CHAPTER 1
CAlculation of dosages and
solution RATES USING RATIO AND
PROPORTION
(3 CONTACT HOURS)
By Alene Burke, MSN, RN, received her Master
of Science in Nursing Administration and Nursing
Education from Adelphi University, and has completed
coursework towards a Ph. D. Alene has been
consulting on the development, design, and production
of competency and educational activities since 1998.
She has authored several publications including
resource books and textbook chapters. She has
provided continuing education for numerous medical
professionals, including pharmacists.
Author Disclosure: Alene Burke and Elite Professional
Education do not have any actual or potential conflicts
of interest in relation to this lesson.
Universal Activity Number (UAN):
0761-9999-13-342-H04-T
Activity Type: Application-based
Initial Release Date: September 10, 2013
Expiration Date: September 10 2015
Target Audience: Pharmacy Technicians in a
community-based setting.
To Obtain Credit: A minimum test score of 70 percent
is needed to obtain a credit. Please submit your answers
either by mail, fax, or online at www.elitecme.com.
Questions regarding statements of credit and other
customer service issues should be directed to 1-888666-9053. This lesson is $15.00.
Educational Review Systems is accredited
by the Accreditation Council of Pharmacy
Education (ACPE) as a provider of
continuing pharmaceutical education. This
program is approved for 3 hours (0.3
CEU’s) of continuing pharmacy education credit. Proof
of participation will be posted to your NABP CPE
profile within 4 to 6 weeks to participants who have
successfully completed the post-test. Participants must
participate in the entire presentation and complete the
course evaluation to receive continuing pharmacy
education credit.
Learning objectives
At the conclusion of this course, you should be
able to accurately:
!! Perform basic arithmetic calculations.
!! Relate the equivalents for a household
measurement system.
!! Relate the equivalents for the apothecaries
system.
!! Relate the equivalents for the metric system.
!! Convert among the systems of measurement.
!! Accurately calculate oral, parenteral
and intravenous dosages using ratio and
proportion, including for pediatric dosages
that are based on body weight.
Introduction
Pharmacy technologists work in a wide variety
of settings. The roles and responsibilities of
pharmacology technologists vary somewhat in
different settings and even among those that are
similar.
For example, pharmacy technicians may not
do intravenous admixtures in a community
pharmacy department within a major retail
store, but they may have to accurately add
medications to intravenous solutions in an acute
care hospital or medical center. Furthermore,
some acute care hospitals and medical centers
may only allow licensed pharmacists to prepare
intravenous admixtures; others may allow
pharmacy technicians to perform this role under
the supervision of a licensed pharmacist.
of the 5 parts, less than a whole, or 1.
Despite these differences, most pharmacy
technicians must be thoroughly prepared and able
to calculate accurate dosages of all types. There is
no room for error; these dosages must be accurate
and without any errors. Even the smallest error
can lead to a serious medication error. This
course will provide you with the knowledge,
skills and abilities to provide safe, accurate
pharmaceutical patient care and drug dosages
without any errors whatsoever.
When the numerator and the denominator are
identical, the fraction is equal to 1. For example,
the fraction 6/6 is equal to 1 and the fraction
987/987 is equal to 1. The numerators and
denominators are identical. Of the 6 parts in the
whole, you have all 6 parts; and of the 987 parts
in the whole, you have all 987 parts, therefore it
is a whole, or 1.
Basic arithmetic calculations
An underlying presumption for this course is that
you, the learner, have the basic ability to add,
subtract, multiply and divide numbers. If you feel
that you are not fully competent in terms of these
basic arithmetic functions, it is recommended that
you review and study these functions at this time
and before continuing with this course.
Did you also notice that the numerators in the
three above improper fractions are more than
the denominators? For example, the 5/3 fraction
represents that there are 3 parts in the whole and
you have 5 parts, which is more than the whole,
or greater than 1.
Reducing fractions
Both proper and improper fractions can be
reduced to their lowest common denominator.
Reducing fractions make them easier to work
with.
Fractions
Reducing fractions involves recognizing a
number that can be evenly divided into both the
numerator and denominator. For example, if
the fraction is 3/9, both the numerator (3) and
the denominator (9) can be evenly divided by
3 without anything left over. When you reduce
3/9, you divide the numerator of 3 by 3, and then
you divide the denominator of 9 by 3, as shown
below:
3÷3=1
9÷3=3
Therefore, 3/9 = 1/3
Proper fractions are less than 1; improper
fractions are more than 1.
Likewise, you can reduce 66/124, as shown
below:
66 ÷ 2 = 33
124 ÷ 2 = 62
Therefore, 66/124=33/62
In addition to the ability to perform basic
addition, subtraction, multiplication and
division, you should also be able to perform
basic mathematical calculations using fractions,
mixed numbers and decimals. These mathematic
calculations are discussed and described below.
There are two types of fractions:
Proper fractions.
Improper fractions.
Fractions are indicated by a slash or a divide
line, with a number above and number below the
slash or divide line. The number above the slash
or divide line is called the numerator, and the
number below is referred to as the denominator.
Here are some examples of proper fractions. All
of these fractions are less than 1:
1 : In both figures, 1 is the numerator
1/2 or −
2
and 2 is the denominator.
2/5 or −2 : In both figures, 2 is the numerator
5
and 5 is the denominator.
88 : In both figures, 88 is the
88/345 or 345
numerator and 345 is the denominator.
Here are some examples of improper fractions.
All of these fractions are more than 1:
5/3: 5 is the numerator and 3 is the
denominator.
19/4: 19 is the numerator and 4 is the
denominator.
