Chapter 6 pharmacy calculation

The Pharmacy The Pharmacy Technician 4ETechnician 4E

Chapter 6Chapter 6Basic Pharmaceutical Basic Pharmaceutical

Measurement CalculationMeasurement Calculation

Comparison of Roman and Arabic Comparison of Roman and Arabic NumeralsNumerals

Example:Example: xxx = 30 or 10 plus 10 plus 10xxx = 30 or 10 plus 10 plus 10 DC = 600 or 500 plus 100DC = 600 or 500 plus 100 LXVI = 66 or 50 plus 10 plus 5 plus 1LXVI = 66 or 50 plus 10 plus 5 plus 1

When the second of two letters has a value greater When the second of two letters has a value greater than that of the first, the smaller is to be subtracted than that of the first, the smaller is to be subtracted from the larger.from the larger.

Adding or Subtracting FractionsAdding or Subtracting Fractions

• When adding or subtracting fractions with unlike When adding or subtracting fractions with unlike denominators, it is necessary to create a common denominators, it is necessary to create a common denominator. denominator. •This is like making both fractions into the same kind This is like making both fractions into the same kind of “pie.”of “pie.”

• Common denominator Common denominator isis a number that each of the a number that each of the unlike denominators of two or more fractions can be unlike denominators of two or more fractions can be divided evenly.divided evenly.

Guidelines for Finding a Common Guidelines for Finding a Common DenominatorDenominator

1.1. Examine each denominator in the given Examine each denominator in the given fractions for its divisors, or factors.fractions for its divisors, or factors.

2.2. See what factors any of the denominators See what factors any of the denominators have in common.have in common.

3.3. Form a common denominator by multiplying Form a common denominator by multiplying all the factors that occur in all of the all the factors that occur in all of the denominators. If a factor occurs more than denominators. If a factor occurs more than once, use it the largest number of times it once, use it the largest number of times it occurs in any denominator.occurs in any denominator.

Decimal PlacesDecimal Places

1000

mg

500

mg

50 mg

5 mg

0.5 mg

WholeWhole 0.5 0.5 0.050.05 0.0050.005 0.00050.0005tenthstenths hundredthshundredths thousandsthousands ten thousandsten thousands

(1 place to (1 place to (2 places to (2 places to (3 places to (3 places to (4 places (4 places toto

the right)the right) the right)the right) the right)the right) the right)the right)

Common Metric Units: WeightCommon Metric Units: Weight

Basic Unit Equivalent

1 gram (g) 1000 milligrams (mg)

1 milligram (mg) 1000 micrograms (mcg)

1 kilogram (kg) 1000 grams (g)

Common Metric ConversionsCommon Metric Conversions kilograms (kg) kilograms (kg) toto grams (g) grams (g)

Multiply by 1000 (move decimal point three places to the Multiply by 1000 (move decimal point three places to the right).right).

Example: 6.25 kg = 6250 gExample: 6.25 kg = 6250 g grams (g) grams (g) toto milligrams (mg) milligrams (mg)

Multiply by 1000 (move decimal point three places to the Multiply by 1000 (move decimal point three places to the right).right).

Example: 3.56 g = 3560 mgExample: 3.56 g = 3560 mg milligrams (mg) milligrams (mg) toto grams (g) grams (g)

Multiply by 0.001 (move decimal point three places to the left).Multiply by 0.001 (move decimal point three places to the left). Example: 120 mg = 0.120 gExample: 120 mg = 0.120 g

Common Metric ConversionsCommon Metric Conversions

Liters (L) Liters (L) toto milliliters (mL) milliliters (mL) Multiply by 1000 (move decimal point three Multiply by 1000 (move decimal point three

places to the right).places to the right). Exmaple: 2.5 L = 2500 mLExmaple: 2.5 L = 2500 mL

Milliliters (mL) Milliliters (mL) toto liters (L) liters (L) Multiply by 0.001 (move decimal point three Multiply by 0.001 (move decimal point three

places to the left).places to the left). Example: 238 mL = 0.238 LExample: 238 mL = 0.238 L

Avoirdupois SystemAvoirdupois System

1 gr (grain)1 gr (grain) - 65 mg- 65 mg 1 oz (ounce)1 oz (ounce) - 437.5 gr or 30 g (28.35 g)- 437.5 gr or 30 g (28.35 g) 1 lb (pound)1 lb (pound) - 16 oz or 7000 gr or 1.3 g- 16 oz or 7000 gr or 1.3 g

