pharmacy calculations [1]

Pharmacy Calculations: of 39

The A-B-Cs of 1-2-3: Performing Pharmacy Calculations. Timothy R. Schnur, SSgt, USAF, Pharmacy Apprentice/Craftsman Instructor, Sheppard AFB, TX,

Description: Accurately performing pharmaceutical calculations is a critical component in providing patient care in every pharmacy practice environment and a vital part of any pharmacy technicians’ duty. Although most pharmaceutical calculations are not overly difficult, they do require flawless accuracy. Correct calculations contribute as much to patient outcomes as the newest methods and guidelines for diagnosis, treatment, and prevention; and errors in calculations can turn the best attempts at optimal patient care catastrophic. This session will present a review of pharmacy calculations for technicians.

Learning Objectives: 1. Identify types of pharmaceutical problems required for pharmacy operations. 2. Convert between the various denominations of each of the basic units of the metric system. 3. Perform pharmaceutical conversions between the apothecary and the Avoirdupois measurement systems. 4. Solve pharmaceutical problems involving reducing or enlarging pharmaceutical formulas. 5. Solve pharmaceutical problems involving ratio and proportion pharmaceutical formulas. 6. Solve pharmaceutical calculation problems involving percentage and ratio strengths. 7. Calculate the amount of diluent to be combined with a given amount of stock preparation to make a product of a lesser strength. 8. Calculate the amounts of two stock preparations required to prepare a specified volume of a stated intermediate strength preparation when given the strengths of the two stock preparations. 9. Calculate the appropriate dose for a patient when given the recommended dosage of that drug and the patient's weight in either pounds or kilograms. 10. Calculate the appropriate drop factors for patients receiving IV therapy. 11. Describe methods for double-checking calculations. 1. Identify types of pharmaceutical problems required for pharmacy operations. Types: conversion between units of measure; reducing and enlarging; ratio and proportion; percentage and ratio strengths; concentration dilution; allegations; drug dosages; flow rates and double check methods. To prepare medications quickly and accurately you must be able to calculate dosages and make conversions. This requires you to be familiar with systems of weights and measures and their equivalents. This section will give you a starting point in refreshing you with some common conversions used within the pharmacy.

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Convert between the systems of pharmaceutical weights and measures

AVOIRDUPOIS SYSTEM - weight only; primarily used for compounding

437.5gr = 1oz = 28.35gm 7000gr = 1lb =16oz = 454gm 1kg = 2.2lb 1gr = 64.8mg

APOTHECARY SYSTEM - comprised of both volume and weight; used for compounding and concentration dilution mixtures

VOLUME

1 teaspoonful (tsp) = 5 milliliters (ml) = 1 dram = 5 cubic centimeters (cc) 1 tablespoonful (tbsp) = 15 milliliters (ml) 29.57milliliters (ml) = 1 fluid ounce (fl oz) 473 milliliters (ml) = 1 pint (pt) = 16 fluid ounce (fl oz) 946 milliliters = 1 quart = 2 pints 3784 milliliters = 1 gallon = 8 pints = 128 fl oz