564/324: 564 is the numerator and 324 is the
denominator.
Now, let’s try to reduce these fractions. (Hint:
If there is no common denominator, the fraction
cannot be reduced.)
6/9
Both 6 and 9 can be reduced by 3 to
the fraction 2/3.
16/24
Both 16 and 24 can be reduced by 8
to the faction 2/3.
16/9
This fraction cannot be reduced or
made smaller because there is no
number you can divide into both
16 and 9. There is no common
denominator.
By reducing fractions to their common
denominators, you are really determining their
equal fractions. So 6/9 is equal or equivalent to
2/3 in the example above.
Practice problems: Reducing fractions
Reduce the following fractions to their lowest
common denominators:
1. 16/22 = _____
2. 7/77 = _____
3. 8/23 = _____
4. 12/67 = _____
5. 34/88 = _____
6. 88/880 = _____
Did you notice that the numerators in the
three above proper fractions are less than the
denominators? All of these fractions are less than
1. For example, the 2/5 fraction represents that
there are 5 parts in the whole and you have only 2 Now check your answers.
Elite
Page 1
Answers to practice problems: Reducing
fractions
1. 16/22 = 8/11
The 16 and the 22 can both be divided by 2,
therefore, 16 divided by 2 is 8; 22 divided by
2 is 11. Thus, 8/11 is the answer because 8
and 11 cannot be divided evenly by any other
number.
2. 7/77 = 1/11
The 7 and the 77 can both be divided by 7,
therefore, 7 divided by 7 is 1; 77 divided by 7
is 11. Thus, 1/11 is the answer because 7 and
77 cannot be evenly divided by any number
other than 7.
3. 8/23 cannot be reduced.
4. 12/67 also cannot be reduced. Only 1 can be
evenly divided into 12 and 67.
5. 34/88 = 17/44
The 34 and the 88 can both be divided by 2,
therefore, 34 divided by 2 is 17; 88 divided
by 2 is 44. Thus, 17/44 is the answer because
17 and 44 cannot be evenly divided by any
other number.
6. 88/880 = 1/10
The 88 and the 880 can both be divided by
88, therefore, 88 divided by 88 is 1; 880
divided by 88 is 10.
Mixed numbers
Mixed numbers are a mix of a whole number and
a fraction. For example, 2 1/2 teaspoons and 4 5/8
tablespoons are both mixed numbers. As you can
see from these two examples, all mixed numbers
are more than 1 or more than a whole. For
example, 2 1/2 teaspoons is 2 whole teaspoons
plus 1/2 a teaspoon.
You have to convert all mixed numbers into
improper fractions, which are also more than 1,
before you can perform any calculations with
them. For example, you have to convert 2 1/2
into 5/2, and you have to convert 4 5/8 into 37/8
as fully discussed below.
To perform this calculation, you:
Multiply the denominator by the whole
number.
Then add the numerator to it.
Then divide this number by the denominator.
2 1/2 = 2 x 2 +1 = 5/2
2
In this example, you multiply the denominator of
2 by the whole number of 2 and then add 1, the
numerator of the fraction. Finally, you divide by
the denominator of 2. So, 2 x 2 = 4; 4 + 1 = 5,
and 5 is then placed over the denominator of 2.
As you may see, the improper fraction of 5/2 can
be converted back to a mixed number as shown
below:
5/2 means 5 divided by 2, which equals 2 1/2.
When you turn mixed numbers back into
improper fractions, you can easily check your
mathematical calculation. If your original
calculation gives you 5/2 and you convert this
back to a mixed number, you should see the
original mixed number.
Now, let’s convert these mixed numbers into
improper fractions:
6 5/8 = 8 x 68+ 5 = 53/8 .
2.3 = 2 and 3 tenths or 2 3/10.
21.98 = 21 and 98 hundredths or
21 98/(100 ).
Next, check your answer by changing the
improper fraction back to the original mixed
number:
53/8 means 53 divided by 8, which equals 6
5/8.
Decimal numbers are often rounded off when
pharmaceutical calculations are done. When you
have to round off to the nearest hundredth, you
must look at the next number, or thousandth, and
determine whether it is less than 5, equal to 5 or
more than 5.
Practice problems: Mixed numbers
Now, perform these practice problems by
converting the mixed numbers into improper
fractions and then converting these improper
fractions back to the mixed number.
1. 3 4/7 = _____
2. 5 3/8 = _____
3. 14 6/9 = _____
4. 11 2/11 = _____
The solution for each of these practice problems
is shown below:
1. 3 4/7 = 7 x73 + 4 = 21 +7 4 = 25/7
To check this improper fraction, do this: 25/7
(or 25 divided by 7) = 3 4/7.
2. 5 3/8 = 8 x85 + 3 = 408+ 3 = 43/8
To check this improper fraction, do this: 43/8
(or 43 divided by 8) = 5 3/8.
3. 14 6/9 = 14 x99 + 6 == 1269+ 6 = 132/9
To check this improper fraction, do this:
132/9 (or 132 divided by 9) = 14 6/9.
4. 11 2/11 = 11 x1111 + 2 = 12111+ 2 = 123/11
To check this improper fraction, do this:
123/11 (or 123 divided by 11) = 11 2/11.
Decimals
Decimals are another way of expressing a
proper fraction, an improper fraction and mixed
numbers. Deci means 10, and all decimals are
based on the system of tens or the “power of
ten.” For example, 0.7 is 7 tenths; 8.13 is 8 and
13 hundredths; likewise, 9.546 is 9 and 546
thousandths.