Household Measure: VolumeHousehold Measure: Volume 1 tsp (teaspoonful) 1 tsp (teaspoonful) - 5 mL- 5 mL 1 tbsp (tablespoonful) 1 tbsp (tablespoonful) - 3 tsp (15 mL)- 3 tsp (15 mL) 1 fl oz (fluid ounce) 1 fl oz (fluid ounce) - 2 tbsp (30 mL (29.57 mL)- 2 tbsp (30 mL (29.57 mL) 1 cup1 cup - 8 fl oz (240 mL)- 8 fl oz (240 mL) 1 pt (pint) 1 pt (pint) - 2 cups (480 mL)- 2 cups (480 mL) 1 qt (quart) 1 qt (quart) - 2 pt (960 mL)- 2 pt (960 mL) 1 gal (gallon) 1 gal (gallon) - 4 qt (3840 mL)- 4 qt (3840 mL)

Household Measure: WeightHousehold Measure: Weight

1 oz (ounce)1 oz (ounce) - 30 g- 30 g 1 lb (pound)1 lb (pound) - 16 oz (454 g)- 16 oz (454 g) 2.2 lb2.2 lb - 1 kg- 1 kg

Numerical RatiosNumerical Ratios

Ratios represent the relationship between: Ratios represent the relationship between: • two parts of the whole two parts of the whole • one part to the wholeone part to the whole

Written as follows: Written as follows: 1:21:2 “1 part to 2 parts”“1 part to 2 parts” ½½ 3:43:4 “3 parts to 4 parts” “3 parts to 4 parts”

¾ ¾

Can use “per,” “in,” or “of,” instead of “to”Can use “per,” “in,” or “of,” instead of “to”• Proportions are frequently used to calculate drug Proportions are frequently used to calculate drug

doses in the pharmacy.doses in the pharmacy.• Use the ratio-proportion method any time one ratio is Use the ratio-proportion method any time one ratio is

complete and the other is missing a component. complete and the other is missing a component.

ProportionsProportions

• An expression of equality between two ratios.An expression of equality between two ratios.• Noted by :: or =Noted by :: or =

3:4 = 15:20 or 3:4 :: 15:20

Rules for Ratio-Proportion MethodRules for Ratio-Proportion Method

• Three of the four amounts must be knownThree of the four amounts must be known• The numerators must have the same unit of The numerators must have the same unit of

measuremeasure• The denominators must have the same unit of The denominators must have the same unit of

measuremeasure

Steps for Solving for XSteps for Solving for X

1.1. Calculate the proportion by placing the ratios in Calculate the proportion by placing the ratios in fraction form so that the fraction form so that the xx is in the upper-left corner. is in the upper-left corner.

2.2. Check that the unit of measurement in the Check that the unit of measurement in the numerators is the same and the unit of measurement numerators is the same and the unit of measurement in the denominators is the same.in the denominators is the same.

3.3. Solve for Solve for xx by multiplying both sides of the proportion by multiplying both sides of the proportion by the denominator of the ratio containing the by the denominator of the ratio containing the unknown, and cancel.unknown, and cancel.

4.4. Check your answer by seeing if the product of the Check your answer by seeing if the product of the means equals the product of the extremes.means equals the product of the extremes.

RememberRemember

When setting up a proportion to solve a When setting up a proportion to solve a conversion, the units in the numerators must conversion, the units in the numerators must match, and the units in the denominators must match, and the units in the denominators must match.match.

Example 3 Solve for XExample 3 Solve for X

PercentsPercents

• The number of parts per 100 can be written as a The number of parts per 100 can be written as a fraction, a decimal, or a ratio.fraction, a decimal, or a ratio.

• Percent means “per 100” or hundredths.Percent means “per 100” or hundredths.• Represented by symbol %.Represented by symbol %.

• Usually GRAMS PER 100 ml (solutions)Usually GRAMS PER 100 ml (solutions) 30% = 30 parts in total of 100 parts30% = 30 parts in total of 100 parts

30:100, 0.30, or

100

30

Percents in the PharmacyPercents in the Pharmacy

• Percent strengths are used to describe IV Percent strengths are used to describe IV solutions and topically applied drugs.solutions and topically applied drugs.

