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Chapter 5

Basic Pharmaceutical Measurements and

Calculations

Learning Objectives

- Describe four systems of measurement commonly

used in pharmacy, and be able to convert units

from one system to another. - Explain the meanings of the prefixes most

commonly used in metric measurement. - Convert from one metric unit to another (e.g.,

grams to milligrams). - Convert Roman numerals to Arabic numerals.

Learning Objectives

- Distinguish between proper, improper, and

compound fractions. - Perform basic operations with fractions,

including finding the least common denominator

converting fractions to decimals and adding,

subtracting, multiplying, and dividing fractions.

Learning Objectives

- Perform basic operations with proportions,

including identifying equivalent ratios and

finding an unknown quantity in a proportion. - Convert percents to and from fractions and

ratios, and convert percents to decimals. - Perform elementary dose calculations and

conversions. - Solve problems involving powder solutions and

dilutions. - Use the alligation method.

SYSTEMS OF PHARMACEUTICAL MEASUREMENT

- Metric System
- Common Measures
- Numeral Systems

BASIC MATHEMATICS USED IN PHARMACY PRACTICE

- Fractions
- Decimals
- Ratios and Proportions

COMMON CALCULATIONS IN THE PHARMACY

- Converting Quantities between the Metric and

Common Measure Systems - Calculations of Doses
- Preparation of Solutions

SYSTEMS OF PHARMACEUTICAL MEASUREMENT

- Metric System
- Common Measures
- Numeral Systems

Measurements in the Metric System

- (a) Distance or length
- (b) Area
- (c) Volume

Système International Prefixes

Table 5.1

Common Metric Units Weight

Table 5.2

Table 5.2

Common Metric Units Length

Table 5.2

Common Metric Units Volume

Measurement and Calculation Issues

Safety Note!

It is extremely important that decimals be

written properly. An error of a single decimal

place is an error by a factor of 10.

Common Metric Conversions

Table 5.3

Common Metric Conversions

Table 5.3

Apothecary Symbols

Table 5.4

Apothecary System Volume

Table 5.5

In reality, 1 fZ contains 3.75 mL however that

number is usually rounded up to 5 mL or one

teaspoonful In reality, 1 f?, contains 29.57 mL

however, that number is usually rounded up to 30

mL.

Apothecary System Weight

Table 5.5

Measurement and Calculation Issues

Safety Note!

For safety reasons, the use of the apothecary

system is discouraged. Use the metric system

instead.

Avoirdupois System

Table 5.6

- In reality, an avoirdupois ounce actually

contains 28.34952 g however, we often round up

to 30 g. It is common practice to use 454 g as

the equivalent for a pound (28.35 g 16 oz/lb

453.6 g/lb, rounded to 454 g/lb).

Household Measure Volume

Table 5.7

- In reality, 1 fl oz (household measure)

contains less than 30 mL however, 30 mL is

usually used. When packaging a pint, companies

will typically present 473 mL, rather than the

full 480 mL, thus saving money over time.

Household Measure Weight

Table 5.7

Measurement and Calculation Issues

Safety Note!

New safety guidelines are discouraging use of

Roman numerals.

Comparison of Roman and Arabic Numerals

Table 5.8

Terms to Remember

BASIC MATHEMATICS USED IN PHARMACY PRACTICE

- Fractions
- Decimals
- Ratios and Proportions

Fractions

- When something is divided into parts, each part

is considered a fraction of the whole.

Fractions

- When something is divided into parts, each part

is considered a fraction of the whole. - If a pie is cut into 8 slices, one slice can be

expressed as 1/8, or one piece (1) of the whole

(8).

Fractions of the Whole Pie

Fractions

- If we have a 1000 mg tablet,
- ½ tablet 500 mg
- ¼ tablet 250 mg

Terminology

fraction

a portion of a whole that is represented as a

ratio

Fractions

Fractions have two parts,

Fractions

- Fractions have two parts,
- Numerator (the top part)

Fractions

- Fractions have two parts,
- Numerator (the top part)
- Denominator (the bottom part)

Terminology

numerator

the number on the upper part of a fraction

Terminology

denominator

the number on the bottom part of a fraction

Fractions

A fraction with the same numerator and same

denominator has a value equivalent to 1. In

other words, if you have 8 pieces of a pie that

has been cut into 8 pieces, you have 1 pie.