Below is a chart that shows the meaning of
decimal places:
Decimal
places
Meaning
Example and
equivalent
1
Tenths
2.3 = 2 and 3 tenths
2
Hundredths
21.98 = 21 and 98
hundredths
3
Thousandths
0.985 = 985
thousandths
4
Tenthousandths
2.4444 = 2
and 4,444 tenthousandths
5
Hundredthousandths
0.77777 =
77,777 hundredthousandths
When the decimal point is preceded with a zero,
the number is less than 1; when there is a whole
number before the decimal point, the number
is more than one or equal to one. Numbers
with decimal points are readily converted into
fractions and mixed numbers. For example:
Page 2
For example, if the number in the third place after
the decimal, or thousandths place, is an 8, which
is greater than 5, then you round up the number
in the hundredths place by 1. For example,
45.758 is rounded to the nearest hundredth, or
45.76, because the 8 in the thousandths place is
greater than 5. Likewise, if you are rounding off
to the nearest tenth, you look at the number in
the hundredths place to see whether it is greater
than 5. For example, 6.2346 is rounded off to 6.2
because the 3 in the hundredths place is not more
than 5 or equal to 5.
Now, here are some numbers rounded off to the
nearest tenth. Remember, if the hundredths place,
or second number after the decimal, is 5 or more,
the tenths place is increased by 1, and if the
second number after the decimal is less than 5,
the number in the tenths place remains the same.
In these examples, the bolded number in the
hundredths place (2 numbers after the decimal)
is the one that determines whether the number
in the tenths place (the first number after the
decimal) moves up 1 or remains the same.
3.44 = 3.4
0.78 = 0.8
0.66 = 0.7
0.99 = 1.0
Here are some numbers rounded off to the nearest
hundredth. Again, the bold numbers are the ones
you have to scrutinize to see whether they are
equal to or less than 5, or greater than 5:
3.456 = 3.46
0.754 = 0.75
0.766 = 0.77
1.999 = 2.00
Practice problems: Rounding off decimals
Round off these numbers to the nearest tenth:
1. 4.5678 = _____
2. 12.087 = _____
3. 88.999 = _____
4. 65.123 = _____
5. 26.656 = _____
Answers to practice problems: Rounding
decimals to the nearest tenth
1. 4.5678 is rounded to 4.6 because the number
in the hundredths place is more than 5.
2. 12.087 is rounded to 12.1 because the number
in the hundredths place is more than 5.
3. 88.999 is rounded to 89.0 because the number
in the hundredths place is more than 5.
4. 65.123 is rounded to 65.1 because the number
in the hundredths place is less than 5.
5. 26.656 is rounded to 26.7 because the number
in the hundredths place is 5.
Elite
Now, round off these numbers to the nearest
hundredth:
1. 4.5678 = _____
2. 12.087 = _____
3. 88.999 = _____
4. 65.123 = _____
5. 26.656 = _____
Lowercase Roman numerals are used in this
system of measurement, and these Roman
numerals follow the unit of measurement. For
example, 4 grains is written as 4 iv.
Answers to practice problems: Rounding
decimals to the nearest hundredth
1. 4.5678 is rounded to 4.57 because the number
in the thousandths place is more than 5.
2. 12.087 is rounded to 12.09 because the
number in the thousandths place is more than
5.
3. 88.999 is rounded to 89.00 because the
number in the thousandths place is more than
5.
4. 65.125 is rounded to 65.13 because the
number in the thousandths place is 5.
5. 26.656 is rounded to 26.66 because the
number in the thousandths place is 5 or more.
The metric system of measurement
The household system of measurement
The household measurement system
The apothecary system table shows the weight
and volume apothecary system measures and
their approximate equivalents.
The metric system is the most commonly used
measurement system in pharmacology. It is used
all over the world. Understanding the metric
system and being able to convert between units
of measurements is critical when working in the
pharmacy.
Volume measurements are liters (L), cubic
milliliters (ml) and cubic centimeters (cc). This
system’s volume measurements are used for oral
medications, such as cough syrups, and with
parenteral drug dosages used intramuscularly,
subcutaneously and intravenously.
The units of weight in this system include
kilograms (kg), grams (g), milligrams (mg) and
micrograms (mcg).
Unit of
measurement
Approximate equivalents
1 teaspoon
3 teaspoons = 1 tablespoon
60 drops
5 mL
1 tablespoon
1 tablespoon = 3 teaspoons
15 mL
1 liquid ounce
1 fluid ounce = 2 tablespoons
30 mL
1 ounce
(weight)
16 ounces = 1 pound
30 g
1 cup
8 ounces
16 tablespoons
240 mL
1 pint
2 cups
480 mL
1 quart
2 pints
4 cups
1 liter
1 gallon
4 quarts
In pharmacology, there are three systems
8 pints
of measurement. These systems include the
The metric system table displays the metric
3,785 mL
household measurement system, the metric
system and the apothecary system. The household length, volume and weight measurements and
1 pound
16 ounces
their equivalents.
measurement system is more often used in the
480 g
outpatient setting, like a local pharmacy, rather
The apothecary system
than within medical settings. It is the least precise
Weight
Approximate equivalents
Volume
Approximate equivalents
and exact of all the measurement systems.
1 grain
Weight of a grain of wheat
1 minim
Quantity of water in a drop
The household system is the system that most
(gr)
60
mg
or 1 grain
of us use at home, usually in the kitchen. The
household system uses measurements for drops,
teaspoons, tablespoons, ounces, cups, pints, quart,
gallons, and pounds.