• The higher the % of dissolved substances, the The higher the % of dissolved substances, the greater the strength.greater the strength.

• A 1% solution contains A 1% solution contains • 1 g of drug per 100 mL of fluid1 g of drug per 100 mL of fluid• Expressed as 1:100, 1/100, or 0.01Expressed as 1:100, 1/100, or 0.01

Equivalent ValuesEquivalent Values

100

45

100

5.0

Converting a Ratio to a PercentConverting a Ratio to a Percent

1.1. Designate the first number of the ratio as the Designate the first number of the ratio as the numerator and the second number as the numerator and the second number as the denominator.denominator.

2.2. Multiply the fraction by 100%, and simplify as Multiply the fraction by 100%, and simplify as needed.needed.

3.3. Multiplying a number or a fraction by 100% Multiplying a number or a fraction by 100% does not change the value.does not change the value.

Converting a Ratio to a PercentConverting a Ratio to a Percent

5:1 = 5/1 × 100% = 5 × 100% = 500%

1:5 = 1/5 × 100% = 100%/5 = 20%

1:2 = 1/2 × 100% = 100%/2 = 50%

Converting a Percent to a RatioConverting a Percent to a Ratio

1.1. Change the percent to a fraction by dividing it Change the percent to a fraction by dividing it by 100.by 100.

2.2. Reduce the fraction to its lowest terms.Reduce the fraction to its lowest terms.3.3. Express this as a ratio by making the Express this as a ratio by making the

numerator the first number of the ratio and numerator the first number of the ratio and the denominator the second number.the denominator the second number.

Converting a Percent to a RatioConverting a Percent to a Ratio

2% = 2 ÷ 100 = 2/100 = 1/50 = 1:5010% = 10 ÷ 100 = 10/100 = 1/10 = 1:1075% = 75 ÷ 100 = 75/100 = 3/4 = 3:4

Converting a Percent to a DecimalConverting a Percent to a Decimal

1.1. Divide by 100% or insert a decimal point two Divide by 100% or insert a decimal point two places to the left of the last number, inserting places to the left of the last number, inserting zeros if necessary. zeros if necessary.

2.2. Drop the % symbol.Drop the % symbol.

Converting a Decimal to a PercentConverting a Decimal to a Percent

1.1. Multiply by 100% or insert a decimal point Multiply by 100% or insert a decimal point two places to the right of the last number, two places to the right of the last number, inserting zeros if necessary. inserting zeros if necessary.

2.2. Add the the % symbolAdd the the % symbol.

Percent to DecimalPercent to Decimal4% = 0.04 4 ÷ 100% = 0.0415% = 0.15 15 ÷ 100% = 0.15200% = 2 200 ÷ 100% = 2

Decimal to PercentDecimal to Percent0.25 = 25% 0.25 × 100% = 25%1.35 = 135% 1.35 × 100% = 135%0.015 = 1.5% 0.015 × 100% = 1.5%

Example 4Example 4

How many milliliters are there in 1 gal, 12 fl oz?How many milliliters are there in 1 gal, 12 fl oz?

According to the values in Table 5.7, 3840 mL are found in According to the values in Table 5.7, 3840 mL are found in 1 gal. Because 1 fl oz contains 30 mL, you can use the ratio-1 gal. Because 1 fl oz contains 30 mL, you can use the ratio-proportion method to calculate the amount of milliliters in proportion method to calculate the amount of milliliters in 12 fl oz as follows:12 fl oz as follows:

Example 4Example 4 How many milliliters are there in 1 gal, 12 fl oz?How many milliliters are there in 1 gal, 12 fl oz?

Example Example A solution is to be used to fill hypodermic syringes, A solution is to be used to fill hypodermic syringes,

each containing 60 mL, and 3 L of the solution is each containing 60 mL, and 3 L of the solution is available. How many hypodermic syringes can be filled available. How many hypodermic syringes can be filled

with the 3 L of solution?with the 3 L of solution?

1 L is 1000 mL. The available supply of solution is therefore1 L is 1000 mL. The available supply of solution is therefore

Determine the number of syringes by using the ratio-proportion Determine the number of syringes by using the ratio-proportion method:method:

Example Example How many hypodermic syringes can be filled with the 3 L of How many hypodermic syringes can be filled with the 3 L of

solution?solution?