WEIGHT

1gr = 64.8mg 1 ounce = 31.1gm = 480gr

METRIC TABLE

K H D Gram

Liter Meter

d c m X X mc

Kilo Hecto Deca deci centi milli micro

x 1000 x 100 x 10 1 1/10 1/100 1/1000 1/1,000,000

0.1 0.01 0.001 0.000001



2. Convert between the various denominations of each of the basic units of the metric system. 1. 25 cl = __________ L

2. 15 Km = ___________m

3. 1,000 mg = __________ gm

4. 500 dl = ___________ Dal

5. 10 mm = ____________ cm

6. 75 mg = _____________ mcg

7. 250 m = _________ cm

8. 0.00085 dg = _____________ mcg

9. 450 cc = ___________ L

10. 2,500 mg = ____________ gm

11. 5 Kl = ___________ dl

12. 8,500 mcg = ___________ mg

13. 750 m = ___________ Hm

14. 45 Dal = ____________ dl

15. 0.00025 Hg = ___________ mcg

16. 0.375 mg = ___________ mcg

17. 3 gm = ____________ mg

18. 12 gms = _________ Kg

19. 2,500 mg = _________ Dag

20. 0.025 Hl = __________ dl

21. 2 Kl = ____________ cc

22. 70,000 mm __________ Hm

23. 5,400,250 mcl = __________ L

24. 0.085 Hg = ____________ gm

25. 375 cm = ___________ Dam

Answers: (1) 0.25 L (2) 15,000 m (3) 1 gm (4) 5 Dal (5) 1 cm (6) 75,000 mcg (7) 25,000 cm (8) 85 mcg (9) 0.45 L (10) 2.5 gm (11) 50,000 dl (12) 8.5 mg (13) 7.5 Hm (14) 4,500 dl (15) 25,000 mcg (16) 375 mcg (17) 3,000 mg (18) 0.012 Kg (19) 0.25 Dag (20) 25 dl (21) 2,000,000 cc (cc = ml) (22) 0.7 Hm (23) 5.40025 L (24) 8.5 gm (25) 0.375 Dam 3. Perform pharmaceutical conversions between the apothecary and the Avoirdupois measurement systems. When converting measures outside of the metric system, the ratio and proportion method works well. A ratio is a given comparison between two numbers - Example - 1 oz = 437.5 gr is a ratio and may be expressed as such "The ratio of ounces to grains in the AV system is 1 to 437.5" this may also be expressed as 1:437.5 or 1/437.5



When converting measures using a ratio and proportion, you must always have a known ratio. Example: We can convert any number of ounces to grains, because we know the relationship between ounces and grains

a. Convert 3 oz to grains:

b. Known ratio between ounces and grains: 1 oz = 437.5 gr

c. Unknown - how many grains are in 3 ounces?: 3 oz = X

gr

d. Ratio and proportion

1 oz 437.5 gr 3 oz X gr

e. Cross multiply the known values -

3 oz x 435.7 gr = 1,312.5 oz/gr

f. Divide that number by the final known value -

1,312.5 divided by 1 = 1,312.5 gr

Perform the following conversions using the ratio and proportion method. Within the AV system. (Round all decimals to 3 places to the right of the decimal point.) 1. 1.25 lb = _____________ oz 2. 15,000 gr = ____________ lb 3. 2,188 gr = ___________ oz 4. 116 oz = ___________ lb 5. 5.6 lb = ____________ oz



6. 3.25 lb = ___________ gr 7. 3,500 gr = ___________ oz 8. 4.5 oz = _____________ gr 9. 1.65 lb = ____________ gr 10. 2.8 oz = ____________ gr 11. 800 oz = ______________ lb 12. 218.8 gr = ___________ oz 13. 105,000 gr = _____________ lb Answers: (1) 20 (2) 2.143 (3) 5.001 (4) 7.25 (5) 89.6 (6) 22,750 (7) 8 (8) 1,968.75 (9) 11,550 (10) 1,225 (11) 50 (12) 0.5 (13) 15 Convert between the AV and metric systems using the ratio and proportion method. 1. 165 lb = __________ kg 2. 5,000 gm = ___________ lb 3. 210 lb = ___________ kg 4. 45 kg = ____________ lb 5. 2.25 lb = ___________ gm 6. 3.5 oz = _____________ gm 7. 2,500 mg = ____________ gr 8. 3.25 kg = _____________ lb 9. 8 oz = _______________ gm 10. 195 lb = _____________ kg 11. 324 mg = _____________ gr



12. 1 gm = ______________ gr (determine the known ratio between the metric system and grains, and convert the grams to the appropriate unit first…) 13. 400 gm = ______________ oz 14. 1 kg = ________________ oz (determine the known ratio and convert within the metric system first…) Answers: (1) 75 (2) 11.013 (3) 95.455 (4) 99 (5) 1,021.5 (6) 99.225 (7) 38.58 (8) 7.15 (9) 226.8 (10) 88.636 (11) 5 (12) 15.432 (13) 14.109 (14) 35.273 Convert the following apothecary problems using the ratio and proportion

method.