1 scruple
20 grains (gr xx)
1 fluid dram 60 minims
1 dram
3 scruples
1 fluid
ounce
8 fluid drams
There are some similarities between the
household measurements and the apothecary
system. For example, a fluid ounce is the same
in both systems. There are some differences
as well, for example, the ounce that is used to
determine weight is different in these systems. In
the apothecary system, there are 12 ounces in a
pound, whereas 16 ounces makes up a household
system pound.
1 ounce
8 drams
1 pint
16 fluid ounces
1 pound
12 ounces
1 quart
2 pints
1 gallon
4 quarts
The household measurement system table
displays household units of measurement and
their approximate equivalents.
The apothecaries system of measurement
The apothecary system of measurement is one
of the oldest forms of measurement. In the
1970s, the United States practically abolished
this system, but some physicians still use it, so it
is important to be educated on this system even
though it is rare and less commonly used than the
metric system.
The metric system
Length
Equivalent
Volume
Equivalent
Weight
Equivalent
1 millimeter
(mm)
0.001 meter
1 milliliter
(mL)
0.001 liter
1 milligram
(mg)
0.001 gram (g)
1 centimeter
(cm)
0.01 meter
1 centiliter (cl)
0.01 liter
1 centigram
(cg)
0.001 gram (g)
1 decimeter
(dm)
0.1 meter
1 deciliter (dl)
0.1 liter
1 decigram
(dm)
0.1 gram (g)
1 kilometer
(km)
1,000 meters
1 kiloliter (kl)
1,000 liters
1 kilogram (kg)
1,000 grams (g)
1,000
1 liter
milliliters (mL)
1 kilogram (kg)
2.2 pounds (lbs)
1 milliliter
(mL)
cubic
centimeter
(cc)
1 pound (lb)
43,592
milligrams (kg)
1 centimeter
(cm)
10 milliliters
(mL)
1 centiliter
(cl)
1 pound (lb)
45,359.237
centigrams (cm)
1 pound (lb)
4,535.9237
decigrams (dg)
In the apothecary system, the basic measurement
of weight is the grain (gr). The other forms of
measurement for weight in this system include
the scruple, the dram, the ounce and the pound.
10 millimeters
(mm)
For volume, the basic unit of measurement is the
minim (m). This is equivalent to the amount of
water in a drop, which is also equal to 1 grain.
Other measurements for volume include a fluid
dram, a fluid ounce, a pint, a quart and a gallon.
10 centimeters 1 decimeter
(cm)
(dm)
10 centiliters
(cl)
1 deciliter
(dl)
10,000
decimeters
(dm)
10,000
deciliters (dc)
1 kiloliter
(kl)
1 kilometer
(km)
Elite
Page 3
called dimensional analysis. The remainder
of this course will teach you about ratio and
Pharmacy technicians often have to convert from proportion and ways to precisely calculate all
one measurement system to another. For example, types of dosages.
if the doctor has ordered a medication in terms of A ratio is two or more pairs of numbers that are
grains (gr) and you have the medication but it is
compared in terms of size, weight or volume. For
measured in terms of milligrams (mg), you will
example, the ratio of women less than 20 years of
have to mathematically convert the grains into
age compared to those over 20 years of age who
milligrams.
attend a specific college can be 6 to 1. This means
Converting between measurement
systems
The table below shows conversion equivalents
among the metric, apothecary and household
measurement systems.
that there are six times as many women less than
20 years old as there are women over 20 years of
age.
Conversions among the systems of
measurement
There are a couple of different ways that ratios
can be written. These different ways are listed
below.
1/6
1:6
1 to 6
Metric
Apothecary
Household
1 milliliter
15-16 minims
15-16 drops
4-5 milliliters
1 fluid dram
1 teaspoon or
60 drops
15-16
milliliters
4 fluid drams
1 tablespoon
or 3-4
teaspoons
30 milliliters
8 fluid drams
or 1 fluid
ounce
2 tablespoons
240-250
milliliters
8 fluid ounces
or 1/2 pint
1 glass or cup
In this problem, you have to determine how many
tablets the patient will take if the doctor orders
500 mg a day and the tablets are manufactured in
tablets of 250 mg.
32 fluid
ounces or 1
quart
4 glasses,
4 cups or 1
quart
1 milligram
1/60 grain
60 milligrams
1 grain
On the other hand, 2/5 and 8/11 do not make a
ratio because 8 x 5 (40) is not equal to 11 x 2
(22).
300-325
milligrams
5 grains
Calculating proportions
1 gram
15-16 grains
The most frequently used conversions are
shown below. It is suggested that you memorize
these. If at any point you are not sure of a
conversion factor, look it up. Do NOT under any
circumstances dispense or prepare a medication
that you are not certain about. Accuracy is
required.
1 Kg = 1,000 g
1 Kg = 2.2 lbs
1 L = 1,000 mL
1 g = 1,000 mg
1 mg = 1,000 mcg
1 gr = 60 mg
1 oz. = 30 g or 30 mL
1 tsp = 5 mL
1 lb = 454 g
1 tbsp = 15 mL
Ratio and proportion
The ratio and proportion method is the
most popular method to calculate dosages
and solutions. Other methods include the
memorization of a number of rules, which are
often forgotten, and a simple, no-rules method
Answers to practice problems: Ratio and
proportion
1. 5/15 = 20/?
15 x 20 = 300; 300 ÷ 5 = 60
2. 8/? = 7/22
8 x 22 = 176; 176 ÷ 7 = 25.14
3. 66/36 = ?/12
66 x 12 = 792; 792 ÷ 36 = 22
4. ?/6 = 43/53
43 x 6 = 258; 258 ÷ 53 = 4.87
5. 4/3 = 9/?