Example Example You are to dispense 300 mL of a liquid preparation. If You are to dispense 300 mL of a liquid preparation. If the dose is 2 tsp, how many doses will there be in the the dose is 2 tsp, how many doses will there be in the

final preparation?final preparation?

Begin solving this problem by converting to a Begin solving this problem by converting to a common unit of measure using conversion values.common unit of measure using conversion values.

Example 6Example 6 If the dose is 2 tsp, how many doses will there be in the final If the dose is 2 tsp, how many doses will there be in the final

preparation?preparation?

Using these converted measurements, the solution can be Using these converted measurements, the solution can be determined one of two ways:determined one of two ways:

Solution 1: Solution 1: Using the ratio proportion method and the Using the ratio proportion method and the metric system.metric system.

Example 6Example 6 If the dose is 2 tsp, how many doses will there be in the final If the dose is 2 tsp, how many doses will there be in the final

preparation?preparation?

Example 7Example 7How many grains of acetaminophenHow many grains of acetaminophen

should be used in a Rx for 400 mg acetaminophen?should be used in a Rx for 400 mg acetaminophen?

Solve this problem by using the ratio-proportion method. Solve this problem by using the ratio-proportion method. The unknown number of grains and the requested The unknown number of grains and the requested number of milligrams go on the left side, and the ratio of number of milligrams go on the left side, and the ratio of 1 gr 65 mg goes on the right side, per Table 5.5.1 gr 65 mg goes on the right side, per Table 5.5.

Example 7Example 7How many grains of acetaminophenHow many grains of acetaminophenshould be used in the prescription?should be used in the prescription?

Example 8Example 8A physician wants a patient to be given 0.8 mg of A physician wants a patient to be given 0.8 mg of

nitroglycerin. On hand are tablets containing nitroglycerin. On hand are tablets containing nitroglycerin 1/150 gr. How many tablets should the nitroglycerin 1/150 gr. How many tablets should the

patient be given?patient be given?

Begin solving this problem by determining the number of Begin solving this problem by determining the number of grains in a dose by setting up a proportion and solving for grains in a dose by setting up a proportion and solving for the unknown.the unknown.

Example 8Example 8 How many tablets should the patient be given?How many tablets should the patient be given?

Common Calculations in the Common Calculations in the PharmacyPharmacy

• Calculations of DosesCalculations of DosesActive ingredient (to be administered)/solution (needed)

=

Active ingredient (available)/solution (available)

Example 9Example 9 You have a stock solution that contains 10 mg of active You have a stock solution that contains 10 mg of active

ingredient per 5 mL of solution. The physician orders a dose of ingredient per 5 mL of solution. The physician orders a dose of 4 mg. How many milliliters of the stock solution will have to 4 mg. How many milliliters of the stock solution will have to

be administered?be administered?

Example 9Example 9How many milliliters of the stock solution will have to be How many milliliters of the stock solution will have to be

administered?administered?

Example 10Example 10 An order calls for Demerol 75 mg IM q4h prn pain. The supply An order calls for Demerol 75 mg IM q4h prn pain. The supply

available is in Demerol 100 mg/mL syringes. How many available is in Demerol 100 mg/mL syringes. How many milliliters will the nurse give for one injection?milliliters will the nurse give for one injection?

Example 10Example 10 How many milliliters will the nurse give for one injection?How many milliliters will the nurse give for one injection?

Example 11Example 11

An average adult has a BSA of 1.72 mAn average adult has a BSA of 1.72 m22 and requires and requires an adult dose of 12 mg of a given medication. A childan adult dose of 12 mg of a given medication. A childhas a BSA of 0.60 mhas a BSA of 0.60 m22. . If the proper dose for pediatric and adult patients is a If the proper dose for pediatric and adult patients is a linear function of the BSA, what is the proper linear function of the BSA, what is the proper pediatric dose? Round off the final answer.pediatric dose? Round off the final answer.

Example 11Example 11 What is the proper pediatric dose?What is the proper pediatric dose?

Example 11Example 11 What is the proper pediatric dose?What is the proper pediatric dose?


