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Math proficiency is considered one of the critical skills necessary to meet one of the requirements of nursing. This proficiency is basic to safely ...
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Cynthia M. McAlister Sandra G. Shapiro ARNP, MSN, CS ARNP, MSN, CS, MS Associate Professor Associate Professor Eastern Kentucky University Eastern Kentucky University
Revised 5/
TO: Nursing Students
FROM: NUR Faculty
RE: Dosage Calculations
Math proficiency is considered one of the critical skills necessary to meet one of the requirements of nursing. This proficiency is basic to safely administering medications and intravenous fluids.
Enclosed is a booklet to guide you in mastering the mathematical competencies necessary for the accurate computation of medication dosages. This self-instructional booklet is designed to allow you to analyze the areas of mathematics that you may need to review. We encourage you to begin utilizing this booklet at the earliest possible date in your nursing program of study.
There are multiple mathematical formulas that may be used to calculate dosages accurately. This booklet will instruct students to use the ratio and proportion method.
One of the major objectives of nursing is that the student be able to administer medications safely. In order to meet this objective, the student must be able to meet the following math competencies.
Preparation for the math in nursing is a personal independent student activity. In order to facilitate this task it is suggested that the student utilize an organized approach.
Students are encouraged to follow the above procedures. It will organize their own learning efforts and also serve as a basis for assistance from tutors or clinical instructors.
*NOTE: Part G – IV Drip Calculations contains material that will be tested on after the first semester. Refer to this section beginning in the second semester to solve practice problems.
There are three measurement systems commonly used in health care facilities: the metric, household, and apothecary system. In order to compare measured amounts in the systems, approximate equivalents have been developed. An example of an approximate equivalent is 1 teaspoon is approximately equal to 5 milliliters. Because the measures are not exactly equal, a conversion which takes more than one step will not produce as accurate a value as a conversion which takes only one step. For example, it is more accurate to convert from teaspoon to milliliters by using the conversion factor directly from teaspoons to milliliters than it is to go from teaspoons to ounces to milliliters.
RULE: Always convert from one unit of measure to another by the shortest number of steps possible.
The following conversion table will have to be memorized in order to accurately calculate dosage problems.
Metric Apothecaries Household
VOLUME
1 minim (m) 1 drop (gtt)
1 milliliter (ml)(cc) 15-16 minims (m) 15-16 gtts
4 milliliters (ml) (cc) 1 dram (dr), (4 ml’s or cc’s)
1 teaspoon (t) (4-5 cc), 60 drops (gtts)
15 milliliters (ml) (cc) 1 tablespoon (T), 3 teaspoons (t)
30 milliliters (ml) (cc) 1 ounce (oz) 2 tablespoon (T)
1000 milliliter (1 liter) 1 quart 1 quart
WEIGHT
1 milligram (mg) 1000 micrograms (mcg)
60 milligrams (mg) 1 grain (gr)
1 gram (gm) 15 grains (gr), 1000 milligrams (mg)
454 grams (gm) 16 ounces (oz) 1 pound (lb)
1 Kilogram (Kg) 2.2 pounds (lb)
Units (u) and milliequivalents (meq) cannot be converted to units in other systems. They have their value given and will never need to be converted. 1 unit – 1000 miliunits *Cubic centimeters (cc’s) and milliliters (ml’s) can be used interchangeably.
AS left ear AD right ear AU each ear IM intramuscular IV intravenous IVPB intravenous piggyback V, PV vaginally OS left eye OD right eye OU each eye PO by mouth R, PR by rectum R right L left SC, SQ subcutaneous S&S swish & swallow
ac before meals ad lib as desired Bid twice a day HS at bedtime pc after meals Prn as needed Q am, QM every morning QD, qd every day Qh every hour Q2h every 2 hours Q3h every 3 hours, and so on Qid four times a day Qod every other day STAT immediately Tid three times a day
D 5 W – 5% Dextrose in water D 5 NS – 5% Dextrose in normal saline D 5 ½NS – 5% Dexrose in ½ normal saline L.R. – Lactated Ringers Remember 1 liter = 1000 ml
AMA against medical advise ASA aspirin ASAP as soon as possible BS blood sugar (glucose) c with C/O complains of D/C discontinue DX diagnosis HX history KVO keep vein open MR may repeat NKA no known allergies NKDA no known drug allergies NPO nothing by mouth R/O rule out R/T related to Rx treatment, prescription s without S/S signs/symptoms Sx symptoms TO telephone order VO verbal order ~ approximately equal to
greater than < less than increase decrease
Numerator Denominator
2 = Proper fraction = numerator is smaller than denominator. 3
3 = Improper faction = numerator is larger than denominator. 2
1 1 = Mixed fraction = whole number and a fraction. 2
To change an improper fraction to a mixed number: a. Divide the numerator by the denominator. 13 = 2 3 b. Place remainder over denominator. 5 5
To change a mixed number to an improper fraction: a. Multiply denominator by the whole number. 3 1 = 7 b. Add numerator. 2 2 c. Place sum over the denominator.
