Pharmacy Calculations!

Anything & Everything you Will Need To Know About Math in Pharmacy

Objectives

• To become familiar with the various computational aspects of pharmacy practice.

• Demonstrate use of:

Basic Arithmetic FunctionsRatiosFractionsDecimalsPercentsCross-HatchUnit Conversions

Standard & Military TimeDose CalculationsPediatric (Weight Based Dosing)Drip RatesAllegations (Compounding & Dilutions)

Step One

Don’t Panic

Step Two!

Ask Questions!

The Basics

Foundational Math

• Be able to do the following (on a calculator if needed); if you have any questions please ask. (Sooner is better than later).

• Addition, Subtraction, Multiplication, Division• Squaring Numbers & Square Roots• Decimals & Fractions

Know how to use your calculator.

Fractions

• Fractions are a numerical way of representing part(s) of a whole.

• Example:

Converting to a Common Denominator

Adding Fractions

Subtracting Fractions

Multiplying Fractions

Dividing Fractions

Decimals

• Like fractions, decimals are a numerical way of representing quantities and part(s) of a whole.

Place Values

When reading a number aloud, the “and” is where the decimal goes.

Converting a Fraction to a Decimal

Unit Conversions

Converting Units

• Almost daily, you will have the need to perform conversions.

• Converting between different measurement systems.

Measurement Systems

• Metric System (THE BEST!)– L, mL, dL, gm, mcg, kg, m, cm, mm

• Household System (This will die eventually)– C, tbsp, tsp, oz, fl oz, lb, ft, inch

• Apothecary System (Really rare, but it happens)– Grain (gr), drams, scruples, oz

• Avoirdupois System – Lb, oz, gr, pt, gallon

Conversion Factors1 kg = 1,000gm = 1,000,000 mg = 1,000,000,000 mcg1gm = = 1,000mg = 1,000,000mcg1mg = = = 1,000mcg1lb = 454gm = 7,500gr = 16oz1kg = 2.2lb1oz = 30gm1gallon = 4qt = 8pt = 16cups 1cup = 8oz = 16tbsp = 48tsp = 240ml 1oz = 2tbsp = 6tsp = 30ml 1tbsp = 3tsp = 15ml 1tsp = 5ml = 1 dram1ml = 20gtts = 10gtts (macro) = 60gtts (micro) 1 grain (gr) = 60-65mg1km = 1,000m = 100,000cm = 1,000,000mm1yard = 3ft = 36inches = 0.911inch = 2.54cm

Rule of Thumb

• Going Small to Big: Divide– Example: 200gm to kg = 200/1,000 = 0.2kg

• Going Big to Small: Multiply– Example: 2gm to mg = 2x1,000 = 2,000mg

The Cross-Hatch

1. Start above/below the X2. Divide across (sideways)3. Multiply up & down

*Like units MUST be NEXT to each other

Divide

1 2

3 X

Multiply

Let’s Practice

Convert 10kg to lbs.

Percents• Percents; like fractions and decimals are used to

describe a portion of a whole.• Converting:– Percent to Decimal: Divide by 100– Percent to Fraction:

• Put Percent as Numerator and 100 as Denominator• Reduce

– Fraction to Percent: • Divide Numerator by Denominator• Multiply by 100

– Decimal to Percent: Multiply by 100

A ratio is a comparison of two quantities. Ratios can be written in several ways. 7 to 5, 7:5, and name the same ratio.7

5

Ratios

12 inches = 1 foot3 feet = 1 yard36 inches = 1 yard

ExampleWrite the ratio 15 bikes to 9 skateboards in simplest form.

159

53

The ratio of bikes to skateboards is , 5:3, or 5 to 3.

=

15 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

53

bikesskateboards

Check It Out! Example 2

Write the ratio 24 shirts to 9 jeans in simplest form.

249

83

The ratio of shirts to jeans is , 8:3, or 8 to 3.

=shirtsjeans

24 ÷ 39 ÷ 3

Write the ratio as a fraction.

= = Simplify.

83

Dosage Calculations

• Use the Cross-Hatch and the idea of unit conversions to calculate doses.

Order Premarin 1.25mg po QD Supply Premarin 0.625mg caplets

Order Zantac 150mg po QIDSupply Zantac 300mg/5ml suspension

Order Cyanocobalamin 80mg IM STATSupply Cyanocobalamin 100mg/ml

Order Potassium 12meq po TIDSupply Potassium 8meq/5ml

Drip Rates & Dimensional Analysis

This process can be used for any multistep conversions. As long as you use the correct conversion factor and

the units cancel properly you will get the correct answer.

Basics of Dimensional Analysis

• Can be used with any units.• First determine what the question is asking.• What are the units of your answer?• Units from the numerator can cancel with the

same units in the denominator.• After only the desired unites remain:– Multiply Numerators– Multiply denominators– Reduce

An Example:Consider the question:Calculate the drops per minute of an infusion 1.5gm in 500ml D5W, infused at 50mg/minute, with a drip factor of 20gtts/ml.

1. Write down all of the ratios from the problem.2. Determine what the question is asking.3. What are the units of the answer?

• What are the units of the answer?

• So, Let’s start with a conversion that uses drops in the numerator.

• Next, we need to cancel mls

•Now, We need to get ride of gms.

• Now, to get rid of the mg

• Remember to check that all of the units cancel.

• Now Multiply

• And Reduce

Alligations

Alligations

• Used to calculate quantities of ingredients when combing components of different concentrations to make a new product.

• Example:– Making a 5% cream from a 1% cream and a 10%

cream.

Roman Numerals

• Number system before current Arabic numeral System that we use.

• Letters Represent Numbers• Numbers are ordered from left to right.• Large to small.• Never more than 3 of same numeral in a row.• Small numbers are added to large• When Small numbers are place in front of a large

number the value is subtracted.• There are no place values with Roman Numerals

Roman Numerals

Numerals• I = 1• V = 5• X = 10• L = 50• C = 100• D = 500• M = 1,000

ExamplesIIIIVVIVIIIXXXVCMLXXXXXIVCCCXIV3

467925198024314

Temperature Conversions

• Fahrenheit: Temperature System used by most in US.

• Celsius: Temperature system used throughout the world, science, and medicine. Based upon the chemical and physical properties of water.

9 C = 5F – 160• Plug in the value you know, and solve for the

unknown.

International & Standard Time