A dry powder antibiotic must be reconstituted for A dry powder antibiotic must be reconstituted for use. The label states that the dry powder occupies use. The label states that the dry powder occupies 0.5 mL. Using the formula for solving for powder 0.5 mL. Using the formula for solving for powder volume, determine the diluent volume (the amount volume, determine the diluent volume (the amount of solvent added). You are given the final volume for of solvent added). You are given the final volume for three different examples with the same powder three different examples with the same powder volume.volume.

Example 12Example 12 Using the formula for solving for powder volume, Using the formula for solving for powder volume,

determine the diluent volume.determine the diluent volume.

Example 12Example 12 Using the formula for solving for powder volume, determine Using the formula for solving for powder volume, determine

the diluent volume.the diluent volume.


You are to reconstitute 1 g of dry powder. The label You are to reconstitute 1 g of dry powder. The label states that you are to add 9.3 mL of diluent to make states that you are to add 9.3 mL of diluent to make a final solution of 100 mg/mL. What is the powder a final solution of 100 mg/mL. What is the powder volume?volume?

Example 13Example 13 What is the powder volume?What is the powder volume?

Step 1. Step 1. Calculate the final Calculate the final volume. The strength of the volume. The strength of the final solution will be 100 final solution will be 100 mg/mLmg/mL.

Example 13Example 13What is the powder volume?What is the powder volume?


Dexamethasone is available as a 4 mg/mL Dexamethasone is available as a 4 mg/mL preparation. An infant is to receive 0.35 mg. Prepare preparation. An infant is to receive 0.35 mg. Prepare a dilution so that the final concentration is 1 mg/mL. a dilution so that the final concentration is 1 mg/mL. How much diluent will you need if the original How much diluent will you need if the original product is in a 1 mL vial and you dilute the entire product is in a 1 mL vial and you dilute the entire vial?vial?

Example 14Example 14 How much diluent will you need if the original product is in a 1 mL vial and you How much diluent will you need if the original product is in a 1 mL vial and you

dilute the entire vial?dilute the entire vial?

Example 14Example 14How much diluent will you need if the original product How much diluent will you need if the original product

is in a 1 mL vial and you dilute the entire vial?is in a 1 mL vial and you dilute the entire vial?


Prepare 250 mL of dextrose 7.5% weight in volume Prepare 250 mL of dextrose 7.5% weight in volume (w/v) using dextrose 5% (D5W) w/v and dextrose (w/v) using dextrose 5% (D5W) w/v and dextrose 50% (D50W) w/v. How many milliliters of each will 50% (D50W) w/v. How many milliliters of each will be needed?be needed?

Example 15Example 15 How many milliliters of each will be needed?How many milliliters of each will be needed?

Step 1. Step 1. Set up a box arrangement and at the upper-left Set up a box arrangement and at the upper-left corner, write the percent of the highest concentration corner, write the percent of the highest concentration (50%) as a whole number.(50%) as a whole number.


Step 2. Step 2. Subtract the center number from the upper-left Subtract the center number from the upper-left number (i.e., the smaller from the larger) and put it at number (i.e., the smaller from the larger) and put it at the lower-right corner. Now subtract the lower-left the lower-right corner. Now subtract the lower-left number from the center number (i.e., the smaller from number from the center number (i.e., the smaller from the larger), and put it at the upper-right corner.the larger), and put it at the upper-right corner.

Example 15 Example 15 How many milliliters of each will be needed?How many milliliters of each will be needed?

7.5

2.5 mL parts D50W

42.5 mL parts D5W45 mL total parts D7.5W

50

5

Example 15 Example 15 How many milliliters of each will be needed?How many milliliters of each will be needed?


Example 15Example 15How many milliliters of each will be neededHow many milliliters of each will be needed??



Terms to RememberTerms to RememberTerms to RememberTerms to Remember

1. Body surface area 1. Body surface area 2. Concentration 2. Concentration 3. Conversions 3. Conversions 4. Denominator 4. Denominator 5. Flow rate 5. Flow rate 6. Least common 6. Least common

denominator denominator 7. Milliequivalent (meq)7. Milliequivalent (meq)

8. Nomogram 8. Nomogram 9. Numerator 9. Numerator 10. Positional notation 10. Positional notation 11. Qs ad 11. Qs ad 12. Total parenteral nutrition 12. Total parenteral nutrition 13. Usual and customary (U&C) 13. Usual and customary (U&C) 14. Valence 14. Valence 15. Variable15. Variable

Technology

Chapter 6 pharmacy calculation