9 x 3 = 27; 27 divided by 4 = 6.75
Because both multiplication calculations yielded
32, this is a ratio.
1 liter
The 10 most frequently used conversions
5/15 = 20/?
8/? = 7/22
66/36 = ?/12
?/6 = 43/53
4/3 = 9/?
Calculating oral dosages with ratio and
proportion
2 glasses or 2
cups
2.2 pounds
1.
2.
3.
4.
5.
When comparing ratios, they should be written
as fractions. The fractions must be equal. If they
are not equal, they are not considered a ratio.
For example, the ratios 2/8 and 4/16 are equal
and equivalent. To prove they are equal, simply
write down the ratios and cross multiply both the
numerators and the denominators. The answer for
both of these would be the same. For example,
you can cross multiply the 2 and 16 as well as the
4 and 8 with this ratio of 2/8 and 4/16:
2 x 16 = 32
8 x 4 = 32
500 milliliters 1 pint
1 kilogram
Practice problems: Ratio and proportion
Proportions are used to calculate how one part
is equal to another part or to the whole. For
these calculations, you cross multiply the known
numbers and then divide this product of the
multiplication by the remaining number to get the
unknown number.
For example:
2/4 = ?/12
Method 1:
12 x 2 = 24
24/4 or 24 ÷ 4 = 6
Answer: 6 is the unknown, so the final
equation will look like this:
2/4 = 6/12
Method 2:
1. 2/4 = ?/12
You can reduce the first fraction by 2
to make the calculation a little easier.
2. 1/2 = ?/12
12 x 1 = 12
12 ÷ 2 = 6
Answer: 6 is the unknown, so the final
equation will look like this:
2/4 = 6/12
Page 4
Oral dosages are calculated in a number of
different ways, including using ratio and
proportion. Using the same techniques that
you just learned for ratio and proportions, you
will now learn how to accurately calculate oral
dosages using this method.
Doctor’s order: 500 mg of medication once a
day
Medication label: 1 tablet = 250 mg
How many tablets should be administered daily?
This problem can be set up and calculated like
this.
500 mg: X tablets = 250 mg: 1 tablet
or
500 mg = 250 mg
x
1 tablet
Then you cross multiply: 500 mg x 1 = 500
mg
250 X = 500 mg
X = 500 mg/250 mg
500 ÷ 250 = 2 tablets
Answer: 2 tablets
Now, if you were working in a medical center
that uses unit dosage, you would deliver two
tablets of this medication each day. If, however,
the doctor wants the outpatient to take 500 mg
per day for 30 days, you would dispense 60
tablets, as shown below.
Daily dosage = 2 tablets x 30 days = 60 tablets
Doctor’s order: Tetracycline syrup 300 mg po
once daily
Medication label: Tetracycline syrup 50 mg/mL
How many mL should be administered per day?
For this oral dosage problem, you have to find
out how many mL of tetracycline the patient will
get when the doctor has ordered 300 mg and the
syrup has 50 mg/ml.
Elite
This problem is set up and calculated as shown
below.
300 mg: X mL = 50 mg: 1 mL
or
300 mg = 50 mg
x mL
1 mL
50 X = 300
X = 300/50
300 ÷ 50 = 6 mL
Answer: 6 mL
And if, for example, the doctor had ordered
this dosage two times a day for 10 days for an
outpatient, in addition to the above calculation,
you also would perform the following
calculation:
6 mL (per dose) x 2 (times per day) = 12 mL
each day. This client would have a total of 12
mL per day in two equal doses of 6 mL each.
Because the doctor ordered 300 mg po
two times a day for 10 days, you would
additionally perform the below calculation:
12 mL per day x 10 days = 120 mL
You would dispense 120 mL of the
medication with instructions that the client
take 6 mL two times per day for 10 days.
Practice problems: Oral dosages using
ratio and proportion
Problem 1:
Doctor’s order: Gantrisin 500 mg po
Medication label: Gantrisin 1 g/tablet
How many tablets should be administered?
Problem 2:
Doctor’s order: Trimethoprin 2.5 mg/kg po
Patient’s weight: 40 kg
Medication label: Trimethoprin 80 mg/tablet
How many tablets should be administered?
Problem 3:
Doctor’s order: Nystatin 6 mg/kg po
Patient’s weight: 230 lbs
Medication label: Nystatin 200 mg/tablet
How many tablets should be administered?
Answers to practice problems: Oral
dosages using ratio and proportion
Problem 1:
Doctor’s order: 500 mg po
Medication label: Gantrisin 1 g/tablet
How many tablets should be administered?
The next step is to calculate what dose, in grams,
should be administered.
x= 500/1000 = 1/2
Answer: 1/2 tablet
Problem 2:
Doctor’s order: Trimethoprin 2.5 mg/kg po
Patient’s weight: 40 kg
Medication label: Trimethoprin 80 mg/tablet
How many tablets should be administered?
This is another two-part question. First you
calculate the number of milligrams to be
administered based on the weight of the patient.
You know that the doctor ordered 2.5 mg/kg po
and the patient weighs 40 kg.
40 kg
x mg
=
1 kg
2.5 mg
X = 40 × 2.5
X = 100 mg will be given
In the next step, you have to calculate the number
of tablets that the patient will be given based
on the patient’s weight and that the doctor has
ordered 2.5 mg for each kg of body weight.