Discussion

- What are the distinguishing characteristics of

the following? - proper fraction
- improper fraction
- mixed number

Remember

The symbol gt means is greater than. The

symbol gt means is less than.

Terminology

proper fraction

- a fraction with a value of less than 1
- a fraction with a numerator value smaller than

the denominators value

Terminology

improper fraction

- a fraction with a value of larger than 1
- a fraction with a numerator value larger than the

denominators value

Terminology

mixed number

a whole number and a fraction

Adding or Subtracting Fractions

- When adding or subtracting fractions with unlike

denominators, it is necessary to create a common

denominator.

Adding or Subtracting Fractions

- When adding or subtracting fractions with unlike

denominators, it is necessary to create a common

denominator. - This is like making both fractions into the same

kind of pie.

Terminology

common denominator

a number into which each of the unlike

denominators of two or more fractions can be

divided evenly

Remember

Multiplying a number by 1 does not change the

value of the number. Therefore, if you

multiply a fraction by a fraction that equals 1

(such as 5/5), you do not change the value of a

fraction.

Guidelines for Finding a Common Denominator

- Examine each denominator in the given fractions

for its divisors, or factors.

Guidelines for Finding a Common Denominator

- Examine each denominator in the given fractions

for its divisors, or factors. - See what factors any of the denominators have in

common.

Guidelines for Finding a Common Denominator

- Examine each denominator in the given fractions

for its divisors, or factors. - See what factors any of the denominators have in

common. - Form a common denominator by multiplying all the

factors that occur in all of the denominators. If

a factor occurs more than once, use it the

largest number of times it occurs in any

denominator.

Example 1 Find the least common denominator of

the following fractions

Step 1. Find the prime factors (numbers divisible

only by 1 and themselves) of each denominator.

Make a list of all the different prime factors

that you find. Include in the list each different

factor as many times as the factor occurs for any

one of the denominators of the given

fractions. The prime factors of 28 are 2, 2, and

7 (because 2 3 2 3 7 5 28). The prime factors of

6 are 2 and 3 (because 2 3 3 5 6). The number 2

occurs twice in one of the denominators, so it

must occur twice in the list. The list will also

include the unique factors 3 and 7 so the final

list is 2, 2, 3, and 7.

Example 1 Find the least common denominator of

the following fractions

Step 2. Multiply all the prime factors on your

list. The result of this multiplication is the

least common denominator.

Example 1 Find the least common denominator of

the following fractions

Step 3. To convert a fraction to an equivalent

fraction with the common denominator, first

divide the least common denominator by the

denominator of the fraction, then multiply both

the numerator and denominator by the result (the

quotient). The least common denominator of 9/28

and 1/6 is 84. In the first fraction, 84 divided

by 28 is 3, so multiply both the numerator and

the denominator by 3.

Example 1 Find the least common denominator of

the following fractions

In the second fraction, 84 divided by 6 is 14, so

multiply both the numerator and the denominator

by 14.

Example 1 Find the least common denominator of

the following fractions

The following are two equivalent fractions

Example 1 Find the least common denominator of

the following fractions

Step 4. Once the fractions are converted to

contain equal denominators, adding or subtracting

them is straightforward. Simply add or subtract

the numerators.

Multiplying Fractions

When multiply fractions, multiply the numerators

by numerators and denominators by denominators.

Multiplying Fractions

When multiply fractions, multiply the numerators

by numerators and denominators by

denominators. In other words, multiply all

numbers above the line then multiply all numbers

below the line.

Multiplying Fractions

When multiply fractions, multiply the numerators

by numerators and denominators by

denominators. In other words, multiply all

numbers above the line then multiply all numbers

below the line. Cancel if possible and reduce to

lowest terms.

Discussion

What happens to the value of a fraction when you

multiply the numerator by a number?

Discussion

What happens to the value of a fraction when you

multiply the numerator by a number? Answer The

value of the fraction increases.

Discussion

What happens to the value of a fraction when you

multiply the denominator by a number?

Discussion

What happens to the value of a fraction when you

multiply the denominator by a number? Answer

The value of the fraction decreases.

