by another, divide as if you are dividing whole
numbers. If the divisor (the number by which you are dividing) is a
decimal number, move the decimal point all the way to the right.
You must also move the decimal points in the dividend (the number
being divided) the same number of places to the right. Add as many
zeroes as necessary to the dividend to allow correct placement of
the decimal point.
Example: ---
8 ÷ 0.16
.16
50.
8.00.
80
0
Decimals (cont.)

Division of Decimals (cont.)
To divide a decimal or whole number by 10, by 100, or
by 1000, etc., move the decimal point as many places
to the left as there are zeroes in the divisor.
Example -- 1 ÷ 10 = 0.1
1 ÷ 100 = 0.01
1 ÷ 1000 = 0.001
Percentages
 The
term percentage means hundredths.
Percents are merely decimal fractions with
denominators of 100. For instance, “6%”
means 6 in every 100 parts and may be
written as 6/100, 0.06, or 6%.
Example: 15% = 15  100 = 0.15
Ratio and Proportion
To determine the value of an “unknown”, use a ratio
and proportion formula. An unknown occurs when the
amount of a medication that is to be given differs from
the actual dosage of the medication you have available
(on hand). Therefore, you will need to calculate how
much of the actual medication you will be required to
give in order to deliver the correct dosage. You will need
to put to work your knowledge of “equivalents” to
determine accurate dosages.
Ratio and Proportion (cont.)
The Ratio and Proportion method can be
accomplished by setting up a basic two-sided
equation. On the left side of the equation, put
what you want to determine (the amount you
wish to administer). On the right side of the
equation, put the information you already know
(the amount of medication you have on hand).
After putting the correct information in to the
equation, simply solve for the unknown (X).
Ratio and Proportion (cont.)

The equations can be set up using a fraction format on
each side and cross multiplying or by using a ratio
format with a colon and multiplying the extremes and
the means to solve for the unknown.
Example: You want to give 300 mg of Drug ABC.
You have available 400 mg/ml.
300 mg
=
400 mg
x ml
1 ml
300
=
400x
x
=
0.75
Ratio and Proportion (cont.)
OR:
300 mg : x ml
=
400 mg : 1 ml
300
=
400x
x
=
0.75
Roman Numerals
 You
should know the basic numbers
Examples:
1=I
5=V
6 = VI
9 = IX
10 = X
15 = XV
16 = XVI
50 = L
100 = C
1000 = M