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Math for Pharmacology: Fractions, Decimals, and Conversions

Learn basic math concepts for pharmacy calculations, including fractions, decimals, ratios, proportions, and systems of measurements. Master essential skills for drug calculations and conversions in pharmacy practice.

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Math for Pharmacology: Fractions, Decimals, and Conversions

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  1. Module B:Basic Math for Pharmacology

  2. Basic Math • Addition • Subtraction • Multiplication • Division

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

  4. Fractions • Simple • Proper • Improper • Mixed numbers • Complex

  5. 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

  6. 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

  7. 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

  8. 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

  9. Fractions • Multiplying Mixed #s • Change to an improper fraction • Dividing Fractions • Invert the divisor

  10. 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

  11. Decimals • Adding • Subtracting

  12. 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

  13. Decimals • Change decimals to common fractions • Remove decimal • Place appropriate D • Reduce to lowest terms

  14. Percents • Change percents to fractions • Ommit percent sign • Use 100 as D • Reduce fraction

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

  16. Ratios • Indicate the relationship of one quantity to another • Form of fraction • Form of ratio

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

  18. Systemsof Measurements Household Apothecary Metric

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

  20. Household

  21. 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.

  22. Apothecary • Weight

  23. Apothecary • Volume

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

  25. Metric System

  26. Other Common Drug Measures • Units = U • Milli unit = mU • Milli equivalent

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

  28. Conversions between systems Metric Apothecary Household

  29. Conversion Equivalents

  30. Drug Calculations

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

  32. 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

  33. 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

  34. Ratio & Proportion • One step Ratio & Proportion • Two step Ratio & Proportion

  35. 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.

  36. 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.

  37. 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.

  38. 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.

  39. International Units • Units • Milliunits

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

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