1. 2,000 gr = ________________ oz (AP) 2. 500 gm = ______________ oz (AP) 3. 500 mg = _______________ gr 4. 100 fl oz = _____________ pt 5. 500 fl oz = ______________ gal 6. 4.5 oz (AP) = _______________ gm 7. 3 gr = __________________ mg 8. 20,000 ml = _________________ gal 9. 3 pt = _______________ ml 10. 119 ml = ________________ fl oz 11. 2.5 gal = __________________ fl oz 12. 5,000 gr = _________________ oz (AP) 13. 25 pt = __________________ gal 14. 1,500 ml = ______________ pt



Answers: (1) 4.167 (2) 16.077 (3) 7.716 (4) 6.25 (5) 3.906 (6) 139.95 (7) 194.4 (8) 5.284 (9) 1,419 (10) 4.024 (11) 320 (12) 10.417 (13) 3.125 (14) 3.171

15. 6 fl oz = _________________ ml 16. 0.75 gal = _________________ ml 17. 1,000 gr = _________________ oz (AP) 18. 3.25 gal = _______________ pt 19. 350 gr = _______________ mg 20. 2.5 oz (AP) = _____________ gr 21. 1.5 tsp = _______________ ml 22. 12.5ml = ______________ tsp 23. 1.5 fl oz = ______________ ml 24. 500 mg = _______________ gr 25. 500 fl oz = ______________ gal 26. 375 ml = _________________ fl oz 27. 24 fl oz = ________________ pt 28. 275 gm = ______________ oz (AP) 29. 500 ml = _____________ Tbsp Answers: (15) 177.42 (16) 2,838.75 (17) 2.083 (18) 26 (19) 22,680 (20) 1,200 (21) 7.5 (22) 2.5 (23) 44.355 (24) 7.716 (25) 3.906 (26) 12.682 (27) 1.5 (28) 8.842 (29) 33.333



Perform the following conversions (you will need to convert many of these twice - see the example.) Example: 7 fl oz = _______________ Tbsp Convert fl oz to ml, then ml to Tbsp Convert fl oz to ml. 7 fl oz X Tbsp 1 fl oz 29.57 ml 29.57 ml x 7 fl oz = 206.99ml/fl oz 206.99 ml/fl oz divided by 1 fl oz = 206.99 ml Now convert ml to Tbsp. 15ml 1 Tbsp 206.99ml X Tbsp 206.99 ml x 1 Tbsp = 206.99 ml/Tbsp 206.99 ml/Tbsp divided by 15 ml = 13.799 Tbsp 1. 0.5 kg = _______________ oz (AP)

2. 0.74 gm = ________________ gr

3. 1.15 gal = _________________ L

4. 1.25 L = ________________ fl oz

5. 3 fl oz = _______________ tsp

6. 2.5 L = _______________ pt

7. 0.65 pt = _______________ tsp

8. 0.25 gal = ______________ Tbsp

9. 1.5 L = ________________ Tbsp

10. 12 pt = ________________ L

11. 1 pt = _________________ Tbsp



12. 12 L = _________________ pt

13. 2 fl oz = _______________ tsp

14. 8 gr = _________________ gm

15. 2.5 pt = _______________ L

16. 0.5 L = ________________ Tbsp

17. 0.65 kg = _______________ oz (AP)

18. 1 gm = __________________ gr

19. 6.3 L = ________________ gal

20. 0.324 gm = ________________ gr

21. 3.25 L = ______________ fl oz

22. 12 Tbsp = ______________ tsp

23. 1,250 gr = ________________ oz (AP)

Answers: (1) 16.077 (2) 11.42 (3) 4.353 (4) 42.273 (5) 17.742 (6) 5.285 (7) 61.49

(8) 63.083

(9) 100 (10) 5.676 (11) 31.533 (12) 25.37 (13) 11.828 (14) 0.518 (15) 1.183 (16)

