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Module B: Basic Math for Pharmacology. Basic Math. Addition Subtraction Multiplication Division. I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000. Examples: VII = XV = III = IX = IV = XIX = XIV =. Roman Numerals. Fractions. Simple Proper Improper Mixed numbers Complex.
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Basic Math • Addition • Subtraction • Multiplication • Division
I = 1 V = 5 X = 10 L = 50 C = 100 D = 500 M = 1000 Examples: VII = XV = III = IX = IV = XIX = XIV = Roman Numerals
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)
Systemsof Measurements Household Apothecary Metric
Household • Most often used by people at home • Least accurate • Used by nurse in teaching patients • Should not be relied on in hospital setting
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
Apothecary • Volume
Metric System • Base Units • Wt - gram • Volume – liter • Length – meter • Prefixes • Centi • Milli • Micro • Deca • Hecto • Kilo
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
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 • Identify the desired unit. • Identify the equivalent needed and set up in fraction form. • Write the equivalent in fraction format, keeping the desired unit in the numerator of the fraction. • Be sure to label all factors in the equation. • Identify undesired units and cancel them. • 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 • Units • Milliunits
Reconstitution of medications • Stability of the drug • Powder mixed with diluent or solvent • Reconstitute medication before giving to client