Pharmacy Calculations!

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# Pharmacy Calculations! - PowerPoint PPT Presentation

Pharmacy Calculations!. Anything &amp; 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 Functions Ratios Fractions Decimals Percents Cross-Hatch

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### 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 Functions
• Ratios
• Fractions
• Decimals
• Percents
• Cross-Hatch
• Unit Conversions
• Standard & Military Time
• Dose Calculations
• Pediatric (Weight Based Dosing)
• Drip Rates
• Allegations (Compounding & Dilutions)
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).
• Squaring Numbers & Square Roots
• Decimals & Fractions
Fractions
• Fractions are a numerical way of representing part(s) of a whole.
• Example:
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 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 Factors

1 kg = 1,000gm = 1,000,000 mg = 1,000,000,000 mcg

1gm = = 1,000mg = 1,000,000mcg

1mg = = = 1,000mcg

1lb = 454gm = 7,500gr = 16oz

1kg = 2.2lb

1oz = 30gm

1gallon = 4qt = 8pt = 16cups

1cup = 8oz = 16tbsp = 48tsp = 240ml

1oz = 2tbsp = 6tsp = 30ml

1tbsp = 3tsp = 15ml

1tsp = 5ml = 1 dram

1ml = 20gtts = 10gtts (macro) = 60gtts (micro)

1 grain (gr) = 60-65mg

1km = 1,000m = 100,000cm = 1,000,000mm

1yard = 3ft = 36inches = 0.91

1inch = 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

Divide

1. Start above/below the X

2. Divide across (sideways)

3. Multiply up & down

*Like units MUST be

NEXT to each other

2

1

Multiply

3

X

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

7 5

Ratios

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.

12 inches = 1 foot

3 feet = 1 yard

36 inches = 1 yard

15 ÷ 3

9 ÷ 3

bikes

skateboards

Example

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

15

9

Write the ratio as a fraction.

=

5

3

Simplify.

=

=

5

3

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

shirts

jeans

24 ÷ 3

9 ÷ 3

Check It Out! Example 2

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

Write the ratio as a fraction.

24

9

=

8

3

Simplify.

=

=

8

3

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

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

### 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.
• 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.

Write down all of the ratios from the problem.

Determine what the question is asking.

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
• 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

Examples

III

IV

VI

VII

IX

XXV

CMLXXX

XXIV

CCCXIV

3

4

6

7

9

25

1980

24

314

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