33.333

(17) 20.9 (18) 15.432 (19) 1.664 (20) 5 (21) 109.91 (22) 36 (23) 2.604

4. Solve pharmaceutical problems involving reducing or enlarging pharmaceutical formulas. Pharmacy personnel prepare pharmaceuticals from specific recipes or formulas. Most manufacturing formulas are based on quantity of 454gm or 1000mls. The pharmacist may need to make a smaller or larger quantity and, therefore, must reduce or enlarge the formula. The desired amount of ingredient by using the following proportion: Ratio and Proportion Method- Total amount in formula = Quantity in formula

Total amount desired Quantity of amount desired



Rearranging this proportion, we see that

Quantity of amount desired = Total amount desired X Quantity in formula Total amount formula

When a formula specifies a total amount, we can determine how much of each ingredient is needed by using the ratio and proportion method, the factor method or the proportional parts method.

Example: Reduce the formula to make 30 ml. BACLOFEN SUSPENSION 10 mg/ml Lioresal tablets 20 mg 30 tablets Cologel 15 ml Simple Syrup qsad 60 ml Step 1: How much will the original (old) formula make? _______ ml How much Loresal tablets does the "old" formula call for? _______ tablet(s) Step 2: How much do you desire to make? ______ ml Step 3: Set problem up. 30 tablets X = 60 ml 30 ml Step 4: Multiply each side by 30 ml. 30 ml x 30 tablets X x 30 ml = 60 ml 30 ml Step 5: Solve for X. 30 tablets = X 2 Step 6: Repeat this procedure for each ingredient, making sure that each value is placed in the correct position in



the formula. NOTE: qsad- quantity sufficient to make. Factor Method (New Total) General Formula: Total Amt Desired = factor Total Amt in Original Formula (Old Total) Step 1: How much will the original (old) formula make? _______ ml Step 2: How much do you desire to make? ______ ml Step 3: Set problem up. 30 ml 60 ml Step 4: Divide the bottom into the top which results in your factor. 30 ml = 0.5 60 ml Step 5: Use this factor to multiply each ingredient in the formula to find the desired amount. Lioresal tablets Colongel 20 tablets 15 ml x 0.5 x 0.5 answer: 10 tablets answer: 7.5 ml

NOTE: When reducing formulas the value of your factor will always be less than one (1), and when enlarging formulas the value of your factor will always be larger

REDUCE AND ENLARGE FORMULA PRACTICE PROBLEMS 1. Reduce this formula to make 100 ml. Liquid coal tar 4 ml ______ Sulfur 10 gm ______ Lime Water 50 ml ______ Bentonite Magma (QSAD) 120 ml ______ 2. Reduce the formula to make 30 ml.



Ephedrine Sulfate 30 gm ______ Chlorobutanol 5 gm ______ Sodium Chloride 3.6 gm ______ Purified Water (qsad 1000 ml______ 3. From the following formula, calculate the quantity of each ingredient required to prepare 1 gallon. Talc 12 gm ______ Bentonite 3.5 gm______ Zinc Oxide 25 gm ______ Distilled Water (QSAD) 100 ml ______ 4. From the following formula, calculate the quantity of each ingredient required to make 1 liter. Orange Oil 12 ml ______ Lemon Oil 3 ml ______ Coriander Oil 1.2 ml ______ Anise Oil 0.3 ml ______ Alcohol USP (QSAD) 60 ml ______ 5. Reduce the following formula to make 1 pint. Peppermint Oil 2.4 ml ______ Cinnamon Oil 0.16 ml______ Diphenhydramine 12 gm ______ Purified Water (QSAD) 500 ml ______ 6. Enlarge the following to make 4 gallons. Glycerin 15 ml ______ Propylene Glycol 30 ml ______ Syrup 100 ml______ Alcohol (QSAD) 473 ml______ 7. Reduce the following formula to make 1 pint. Terpin Hydrate 30 gm ______ Orange Tincture 65 ml ______ Syrup (QSAD) 1000 ml ______



8. How many mg of zinc oxide are needed to make 4 quarts of the following? Talc 15 gm ______ Zinc Oxide 75 gm ______ Purified Water (QSAD) 800 ml______