Discussion

What happens to the value of a fraction when you

multiply the numerator and denominator by the

same number?

Discussion

What happens to the value of a fraction when you

multiply the numerator and denominator by the

same number? Answer The value of the fraction

does not change because you have multiplied the

original fraction by 1.

Multiplying Fractions

Dividing the denominator by a number is the same

as multiplying the numerator by that number.

Multiplying Fractions

Dividing the numerator by a number is the same as

multiplying the denominator by that number.

Dividing Fractions

To divide by a fraction, multiply by its

reciprocal, and then reduce it if necessary.

Terms to Remember

The Arabic System

The Arabic system is also called the decimal

system.

Terminology

Arabic numbers

The numbering system that uses numeric symbols to

indicate a quantity, fractions, and decimals.

Uses the numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.

The Arabic System

- The decimal serves as the anchor.
- Each place to the left of the decimal point

signals a tenfold increase. - Each place to the right signals a tenfold

decrease.

Decimal Units and Values

Terminology

place value

the location of a numeral in a string of numbers

that describes the numerals relationship to the

decimal point

Terminology

leading zero

a zero that is placed to the left of the decimal

point, in the ones place, in a number that is

less than zero and is being represented by a

decimal value

Decimals

- A decimal is a fraction in which the denominator

is 10 or some multiple of 10. - Numbers written to the right of decimal point lt

1. - Numbers written to the left of the decimal point

gt 1

Example 2 Multiply the two given fractions.

Terminology

decimal

a fraction value in which the denominator is 10

or some multiple of 10

Remember

- Numbers to the left of the decimal point are

whole numbers. - Numbers to the right of the decimal point are

decimal fractions (part of a whole).

Decimal Places

Decimals

- Adding or Subtracting Decimals
- Place the numbers in columns so that the decimal

points are aligned directly under each other. - Add or subtract from the right column to the left

column.

Decimals

- Multiplying Decimals
- Multiply two decimals as whole numbers.
- Add the total number of decimal places that are

in the two numbers being multiplied. - Count that number of places from right to left in

the answer, and insert a decimal point.

Decimals

- Dividing Decimals
- Change both the divisor and dividend to whole

numbers by moving their decimal points the same

number of places to the right. - divisor number doing the dividing, the

denominator - dividend number being divided, the numerator
- If the divisor and the dividend have different

number of digits after the decimal point, choose

the one that has more digits and move its decimal

point a sufficient number of places to make it a

whole number.

Decimals

- Dividing Decimals
- 3. Move the decimal point in the other number the

same number of places, adding zeros at the end if

necessary. - Move the decimal point in the dividend the same

number of places, adding a zero at the end.

Decimals

Dividing Decimals 1.45 3.625 0.4

Decimals

- Rounding Decimals
- Rounding numbers is essential for accuracy.
- It may not be possible to measure a very small

quantity such as a hundredth of a milliliter. - A volumetric dose is commonly rounded to the

nearest tenth. - A solid dose is commonly rounded to the hundredth

or thousandth place, pending the accuracy of the

measuring device.

Decimals

- Rounding to the Nearest Tenth
- Carry the division out to the hundredth place
- If the hundredth place number 5, 1 to the

tenth place - If the hundredth place number 5, round the

number down by omitting the digit in the

hundredth place - 5.65 becomes 5.7 4.24 becomes 4.2

Decimals

Rounding to the Nearest Hundredth or Thousandth

Place 3.8421 3.84 41.2674 41.27 0.3928

0.393 4.1111 4.111

Decimals

Rounding the exact dose 0.08752 g . . . to the

nearest tenth 0.1 g . . . to he nearest

hundredth 0.09 g . . . to the nearest

thousandth 0.088 g

Discussion

When a number that has been rounded to the tenth

place is multiplied or divided by a number that

was rounded to the hundredth or thousandth place,

the resultant answer must be rounded back to the

tenth place. Why?

Discussion

When a number that has been rounded to the tenth

place is multiplied or divided by a number that

was rounded to the hundredth or thousandth place,

the resultant answer must be rounded back to the

tenth place. Why? Answer The answer can only be

accurate to the place to which the highest

rounding was made in the original numbers.

Decimals

- In most cases, a zero occurring at the end of a

digits is not written. - Do not drop the zero when the last digit

resulting from rounding is a zero. Such a zero is

considered significant to that particular problem

or dosage.