To reduce a fraction to its lowest denominator: a. Divide numerator and denominator by the greatest common divisor. b. The value of the fraction does not change.
EXAMPLE: Reduce 12 60
12 divides evenly into both numerator and denominator
12 12 = 1 12 = 1 60 12 = 5 60 5
EXAMPLE: Reduce 9 12
3 divides evenly into both
9 3 = 3 12 3 = 4
EXAMPLE: Reduce 30 45
15 divides evenly into both
30 15 = 2 45 15 = 3
30 = 2 45 3
You can multiply or divide when denominators are NOT alike. You CANNOT add or subtract unless the fractions have the same denominator.
Addition of fractions: a. Must have common denominator. b. Add numerators.
1+ 2 = (change 2 to 1 ) = 1 + 1 = 2 = 1 4 8 8 4 4 4 4 2
Subtraction of fractions: a. Must have common denominator. b. Subtract numerators.
6 - 3 = (change 6 to 3 ) = 3 - 3 = 0 8 4 8 4 4 4
Multiplication of fractions: a. To multiply a fraction by a whole number, multiply numerator by the whole number and place product over denominator.
4 x 3 = 12 = 1 4 = 1 1 8 8 8 2
b. To multiply a fraction by another fraction, multiply numerators and denominators.
5 x 3 = 15 = 5 6 4 24 8
Division of fractions: a. Invert terms of divisor. b. Then multiply.
EXAMPLE 1: 2 4 3 5
2 x 5 = 10 5 3 4 12 Reduced to lowest terms = 6
Changing fractions to decimals:
Divide the numerator by the denominator.
EXAMPLE 1: 3 4 *3.00 so 3 = 0. 4 28 4 20 20 0
EXAMPLE 2: 8 40 *8.0 so 8 = 0. 40 80 40 0
Addition and Subtraction of decimals:
Use the decimal point as a guide and line up the numbers by their decimal place so that all the ones places are lined up under each other, all the tens places lined up and so on.
ADDITION EXAMPLE 1: 7.4 ADDITION EXAMPLE 2:. +12.39 2. 19.79. +.
Multiplication of decimals:
a. Multiply the numbers as if they were whole numbers. b. Count the total number of decimal places to the right of the decimal point for each of the numbers. c. Use that total to count decimal places in the answer.
a. 17.3 17.3 b. 17.3 has 1 decimal place past the decimal point. x 0.45 x 0. 865
c. Count 3 places for decimal in answer - 7.
Division of decimals:
To divide a decimal by a whole number, the decimal is placed directly above the decimal in the dividend.
Quotient 1. Divisor *Dividend 5 *6. 5 18 15 35 35 0
To divide a decimal by a decimal:
Shift the decimal of the divisor enough places to make it a whole number. The decimal in the dividend is moved the same number of places as the divisor. Decimal point of quotient is placed directly above the new place of the decimal in the dividend.
. 5. EXAMPLE 1: .6 *3.0 6 *30. 30 0
Rounding off decimals:
Decide how far the number is to be rounded, such as to the tenths place or the hundredths place. Mark that place by putting a line under it.
If the digit to the right of that place is less than 5, drop that digit and any others to the right. If the digit to the right of the place to be rounded to is 5 or greater, increase the number in the place by 1 and drop the digits to the right.
EXAMPLE 1: 7.423957 7.
Rounded to nearest hundredth
Basic Math Practice Practice # Roman Numerals
ANSWERS: Page 60
Practice # Fractions
ANSWERS: Page 60