100 mg
x tablet
=
80 mg
1 tablet
80 X = 100
X = 100/80
100 ÷ 80 = 1.25 tablets
Answer: 11/4 tablets
Problem 3:
Doctor’s order: Nystatin 6 mg/kg po
Patient’s weight: 230 lbs
Medication label: Nystatin 200 mg/tablet
This problem has three steps. In the first step, you
calculate the patient’s weight in kilograms. There
are 2.2 pounds in each kilogram, so this problem
is set up as below.
230 lbs = 2.2 lbs
1 kg
x kg
2.2 X = 230 kg
X = 230/2.2
230 ÷ 2.2 = 104.55 kg
Round off the patient’s weight to 105 kg because
the number in the tenths place is 5 or more.
You then have to calculate the dosage of the
medication, based on the patient’s weight of 105
kg.
105 kg
x mg
=
1 kg
6 mg
This is a two-step problem. The first step
calculates the number of grams equal to the 500
mg dose. This is done because the drug label is
written in grams, and the doctor’s order is written
in mg. What you do know, however, is that there
are 1,000 mg in 1 g.
105 × 6 = 630 mg
Below is how you set this up to find out how
many grams are equal to 500 mg.
500 mg = 1000 mg
g
1g
200 X = 630
X = 630/200
630 ÷ 200 = 3.1 tablets; rounded off to 3 tablets
When you cross multiply, you will get 1000 X =
500 x 1, and then you set this up:
X = 500/1000
X = 1/2 g
1/2 g = 0.50 g is equal to 500 mg
In the last step, you have to calculate how many
tablets will be administered when each tablet is
200 milligrams.
x tablets
630 mg
tablet
= 1200
mg
Answer: 3 tablets
Calculating intramuscular and
subcutaneous dosages with ratio and
proportion
The process for calculating intramuscular and
subcutaneous dosages is practically identical to
Elite
that of calculating oral dosages using ratio and
proportion.
Doctor’s order: Meperidine 20 mg IM q4h prn
for pain
Medication label: Meperidine 60 mg/mL
How many mL or cc will you give?
Using ratio and proportion, this problem is set up
and solved as shown below.
20 mg = 60 mg
x
1 mL
60 X = 20 x 1
x = 20/60
20 ÷ 60 = 0.33 mL, which rounded off to the
nearest tenth is 0.3 mL
Answer: 0.3 mL
Here is another example:
Doctor’s order: Amikacin 10 mg/kg IM tid
Patient’s weight: 230 lbs
Medication label: 250 mg/1 mL
How many milliliters need to be administered?
For the first step, you calculate the patient’s
weight in kilograms.
239 lbs = 2.2 lbs
Xkg
1 kg
2.2 X = 230
X = 230/2.2
230 ÷ 2.2 = 104.54 kg
The patient’s weight can be rounded off to 105 kg
because the tenths place (5) is equal to or more
than 5.
The next step is to figure out how many milliliters
the patient will get in each of the three doses per
day.
10 mg
X mg
= 105
1 kg
kg
1 X = 105 × 10
105 × 10 = 1050 mg
In the final step, you will need to calculate how
many milliliters are needed to administer the
ordered number of milligrams.
250 mg = 1050 mg
1 mL
X mL
250 X = 1050 = 1050/250
1050 ÷ 250 = 4.2 mL
Answer: 4.2 mL
Now, let’s do this one together:
Doctor’s order: Heparin 2,500 units
subcutaneously
Medication label: 5,000 units/mL
How many milliliters will be administered for
this patient?
X mL
2,500 Units
1 mL
= 5,000 Units
5,000 X = 2,500
X = 2,500/5,000
2,500 ÷ 5,000 = 0.5
Answer: 0.5 mL
And one more:
Doctor’s order: Ticarcillin 300 mg IM
Medication label: Ticarcillin reconstituted with
2 mL of sterile water to yield 1 g of Ticarcillin in
2.6 mL of solution
How many milliliters need to be administered?
Page 5
For these kinds of problems, the information
about how much sterile water is added for
reconstitution is not used in the calculation. What
is, however, used in the calculation is how many
grams are yielded after the sterile water has been
added. In this case, 1 g is contained in every 2.6
mL. You will be doing these types of calculations
when you are adding medications to intravenous
fluids (admixtures), particularly when you are
doing IV piggybacks in an acute care setting.
The first step is to find out how many g there are
in 300 mg:
300 mg = 1000 mg
xg
1g
1000 X = 300
X = 300/1000
300 ÷ 1000 = 0.3 g
The next step is to determine how many mL will
be administered when the ordered dosage is 300
mg or 0.3 g
0.3 g = 1 g
x mL
2.6 mL
X = 0.3 × 2.6
0.3 × 2.6 = 0.78 mL
Rounded off to: 0.8 mL
Answer: 0.8 mL
Practice problems: Intramuscular and
subcutaneous dosages using ratio and
proportion
Problem 1:
Doctor’s order: Neomycin 40 mg/kg/day IM in
3 divided doses
Patient’s weight: 160 lbs
Medication label: Neomycin 250 mg/mL
How many milliliters are needed for each of the
three daily doses?
Problem 2:
Doctor’s order: Heparin 2000 units
subcutaneously
Medication label: 3500 units/mL
How many milliliters would this patient need to
have administered?
Problem 3:
Doctor’s order: Ceruroxime 250 mg IM
Medication label: The addition of 3.2 mL of
sterile water yields a suspension of 750 mg in 4.2
mL
How many milliliters need to be administered in
this case?
Problem 4:
Doctor’s order: Cephalothin 200 mg IM
Medication label: The addition of 4 mL of sterile
water yields 0.5 g in 2.2 mL of suspension
How many milliliters would you administer in
this situation?