Numerical Ratios

- Ratios represent the relationship between
- two parts of the whole
- one part to the whole

Numerical Ratios

- Written with as follows
- 12 1 part to 2 parts ½
- 34 3 parts to 4 parts ¾
- Can use per, in, or of, instead of to

Terminology

ratio

a numerical representation of the relationship

between two parts of the whole or between one

part and the whole

Numerical Ratios in the Pharmacy

1100 concentration of a drug means . . .

Numerical Ratios in the Pharmacy

1100 concentration of a drug means . . . . . .

there is 1 part drug in 100 parts solution

Proportions

- An expression of equality between two ratios.
- Noted by or
- 34 1520 or 34 1520

Terminology

proportion

an expression of equality between two ratios

Proportions

If a proportion is true . . . product of means

product of extremes 34 1520 3 20

4 15 60 60

Proportions

product of means product of extremes

ab cd b c a d

Proportions in the Pharmacy

- Proportions are frequently used to calculate drug

doses in the pharmacy. - Use the ratio-proportion method any time one

ratio is complete and the other is missing a

component.

Terminology

ratio-proportion method

a conversion method based on comparing a complete

ratio to a ratio with a missing component

Rules for Ratio-Proportion Method

- Three of the four amounts must be known.
- The numerators must have the same unit of

measure. - The denominators must have the same unit of

measure.

Steps for solving for x

- Calculate the proportion by placing the ratios in

fraction form so that the x is in the upper-left

corner.

Steps for solving for x

- Calculate the proportion by placing the ratios in

fraction form so that the x is in the upper-left

corner. - Check that the unit of measurement in the

numerators is the same and the unit of

measurement in the denominators is the same.

Steps for solving for x

- Calculate the proportion by placing the ratios in

fraction form so that the x is in the upper-left

corner. - Check that the unit of measurement in the

numerators is the same and the unit of

measurement in the denominators is the same. - Solve for x by multiplying both sides of the

proportion by the denominator of the ratio

containing the unknown, and cancel.

Steps for solving for x

- Calculate the proportion by placing the ratios in

fraction form so that the x is in the upper-left

corner. - Check that the unit of measurement in the

numerators is the same and the unit of

measurement in the denominators is the same. - Solve for x by multiplying both sides of the

proportion by the denominator of the ratio

containing the unknown, and cancel. - Check your answer by seeing if the product of the

means equals the product of the extremes.

Remember

When setting up a proportion to solve a

conversion, the units in the numerators must

match, and the units in the denominators must

match.

Example 3 Solve for x.

Example 3 Solve for x.

Example 3 Solve for x.

Percents

- Percent means per 100 or hundredths.
- Represented by symbol
- 30 30 parts in total of 100 parts,
- 30100, 0.30, or

Terminology

percent

the number of parts per 100 can be written as a

fraction, a decimal, or a ratio

Discussion

If you take a test with 100 questions, and you

get a score of 89, how many questions did you

get correct?

Discussion

If you take a test with 100 questions, and you

get a score of 89, how many questions did you

get correct? Answer 89 89100, 89/100, or

0.89

Percents in the Pharmacy

- Percent strengths are used to describe IV

solutions and topically applied drugs. - The higher the of dissolved substances, the

greater the strength.

Percents in the Pharmacy

- A 1 solution contains . . .
- 1 g of drug per 100 mL of fluid
- Expressed as 1100, 1/100, or 0.01

Percents in the Pharmacy

- A 1 hydrocortisone cream contains . . .
- 1 g of hydrocortisone per 100 g of cream
- Expressed as 1100, 1/100, or 0.01

Safety Note!

The higher the percentage of a dissolved

substance, the greater the strength.

Percents in the Pharmacy

- Multiply the first number in the ratio (the

solute) while keeping the second number

unchanged, you increase the strength. - Divide the first number in the ration while

keeping the second number unchanged, you decrease

the strength.

Equivalent Values

Converting a Ratio to a Percent

- Designate the first number of the ratio as the

numerator and the second number as the

denominator. - Multiply the fraction by 100, and simply as

needed.

Remember

Multiplying a number or a fraction by 100 does

not change the value.