ANSWERS: (1) 3.32 ml, 8.3 gm, 41.5 ml, 100 ml (2) 0.9 gm, 0.15 gm, 0.108 gm, 30 ml (3) 454.2 ml, 132.48 gm, 946.25 gm, 3784 ml (4) 200.04 ml, 50.01 ml, 20 ml, 5 ml, 1000 ml (5) 2.27 ml, 0.15 ml, 11.35 gm, 473 ml (6) 480 ml, 960 ml, 3200 ml, 15140 ml (7) 14.19 gm, 30.75 ml, 473 ml (8) 70.95 gm, 354.75 mg, 3784 ml 5. Solve pharmaceutical problems involving ratio and proportion pharmaceutical formulas. Sterile Liquid Medications- Read the package insert, product label or other reference material to find the drug concentration. (Concentration = amount of drug per volume of solution.) Sterile Solid Medications (Dry powders) Read package insert, product label or other reference, to find the amount of diluent needed and the concentration of the product after reconstitution. (Diluent = liquid, used to liquefy powder. Reconstitution = adding a suitable diluent.) When the resulting concentration has been found a ratio and proportion can be used to find the amount of medication needed for the prescribed dose.

EXAMPLE: A vial of Rocephin contains 100 milligrams per milliliter. How many milliliters should be given to a patient to obtain 650 milligrams? The expression of strength will be the first ratio of the proportion: 1 ml = 100 mg Assign the "X" value: 1 ml = X ml 100 mg Find the other known factor: 1 ml = X ml 100mg 650 mg



Then, cross-multiply: 100 X = 650 (1) Solve for "X":

X = 6.5 ml (NOTE: Don't forget to add the unit of measurement.) Basic Principles- Always look for what is being asked: *Number of doses *Total amount of drug *Size of dose Given any two of the above, you can solve for the third. General Formula: Number of doses = Total amount Size of dose Can also be rearranged to: Total amt = number of doses x size of dose Size of dose = Total amount Number of doses EXAMPLE: How many doses are in 120 ml of Benadryl Elixir, if one dose contains 1 dram? X numbers of doses = 120 ml 5 ml Divide to solve for (X): X = 24 doses EXAMPLE: How many milligrams of theophylline does a patient receive per day if the prescription indicates 300 mg tid ? X total amt = 3 X 300 mg Multiply to solve for (X): X = 900 mg total



EXAMPLE: How much propranolol will a patient receive every 6 hours if he is to receive 160 mg per day? X dose = 160 mg 4 doses Divide to solve for (X): X = 40 mg DRUG ADMINISTRATION RATE PRACTICE PROBLEMS 1. If you stock Aminophylline for Injection, 250mg/10ml, how many milliliters should be used to deliver a 200mg dose? 2. When Erythromycin Lactobionate is reconstituted, it yields a concentration of 50mg/ml. How many milliliters are required to give a 0.9gm dose? 3. If 20 milli-equivalents (mEq) of a drug is ordered daily and the drug on hand contains 40mEq/2ml, how many milliliters should be dispensed for a 30-day supply? 4. A 1,000,000 unit vial of Penicillin G Potassium contains 100,000 units/ml when reconstituted with 9.6ml of sterile water for injection. How many milliliters are needed to administer a dose of 600,000 units? 5. If an injectable medication is labeled 500mcg/2ml, and the dose needed is 0.125mg, how many milliliters would you need?



