Basic Math Review

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Basic Math Review

• Raquel D. Esguerra RN, MAN, CCRN

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I. PERCENTAGES

• Any quantity stated as the proportion per
  hundred expressed with sign meaning for every
  hundred

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A. Convert a percent to a decimal

• RULES
• Delete the sign
• Divide the remaining number by 100, which is the
  same as moving the decimal point 2 places to the
  left.
• Ex 25 25/100 0.25

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B. Convert a decimal to a percentage

• RULES
• Multiply the decimal number by 100 (move the
  decimal point 2 places to the right) and
• Add sign
• Ex 0.25 x 100 25

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C. Converting a common fraction to a percentage

• RULES
• Convert the fraction to a decimal by dividing the
  numerator by the denominator
• 3/8 (0.375)
• Move the decimal point two places to the right,
  round off if necessary
• 37.5 or 38
• Add the sign
• 37.5 or 38

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Convert a percent to a fraction

• RULES
• Delete the sign
• Write the remaining number as the numerator
• Write the 100 as the denominator
• Divide the numerator by the denominator
• Ex 25 __________
• 50 ___________

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II. RATIOS AND FRACTIONS IN PROPORTIONS

• Numerical ways to compare items.
• A proportion is a set of two equal ratios or
  fractions

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Ratios in proportions

• Written with a double colon separating the ratios
  (Example 31 62)
• The outer numbers (32) are the extremes.
• The inner numbers (16) are the means
• The product of the extremes must equl the product
  of the means
• Solve for X in this proportion
• 31 6X

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B. Fractions in proportions

• Cross products should be equal
• 5 X
• --- ---
• 2 4
• Rewrite the problem to multiply cross products
• 2 x X 5 x 4
• Obtain the cross products
• 2X 20
• Solve for X by dividing both sides by 2
• Find X (10)

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Convert a fraction to a decimal

• RULE To convert a fraction to a decimal, divide
  the numerator by the denominator.
• Ex 1/ 4 _________
• 2/5 ____________
• 4/10 _____________

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Convert decimal to a fraction

• Decimal fractions are fractions with a
  denominator of 10, 100, 1000 or any multiple or
  power of 10.
• Ex 0.1 _________
• 0.01 _______
• 0.001 ___________

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SYSTEMS OF DRUG MEASUREMENT

• I. METRIC SYSTEM
• Basic units of measurement
• Meter (m) unit of length
• Liter (L) unit of volume
• Gram (G, GM, Gm) unit of weight

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MEASUREMENTS

• Metric Units
• Kkilo 1000 King
• Hhecto 100 Henry
• Ddeca 10 Died
• BASE Gram Liter and Meter (from a)
• Ddeci .0001 Disease
• Ccenti .00001 Called
• Mmilli .001 Mumps

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METRIC SYSTEM
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Metric Conversions

• To convert a smaller unit to a larger one, move
  the decimal point to the left or divide by the
  appropriate multiple of 10
• Example milligrams to grams
• 1000 milligrams / 1000 1
• To convert a larger unit to a smaller one, move
  the decimal point to the right or multiply by the
  appropriate multiple of 10
• Example gram to milligrams
• 1 gram x 1000 1000 mg

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• Larger to smaller unit MULTIPLY (L-S-M)
• Smaller to larger unit DIVIDE (S-L-D)
• Identify conversion factors
• Convert 2 grams to equivalent milligrams
• Equivalent conversion 1g1000mg
• 2 g 2 x 10002000 mg- by multiplication OR
• 2.000 2000 mg(moving decimal 3 places to right)

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II. HOUSEHOLD SYSTEM

• Usually used at home
• Drop gtt (standard measure varies)
• Teaspoon t (tsp)
• Tablespoon T(tbs) 1 T 3 t
• Ounce(fluid) oz 2 T 1 oz
• Ounce(wt) oz 1 lb 16 oz
• Cup cup 1 cup 8 oz
• Pint pt 1 pt 2 cups
• Quart qt 1 qt 4 cups 2 pints

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III. Apothecaries System

• Uses Roman numerals
• Unit of measurement is placed before the Roman
  numeral (Example 5 grins is written as grains v
  )
• Basic units of measurement
• Minim for liquid volume
• Grain (gr) for solid weight

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IV. Avoirdupois System

• Used for ordering and purchasing some
  pharmaceutical products and for weighing patients
  in clinical settings
• Units of weight include grains, ounces, pounds

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V. Unit System

• USP United States Pharmacopeia Units
• IU International Units
• Common drugs in units
• Insulin
• Heparin

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VI. Milliequivalent System

• Most electrolytes are measured in mEq
• Example Potassium Chloride

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APPROXIMATE EQUIVALENTS

• 1 g gr(grains) xv
• gr 1 60 mg
• 1 t 5 ml
• 1 T 3 t 15 ml ½ oz
• 1 oz 30 ml 6 t
• 1 L qt I oz 32 pt ii 4 c
• pt I 500ml oz 16 2 cups
• 1 cup 250 ml oz 8
• 1 kg 2.2 lbs
• 1 inch 2.5 cm

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ORAL DOSAGE FORMS

• Steps
• Ensure that all measurements are in the same
  system of measurement and the same size unit of
  measurement. If not, convert.
• Calculate using this formula

D

Amount to be given
H
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Oral Dosage Forms Liquid Preparations

• Steps
• Ensure that all measurements are in the same
  system of measurement and the same size unit of
  measurement. If not, convert.
• Calculate using this formula
• D

Amount to be given
X
Q
H
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Examples

• The physician writes an order for secobarbital
  0.2 g every 6 hours prn for sleep. Each
  secobarbital capsule is labeled 100 mg. The nurse
  should administer______ capsules per dose.

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Examples

• The physician orders 500 mg of amoxicillin by
  mouth to be given every 6 hours. Available are
  250 mg of amoxicillin capsules. The nurse should
  administer _________ capsule(s) for each dose.

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Examples

• The physician writes an order for acetaminophen
  240 mg po for an elderly adult. You have on hand
  80 mg acetaminophen oral liquid in 0.8 ml. The
  nurse should administer _________ ml per dose.

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Examples

• The physician orders amoxicillin 250 mg po. The
  pharmacy supplies amoxicillin suspension 250 mg/5
  ml. in a 50 ml. bottle. The nurse should instruct
  the client to take _________ ml per dose.

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Practice Questions

• A physicians order reads 2 Tbs milk of magnesia.
  How many milliliters will the nurse administer?
• The Physicians order reads Tylenol supp. Gr x
  every 4 hrs p.r.n. for temp. 101 F. The
  package label states that each suppository
  contains 10 grains of Tylenol. How many
  suppositories should the nurse administer?
• The order states Lithium Carbonate gr x p.o. tid.
  The drug is labeled Lithium Carbonate 300
  milligrams/capsule. How many capsules should the
  nurse give?

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• The order for Coumadin is 5 mg. It is available
  in 2.5 mg tablets. How many tablets should be
  given?
• The physicians order is Ferrous Sulfate 300 mg
  p.o. tid X 1 week. How many tablets in total
  should be dispensed for the patient?