Converting a Ratio to a Percent

51 5/1 100 5 100 500 15 1/5

100 100/5 20 12 1/2 100 100/2

50

Converting a Percent to a Ratio

- Change the percent to a fraction by dividing it

by 100.

Converting a Percent to a Ratio

- Change the percent to a fraction by dividing it

by 100. - Reduce the fraction to its lowest terms.

Converting a Percent to a Ratio

- Change the percent to a fraction by dividing it

by 100. - Reduce the fraction to its lowest terms.
- Express this as a ratio by making the numerator

the first number of the ratio and the denominator

the second number.

Converting a Percent to a Ratio

2 2 100 2/100 1/50 150 10 10 100

10/100 1/10 110 75 75 100 75/100

3/4 34

Converting a Percent to a Decimal

- Divide by 100 or insert a decimal point two

places to the left of the last number, inserting

zeros if necessary. - Drop the symbol.

Remember

Multiplying or dividing by 100 does not change

the value because 100 1.

Converting a Decimal to a Percent

- Multiply by 100 or insert a decimal point two

places to the right of the last number, inserting

zeros if necessary. - Add the the symbol.

Percent to Decimal 4 0.04 4 100 0.04 15

0.15 15 100 0.15 200 2 200 100

2 Decimal to Percent 0.25 25 0.25 100

25 1.35 135 1.35 100 135 0.015

1.5 0.015 100 1.5

Terms to Remember

COMMON CALCULATIONS IN THE PHARMACY

- Converting Quantities between the Metric and

Common Measure Systems - Calculations of Doses
- Preparation of Solutions

COMMON CALCULATIONS IN THE PHARMACY

- Converting Quantities between the Metric and

Common Measure Systems

Example 4 How many milliliters are there in 1

gal, 12 fl oz?

According to the values in Table 5.7, 3840 mL are

found in 1 gal. Because 1 fl oz contains 30 mL,

you can use the ratio-proportion method to

calculate the amount of milliliters in 12 fl oz

as follows

Example 4 How many milliliters are there in 1

gal, 12 fl oz?

Example 4 How many milliliters are there in 1

gal, 12 fl oz?

Example 4 How many milliliters are there in 1

gal, 12 fl oz?

Example 5 A solution is to be used to fill

hypodermic syringes, each containing 60 mL, and 3

L of the solution is available. How many

hypodermic syringes can be filled with the 3 L of

solution?

From Table 5.2, 1 L is 1000 mL. The available

supply of solution is therefore

Example 5 How many hypodermic syringes can be

filled with the 3 L of solution?

Determine the number of syringes by using the

ratio-proportion method

Example 5 How many hypodermic syringes can be

filled with the 3 L of solution?

Example 5How many hypodermic syringes can be

filled with the 3 L of solution?

Example 6You are to dispense 300 mL of a liquid

preparation. If the dose is 2 tsp, how many doses

will there be in the final preparation?

Begin solving this problem by converting to a

common unit of measure using conversion values in

Table 5.7.

Example 6 If the dose is 2 tsp, how many doses

will there be in the final preparation?

Using these converted measurements, the solution

can be determined one of two ways. Solution 1

Using the ratio proportion method and the metric

system,

Example 6 If the dose is 2 tsp, how many doses

will there be in the final preparation?

Example 6 If the dose is 2 tsp, how many doses

will there be in the final preparation?

Example 7How many grains of acetaminophenshould

be used in a Rx for 400 mg acetaminophen?

Solve this problem by using the ratio-proportion

method. The unknown number of grains and the

requested number of milligrams go on the left

side, and the ratio of 1 gr 65 mg goes on the

right side, per Table 5.5.

Example 7How many grains of acetaminophenshould

be used in the prescription?

Example 7 How many grains of acetaminophenshould

be used in the prescription?

Example 8A physician wants a patient to be given

0.8 mg of nitroglycerin. On hand are tablets

containing nitroglycerin 1/150 gr. How many

tablets should the patient be given?

Begin solving this problem by determining the

number of grains in a dose by setting up a

proportion and solving for the unknown.

Example 8 How many tablets should the patient be

given?

Example 8How many tablets should the patient be

given?

Example 8How many tablets should the patient be

given?

Example 8How many tablets should the patient be

given?