6. An IV order calls for 100mg of hydrocortisone. The available stock is 250mg/2ml vials. How many milliliters would you need to fill the order? 7. How many 5gr tablets should be dispensed to fill the following prescription? Rx: 648mg of ASA q8h X 2 weeks 8. How many tablets would be dispensed for the following prescription? Rx: Take 2 grams initially then 500mg qid for 6 days (Note: Each tablet is 250mg) 9. How many milliliters of alcohol would be used to make 240ml of preparation if each teaspoonful contains 2.8ml of alcohol? 10. In supply you find a vial of Kanamycin Injection labeled 1.0g per 3ml. How many milliliters of this solution must be given to administer a dose of 750mg of drug? 11. You have a vial of Ephedrine Injection labeled 25mg/ml. How many milliliters must be injected in order to administer a dose of 12.5mg? 12. How many milligrams of drug are contained in a 30ml vial of Naloxone, labeled 0.4mg/ml ? 13. How many tablets you would you dispense for the following prescription? Rx: 0.9gm initially then 0.3gm po tid for 14 days (Note each tablet is 300mg)



14. How many milligrams of drug would be in one pint if each dram has 1/8th of a grain? 15. If 0.3mg is the dose to taken daily for 30 days, how many grams will you dispense? 16. The prescription calls for the patient to take one teaspoonful four times a day for 10 days. How many milliliters will you dispense? 17. The dose is one tablespoonful every 6 hours for 1 week. How many milliliters will you dispense? 18. How many doses are in 180ml if each dose contains 2 tablespoonfuls? 19. How many teaspoonful doses are contained in 60ml of a preparation? 20. The physician prescribes 8 fluid ounces of penicillin to be taken in 10ml doses. How many doses will the patient receive? 21. The patient will take 350mg in each dose which is to be taken six times a day for 14 days. How many total grams will this patient need?



22. Twenty doses are to be obtained from 1oz of a chemical. How many milligrams are in each dose? 23. Forty grams of a medication is to be divided into 500 doses. What is the strength of each dose in milligrams? 24. One pound of chemical will make 60 doses. How many milligrams will each dose contain? 25. Six fluid ounces are to be divided into 20 doses. How many milliliters are in each dose? 26. What is the dosage in tablespoonfuls if 480ml of medication is divided into 64 doses? 27. How many tablets would you dispense if 2 tablets are to be taken every 3 hours for 15 days? 28. If a patient takes 2 and 1/2 teaspoonfuls every 8 hours for 10 days how many milliliters of medication would you dispense? 29. If 250mg of medication are to be taken daily for 3 weeks how many grams would you dispense?



30. How many doses can be obtained from 450ml of medication if the size of each dose is 1.5 teaspoonfuls? ANSWERS: (1) 8 ml (2) 18 ml (3) 30 ml (4) 6 ml (5) 0.5 ml (6) 0.8 ml (7) 84 tabs (8) 56 tabs (9) 134.4 ml (10) 2.25 ml (11) 0.5 ml (12) 12 mg (13) 45 tabs (14) 766.26 mg (15) 0.009 gm (16) 200 ml (17) 420 ml (18) 6 doses (19) 12 doses (20) 23.65 doses (21) 29.4 gms (22) 1,417.5 mg (23) 80 mg (24) 7,566.6 mg (25) 8.87 ml (26) ½ tablespoonsful (27) 240 tabs (28) 375 ml (29) 5.25 gm (30) 60 doses 6. Solve pharmaceutical calculations problems involving percentage and ratio strengths. Percentage Preparations Weight-in-weight(w/w) percentage means parts of a drug in parts of a mixture by weight. Percent weight-in-weight expresses the number of grams of a drug or active ingredient in 100 grams of a mixture (g/g). Volume-in-volume(v/v) percentage is parts by volume of the total mixture. Percentage volume in volume expresses the number of milliliters of a drug or active ingredient in 100 milliliters of a mixture and is usually used for mixtures of liquids in liquids. Weight-in-volume (w/v) percentage is parts by weight in parts by volume expresses the number of grams of a drug or active ingredient in 100 milliliters of a mixture. Ratio strength (1:N) is one part by weight or volume in N parts by weight or volume. A 1:200 ratio strength can be 1 gm solid to 200 ml solid or 1 ml liquid to 200 ml liquid or 1 gm solid to 200 ml liquid. EXAMPLE: (w/w) 1. If 2000 gm of ointment contain 75 gm of hydrocortisone, what is the percentage strength (w/w) of the ointment? 75 gm (Active ingredient) (Total Amt) 2000 gm X % Divide to solve for X. 2000 / 75 = x x = 0.0375 *Must change decimal to % x = 3.75 %



EXAMPLE: (v/v) 2. If 8 ml of phenol were added to 480 ml of lotion, what is the percentage of phenol in the lotion? 8 ml (Active Ingredient) (Total Amt) 480 ml X % Divide to solve for X. 8 / 480 = X

EXAMPLE: (w/v) 3. If 1.2 gm of menthol is added to 480 ml of lotion, what is the percentage of menthol in the lotion?