Problem 5:
Doctor’s order: Neomycin 40 mg/kg/day IM in
3 doses
Patient’s weight: 240 lbs
Medication label: Neomycin in 500 mg/mL
How many milliliters should be given?
Problem 6:
Doctor’s order: 250,000 Units of Ampicillin
Medication Label: 50,000 units/mL
How many milliliters should be administered to
this patient?
Answers to the practice problems:
Intramuscular and subcutaneous dosages
using ratio and proportion
Problem 1:
Doctor’s order: Neomycin 40 mg/kg/day IM in
3 divided doses
Patient’s weight: 160 lbs
Medication label: Neomycin 250 mg/mL
How many milliliters are needed for each of the
three daily doses?
This, again, is a three-step problem. In the first
step, you will find out the patient’s weight in
kilograms.
160 lbs = 2.2 lbs
x kg
1 kg
2.2 X = 160
X = 160/2.2
160 ÷ 2.2 = 72.72 kg
Patient’s weight can be rounded off to 73 kg.
In step two, you will figure out how many mg
there are in the total daily dosage.
40 mg
1 kg
=
x mg
73 kg
X = 73 × 40
73 × 40 = 2920 mg
The medication label states that there are 250 mg/
mL, so you will now calculate how many mL the
patient will get.
250 X = 2920
X = 2920/250
2920 × 250 = 11.68 mL
The final step for this problem is to calculate
each dosage based on a total of 11.68 mL in three
divided doses.
11.68 ÷ 3 = 3.89
The dosage can be rounded to 3.9 mL per dose,
and the patient will get this dose three times per
day
Answer: 3.9 mL per dose
Problem 2:
Doctor’s order: Heparin 2000 units
subcutaneously
Medication label: 3500 units/mL
How many milliliters would this patient need to
have administered?
2,000 units
X mL
=
3,500
1 mL
3500 X = 2000
X = 2000/3500
2000 ÷ 3500 = 0.57 mL
This dosage can be rounded off to 0.60 mL or 0.6
mL
Answer: 0.6 mL
Page 6
Problem 3:
Doctor’s order: Ceruroxime 250 mg IM
Medication label: The addition of 3.2 mL of
sterile water yields a suspension of 750 mg in 4.2
mL
How many milliliters should be dispensed?
250 mg
X mL
=
750 mg
4.2 mL
750 X = 250 × 4.2
750 X = 1050
X = 1050/750
1050 ÷ 750 = 1.4 mL
Answer: 1.4 mL
Problem 4:
Doctor’s order: Cephalothin 200 mg IM
Medication label: The addition of 4 mL of sterile
water yields 0.5 g in 2.2 mL of suspension
How many milliliters would you administer in
this situation?
200 mg
xg
=
1000 mg
1g
1000 X = 200
X = 200/1000
200 ÷ 1000 = 0.2 g
0.5 g
0.2 g
X mL
= 2.2 mL
0.5 X = 0.2 × 2.2 mL
0.5 X = 0.44
X = 0.44/(0.5 )
0.44 ÷ 0.5 = 0.88, which is rounded off to 0.9 mL
Answer: 0.9 mL
Problem 5:
Doctor’s order: Neomycin 40 mg/kg/day IM in
3 doses
Patient’s weight: 240 lbs
Medication label: Neomycin in 500 mg/mL
How many milliliters should be given?
240 lbs
Xg
=
2.2 lbs
1 kg
2.2 X = 240
240/2.2
240 ÷ 2.2 = 109.09 kg
Rounded off to 109 kg
109 kg
x mg
=
1 kg
40 mg
109 x 40
X=
1
109 × 40 = 4360
4360
X mL
=
500 mg
1 mL
500 X = 4360
4360/500
4360 ÷ 500 = 8.72
Rounded off to 8.7 mL
8.7 ÷ 3 doses = 2.9 mL for each of the three doses
Answer: 2.9 mL
Problem 6:
Doctor’s order: 250,000 units of Ampicillin
Medication label: 50,000 units/mL
How many milliliters should be administered to
this patient?
250,000 units
X mL
=
50,000 units
X mL
Elite
50,000 X = 250,000
X = 250,000/50,000
250,000 ÷ 50,000 = 5 mL
Answer: 5 mL
Calculating intravenous flow rates with
ratio and proportion
The rule for intravenous flow rates is:
gtts/min = Total number of mL × Drip or drip factor
Total number of minutes
Now, here is how it is set up and calculated:
Doctor’s order: 0.9% MaCl solution at 50 mL
per hour
How many gtts per minute should be
administered if the tube delivers 20 gtt/mL?
x 20
X gtts per min = 5060
= 1000/60 = 16.6 gtt
Rounded off to 17 gtt/min
Here’s another example:
Doctor’s order: 500 mL of 5% D 0.45 normal
saline solution to infuse over 3 hours
How many gtt per minute should be given if the
tubing delivers 10 gtt/mL?
x 10
X gtts per minute = 500180
= 5000/180
5000 ÷ 180 = 27.7 gtt
Rounded off to 28 gtts per minute
Answer: 28 gtts/min
And now, here is one more:
Doctor’s order: 15 mL/h of 5% DO 0.45 normal
saline solution
How many gtt per minute should be administered
if the tubing delivers 60 gtt/mL?
15 x 60
X gtts per minute = 60 = 900/60 = 15 gtt
The answer is 15 gtts/min
Practice problems: Intravenous
medications
Problem 1:
Doctor’s order: 50 mL/h
How many gtt per minute should be administered
if the tubing is 60 gtt/mL?
