Module B: Basic Math for Pharmacology

Basic Math Addition Subtraction Multiplication Division

Roman Numerals I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 Examples: VII = XV = III = IX = IV = XIX = XIV =

Fractions Simple Proper Improper Mixed numbers Complex

Fractions Reducing to lowest terms –Divide N & D with a common D Changing improper fractions –Top number is larger than the bottom, divide bottom # into top#. - Write the remainder as a fraction and reduce to lowest terms

Fractions Change mixed #’s into improper fractions –Multiply the whole # by the bottom # –Add total to the top # –Write sum at top; bottom remains same

Fractions Adding and subtracting fractions –If same bottom #, then add the top, bottom remains same. –If D is different, then find the lowest common D. Adding and Subtracting mixed numbers

Fractions Multiple a Whole # by a fraction –Always reduce to the lowest term –Always change improper fractions Multiplying two fractions –Use cancellation to speed the process

Fractions Multiplying Mixed #s –Change to an improper fraction Dividing Fractions –Invert the divisor

Decimals Decimal Places –Numbers on left of decimal are whole numbers –Number on the right of the decimal are as follows: Tenths Hundredths Thousandths Ten thousandths

Decimals Adding Subtracting

Decimals Rounding the answer Multiplying decimals Dividing decimals –Make the divisor a whole # by moving the decimal –Move the decimal in the dividend the same amount of places as in the divisor. –Place directly above in bracket

Decimals Change decimals to common fractions –Remove decimal –Place appropriate D –Reduce to lowest terms

Percents Change percents to fractions –Ommit percent sign –Use 100 as D –Reduce fraction

Percent Change percent to decimals –Omit percent sign –Insert a decimal point 2 places to the left.

Ratios Indicate the relationship of one quantity to another –Form of fraction –Form of ratio

Proportions Shows how 2 equal ratios are related Three factors are known One factor is unknown (x)

Systems of Measurements HouseholdApothecaryMetric

Household Most often used by people at home Least accurate Used by nurse in teaching patients Should not be relied on in hospital setting

Household UnitAbbreviationEquivalent Dropgttnone teaspoontsp (t)1T = 3t Tablespoontbs (T)

Apothecary System Ancient system “Old English” Not very accurate Use Roman Numerals The symbol is placed in front of the number. Change to metric system when possible.

Apothecary Weight UnitAbbreviationEquivalent Graingr***

Apothecary Volume UnitAbbreviationEquivalent Quartqtqt 1 = pt 2 qt 1 = oz 32 Pintptpt 1 = oz 16 Fluid- ounce ozoz 1= 8 drams Dram Minimm

Metric System Base Units –Wt - gram –Volume – liter –Length – meter –Prefixes Centi Milli Micro Deca Hecto Kilo

Metric System UnitAbbreviationEquivelent Weightgramg1 g = 1000mg Milligrammg1 mg = 1000mcg microgramMcg kilogramkg1 kg = 1000g VolumeliterL1 L = 1000ml mililiterml1ml = 1cc Cubic cent.cc1cc = 1 ml LengthMeterm1m=100cm=1000mm centimetercm1cm =10mm milimetermm

Other Common Drug Measures Units = U Milli unit = mU Milli equivalent

Conversions Use: – Ratio and Proportion 1 step problems 2 step problems (know) = (want to know) X : Y = X : Y mg : g = mg : g

Conversions between systems Metric Apothecary Household

Conversion Equivalents 1ggr xv gr 160mg 1 t5 ml 1 T3 t15ml½ oz 1oz30 ml6 t 1Lqt 1pt 2oz 324 cups pt 1500 mloz 162 cups 1 cup250 mloz 8 1 kg2.2 lbs 1lb16 oz

Drug Calculations

Perform Calculation by Ratio and Proportion or Dimensional Analysis or Formula –D/H x Q = X

Ratio & Proportion Ratios you many see: –Wt or strength of a drug in a tab or capsule Example: 50mg: 1 tab Meaning : each tablet has 50 mg Weight or strength of a drug in a volume Example = 50mg:2ml Meaning = 50 mg in 2ml of volume

Ration & Proportion When administering medication you can give –Tablets, Capsules, and ml (in a syringe) Remember: –The ratios must be written in the same sequence of measurements

Ratio & Proportion One step Ratio & Proportion Two step Ratio & Proportion

Dimensional Analysis 1)Identify the desired unit. 2)Identify the equivalent needed and set up in fraction form. 3)Write the equivalent in fraction format, keeping the desired unit in the numerator of the fraction. 4)Be sure to label all factors in the equation. 5)Identify undesired units and cancel them. 6)Perform the mathematical process indicated.

Dimensional Analysis By flipping the fraction, no value is changed. Remember: They are ratios in fraction form. Starting the equivalent incorrectly will not allow you to eliminate desired units. Knowing when the equation is set up correctly is an important part of using Dimensional Analysis.

Formulas D/H x Q = X D = Dose desired Hand = have on hand Q = the quantity or the unit of measure that contains the dose.

Formulas Memorize the formula Place the information from the problem into the formula in the correct position, with all terms in the formula labeled correctly. Make sure all measures are in the same units and system of measure or a conversion must be done before calculating the dose.

International Units oUnits oMilliunits

Reconstitution of medications Stability of the drug Powder mixed with diluent or solvent Reconstitute medication before giving to client