Introduction to Pharmacology Pharmacology Mathematics

Basic Rules Zero Always use prior to a decimal 0.5 mg Never Use it following a decimal if not needed 5.0 mg – do not use 5 mg – use

Basic Rules 1 kg = 2.2 pounds 1 g = 1000 mg 1mg = 1000 mcg (0.1mg = 100 mcg) 1L = 1000 mL 5ml = 1 tsp 16oz = 1 lb 30ml = 1 fluid ounce 15 gtt = 1 ml 1 grain = 60 mg

FYI The units of measure mL and cc, meaning milliliter and cubic centimeter, respectively, are often interchangeable in medicine. It is advised to stay away from cc because of a possible mistake of reading it as 00.

Basic Rules PEMDAS ( ) 𝑥 2 * ÷ + -

Basic Rules DOES IT MAKE SENSE?!?!?!?!?!?!?! 10 UNITS of insulin or 10 MILLILITERS of insulin – USE YOUR HEAD

Proportions Equation that contains two ratios of equal value A:B :: C:D 1:2 :: 2:4

Fractions In fraction form, any whole number is equivalent to that number over one 5 = 5 1 34 = 34 1 29.5 = 29.5 1

Basic Math Skills : Conversions Fractions to Whole Numbers: Divide numerator by denominator 1 3 = 1 ÷ 3 = 0.33

Basic Math Skills : Conversions Percentages are fractions of 100 3% = 3 100 Convert Percentages to Decimal or Whole Number by dividing by 100 5% = 5 100 = 5 ÷100= 0.05

Basic Math Skills : Conversions Ratios are fractions in a different format 1 : 2 = 1 part per 2 parts = 1 2

Dimensional Analysis How many kg in 50lb? 50𝑙𝑏 1 * 1𝑘𝑔 2.2𝑙𝑏 = 22.7 kg

Dimensional Analysis Order: 1L NSS over 8 hours Tubing Drip Factor: 10 gtt/mL How Many gtt/min will there be? 1000𝑚𝑙 480 𝑚𝑖𝑛 ∗ 10 𝑔𝑡𝑡 𝑚𝐿 = 10,000 𝑔𝑡𝑡 480 𝑚𝑖𝑛 = 20.8 gtt/ min = 21 gtt/min

Desired/Have/Vehicle 𝐷 𝐻 ∗𝑉=𝐺 Order: 1 mg Ativan PO Available: 0.5 mg Tabs How many tabs do you give? D = Desired = 1 mg H = Have = 0.5 mg V = Vehicle = Tablet G = Given = x

Desired/Have/Vehicle 𝐷 𝐻 ∗𝑉=𝐺 = 1𝑚𝑔 0.5 𝑚𝑔 ∗1 𝑡𝑎𝑏=2 𝑡𝑎𝑏𝑠

Desired/Have/Vehicle 𝐷 𝐻 ∗𝑉=𝐺 Order: 50 mg Rocephin IM Available: 100 mg/2mL How many mL do you give? D = Desired = 50 mg H = Have = 100 mg V = Vehicle = 2 mL G = Given = x

Desired/Have/Vehicle 𝐷 𝐻 ∗𝑉=𝐺 = 50𝑚𝑔 100𝑚𝑔 ∗2𝑚𝐿= 100 100 = 1 ml

Basic Math Skills To Multiply Fractions Numerator * Numerator Denominator * Denominator Reduce 𝐴 𝐶 * 𝐵 𝐷 = 𝐴𝐵 𝐶𝐷 2 3 * 4 8 = 8 24 = 1 3

Basic Math Skills To Divide Fractions Easier to convert to a decimal first, otherwise… Invert Second Fraction Convert Division Sign to Multiplication Sign Multiply Fractions 𝐴 𝐶 ÷ 𝐵 𝐷 = 𝐴 𝐶 ∗ 𝐷 𝐵 2 3 ÷ 4 8 = 2 3 ∗ 8 4 = 16 12 = 4 3 = 1 1 3

Basic Math Skills Order: 40 mg Lasix IV Available: 10mg/mL in 10 mL vial How many ml will you give?

Basic Math Skills Order: 0.5 mg lorazepam Available: 1 mg tablets How many tablets will you give?

Basic Math Skills Order: Lovenox 1mg / kg Available: 100 mg / ml Patient: 100 pounds How many kg does the patient weigh? How many mg will the patient receive? How many ml will you give?

Basic Math Skills Order: 75 mg Amoxicillin PO Available: 125 mg/5ml Amoxicillin Oral Suspension How many ml will you give?

Basic Math Skills Order: Insulin Drip at 2 units / hour Available: 100 units Insulin in 100 ml NSS How many ml / hr will you give?

Basic Math Skills Order: atropine 0.4 mg IV Available: atropine 400 mcg / mL How many mL will you give?