Problem 2:
Doctor’s order: 75 mL/h
How many gtt per minute should be administered
if the tubing is 10 gtt/mL?
Problem 3:
Doctor’s order: 300 mL/h
How many gtt per minute should be administered
if the tubing is 20 gtt/mL?
Problem 4:
Doctor’s order: 40 mL/h
How many gtt per minute should be administered
if the tubing is 60 gtt/mL?
Problem 5:
Doctor’s order: 300 mL/h
How many gtt per minute should be administered
if the tubing is 30 gtt/mL?
Answers to the practice problems:
Intravenous medications
This course has provided you with the
knowledge, skills and abilities to prepare and
dispense oral, intramuscular, subcutaneous, and
intravenous medications and solutions in an
accurate and precise manner using the ratio and
proportion method.
x 60 = 50 gtt (This fraction
X gtts per min = 5060
was reduced by 60)
As always, check and double-check your
calculations, and consult resources, both human
and written, whenever you are not sure and
certain about the accuracy of your mathematical
calculations.
Problem 1:
Doctor’s order: 50 mL/h
How many gtt per minute should be administered
if the tubing is 60 gtt/mL?
Answer: 50 gtt/min
Problem 2:
Doctor’s order: 75 mL/h
How many gtt per minute should be administered
if the tubing is 10 gtt/mL?
x 10
X gtts per min = 7560
= 75/6
75 ÷ 6 = 12.5, which is rounded off to 13 gtt
because the tenths place is 5 or more
(Final examination on next page)
Answer: Rounded to: 13 gtt/min
Problem 3:
Doctor’s order: 300 mL/h
How many gtt per minute should be administered
if the tubing is 20 gtt/mL?
300 x 20
60 = 6000/60
6000 ÷ 60 = 100 gtt
Answer: 100 gtt/min
Problem 4:
Doctor’s order: 40 mL/h
How many gtt per minute should be administered
if the tubing is 60 gtt/mL?
x 60 = 2400/60
X gtts per min = 4060
2400 ÷ 60 = 40
Answer: 40 gtt/min
Problem 5:
Doctor’s order: 300 mL/h
How many gtt per minute should be administered
if the tubing is 10 gtt/mL?
X gtts per min = 30060X 10
3000 ÷ 60 = 50
Answer: 50 gtt/min
Conclusion
Pharmacology is a precise science. Medical
errors, including medication errors, can lead to
disastrous results. Medication errors can occur
at any point of this complex multidisciplinary
process.
For example, medication errors can occur as
the result of an incorrect or illegible doctor’s
order; they can occur during the preparation and
dispensing of the medication; and they can also
occur at the point of administration.
It is the professional responsibility of the
pharmacology technician to insure that NO
errors occur in the preparation and dispensing
of medications. Pharmacy technicians must
check the doctor’s order for completeness and
correctness; they must validate that the patient
is not allergic to the ordered medication; they
must determine whether there are any drug
interactions; and they must also ensure that
the dosage is accurately prepared, labeled and
dispensed.
Elite
Page 7
CAlculation of dosages and
solution RATES USING RATIO AND
PROPORTION
Final Examination Questions
Choose the best answer for questions
1 through 10 and mark your answers on the
Final Examination Sheet found on page 19
or complete your test online at
www.elitecme.com.
1. Round 23.6547 to the nearest hundredth.
a. 23.7
b. 23.66
c. 2.36
d. 23.6
2. Round 1.978 to the nearest tenth.
a. 1.98
b. 1.97
c. 2
d. 1.979
3. Which of the following is equivalent to 1
fluid dram?
a. 60 drops
b. 2 teaspoons
c. 10 mL
d. 20 mL
4. Select the accurate conversion.
a. 2.2 lbs = 1 Kg
b. 1 g = 1,000 mg
c. 60 gr = 1 mg
d. 1 oz. = 20 mL
8. The doctor has ordered an oral tablet of a
medication. The order states that the patient
will get 3 mg/kg and the patient weighs
130 pounds. How many total tablets will
be delivered to the nursing unit into the
patient’s unit dose cassette for 24 hours if
this dosage is given 3 times per day and the
label on the medication states that there are
120 mg per tablet?
a. 4
b. 4.5
c. 5
d. 5.5
NOTES
9. The doctor has ordered 40 mg/kg/day in 2
equally divided doses. The patient weighs
80 pounds and the medication label states
that there are 250 mg/mL. How many mL
will the patient get in each dose?
a. 2 mL
b. 2.5 mL
c. 0.3 mL
d. 3 mL
10. The doctor has order 500 mg of an
antibiotic to run over one hour. You have
mixed the antibiotic into 250 mL of
normal saline. How many drops should be
administered per minute if the nurses use a
10 gtt/mL intravenous set?
a. 83 gtt/min
b. 20 gtt/min
c. 42 gtt/min
d. 40 gtt/min
5. Which statement about a ratio is correct?
a. A ratio is always more than one.
b. A ratio is always less than one.
c. A ratio is two or more pairs of numbers
that are compared in terms of size,
weight or volume.
d. It is a whole number and a fraction.
6. Solve this equation for X: 27/100 = x/12
a. 3.24
b. 32.4
c. 44.4
d. 225
7. You are working in a local outpatient
pharmacy. The doctor calls in an order for
a liquid cough medicine. The doctor has
ordered 40 mg po two times a day for 10
days. How many mLs will you dispense
when there are 20 mg per mL?
a. 20
b. 10
c. 200
d. 40
RPTVA03CDE13
Page 8
Elite