Example 8How many tablets should the patient be

given?

COMMON CALCULATIONS IN THE PHARMACY

- Calculations of Doses

active ingredient (to be administered)/solution

(needed) active ingredient (available)/solutio

n (available

Measurement and Calculation Issues

Safety Note!

Always double-check the units in a proportion and

double-check your calculations.

Example 9 You have a stock solution that

contains 10 mg of active ingredient per 5 mL of

solution. The physician orders a dose of 4 mg.

How many milliliters of the stock solution will

have to be administered?

Example 9How many milliliters of the stock

solution will have to be administered?

Example 9 How many milliliters of the stock

solution will have to be administered?

Example 10 An order calls for Demerol 75 mg IM

q4h prn pain. The supply available is in Demerol

100 mg/mL syringes. How many milliliters will the

nurse give for one injection?

Example 10 How many milliliters will the nurse

give for one injection?

Example 10 How many milliliters will the nurse

give for one injection?

Example 11An average adult has a BSA of 1.72 m2

and requires an adult dose of 12 mg of a given

medication. If the child has a BSA of 0.60 m2,

and if the proper dose for pediatric and adult

patients is a linear function of the BSA, what is

the proper pediatric dose? Round off the final

answer.

Example 11 What is the proper pediatric dose?

Example 11What is the proper pediatric dose?

Example 11 What is the proper pediatric dose?

Example 11What is the proper pediatric dose?

COMMON CALCULATIONS IN THE PHARMACY

- Preparation of Solutions

powder volume final volume diluent volume

Example 12 A dry powder antibiotic must be

reconstituted for use. The label states that the

dry powder occupies 0.5 mL. Using the formula for

solving for powder volume, determine the diluent

volume (the amount of solvent added). You are

given the final volume for three different

examples with the same powder volume.

Example 12 Using the formula for solving for

powder volume, determine the diluent volume.

Example 12 Using the formula for solving for

powder volume, determine the diluent volume.

Example 13You are to reconstitute 1 g of dry

powder. The label states that you are to add 9.3

mL of diluent to make a final solution of 100

mg/mL. What is the powder volume?

Example 13 What is the powder volume?

Step 1. Calculate the final volume. The strength

of the final solution will be 100 mg/mL.

Example 13 What is the powder volume?

Example 13 What is the powder volume?

Example 13What is the powder volume?

Measurement and Calculation Issues

Safety Note!

An injected dose generally has a volume greater

than 0.1 mL and less than 1 mL.

Example 14 Dexamethasone is available as a 4

mg/mL preparation an infant is to receive 0.35

mg. Prepare a dilution so that the final

concentration is 1 mg/mL. How much diluent will

you need if the original product is in a 1 mL

vial and you dilute the entire vial?

Example 14 How much diluent will you need if the

original product is in a 1 mL vial and you dilute

the entire vial?

Example 14How much diluent will you need if the

original product is in a 1 mL vial and you dilute

the entire vial?

Example 14 How much diluent will you need if the

original product is in a 1 mL vial and you dilute

the entire vial?

Example 15Prepare 250 mL of dextrose 7.5 weight

in volume (w/v) using dextrose 5 (D5W) w/v and

dextrose 50 (D50W) w/v. How many milliliters of

each will be needed?

Example 15 How many milliliters of each will be

needed?

Step 1. Set up a box arrangement and at the

upper-left corner, write the percent of the

highest concentration (50) as a whole number.

Example 15 How many milliliters of each will be

needed?

Step 2. Subtract the center number from the

upper-left number (i.e., the smaller from the

larger) and put it at the lower-right corner. Now

subtract the lower-left number from the center

number (i.e., the smaller from the larger), and

put it at the upper-right corner.

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Example 15 How many milliliters of each will be

needed?

Terms to Remember

Discussion

Visit www.malpracticeweb.com, and look under

Miscellaneous to find legal summaries of the

following cases. Describe the decision and

explain how this decision affects pharmacy

technicians. a. J.C. vs. Osco Drug b. P.H. vs.

Osco Drug

Discussion

What activities of the pharmacy technician

require skill in calculations?

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Copyright 2017 CrystalGraphics, Inc. — All rights Reserved. PowerShow.com is a trademark of CrystalGraphics, Inc.

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