1.2 gm (Active Ingredient) (Total Amt) 480 ml X % Divide to solve for X. 1.2 / 480 = x x = 0.0025 *Must change decimal to % x = 0.25% PERCENTAGE PREPARATIONS 1. How many grams of mercuric chloride are required to prepare 250ml of a 5% solution? 2. How many grams of boric acid are there in 30ml of a 2% solution? 3. How many grams of phenol are required to prepare 480ml of a 1/10% solution?



4. How many grains of silver nitrate will be required to prepare 6 fl oz of a 0.25% solution? 5. If 425gm of sucrose is dissolved in enough water to make 500ml, what is the percentage strength of the solution? 6. If 2 liters of a solution of iodine in alcohol contains 7 grams of iodine, what is the percentage strength of the solution? 7. What are the percentages of the ingredients in the following prescription? Zinc Sulfate 2 grains ______ % Boric Acid 20 grains ______ % Distilled Water (QSAD) 1 fl 8. How many milliliters of a 0.1% solution can be made from one gram of atropine sulfate? 9. How many fluid ounces of a 0.55% solution can be prepared from 75 grains of scopolamine hydrobromide? 10. With 43gm of hydrocortisone powder, how many grams of a 1.5% ointment could you make? 11. How many liter of a 2% iodine tincture can be made from 123gm of iodine?



12. If 1 gallon of a solution contains 474gm of solute, what is the percentage strength of the solution? 13. How many grains of gentian violet should be used in preparing 2 fl oz of a 1/2% solution? 14. How many milliliters of a 6% solution can be prepared from 14gm of neomycin sulfate? 15. What is the percentage strength of solution if 1/4 pound of chemical is dissolved in 0.25 liters? 16. How many pounds of medication are required to make 3 gallons of 7% solution? 17. How many fl oz of 16% solution can be made from 7000 grains of chemical? 18. How many quarts of 5% solution can be made from 47.3 grams of drug? 19. How many grains are needed to make 4 quarts of a 1/8% solution?



20. How many fl oz. (apothecary) of a 16% solution can be made from 9100 grains of drug? 21. If 12 grains of powder are dissolved in enough water to make one pint of solution, what is the percentage strength? 22. How many grains of NaCl are needed to make 8 fl oz of 0.9% solution? 23. How much Thymol would be needed if a prescription was written for 240gm of 4%? 24. If 1000ml contains 0.25mg, what is the percentage of the solution? 25. If 10 grains are dissolved in 250ml of solution, what is the percentage of this solution? ANSWERS: (1) 12.5 gm (2) 0.6 gm (3) 0.48 gm (4) 6.83 gr (5) 85% (6) 0.35% (7) 0.43%, 4.3% (8) 1000 (9) 29.97 fl oz (10) 2866 gm (11) 6.15 L (12) 12.5% (13) 4.55 gr (14) 233.3 ml (15) 45.4% (16) 1.75 lbs (17) 96.15 fl oz (18) 1 quart (19) 72.8 gr (20) 124.65 fl oz (21) 0.164% (22) 32.76 gr (23) 9.6 gm (24) 0.00002% (25) 0.25% 7. Calculate the amount of diluent to be combined with a given amount of stock preparation to make a product of a lesser strength. Concentration and dilution Stock solutions are bulk solutions of known concentration frequently prepared for convenience in dispensing. They are frequently concentrated solutions from which more dilute solutions can be quickly prepared. Although, dilute solutions are also compounded. These solutions can be used with ratio strengths or percentage strengths.



General formula for solving: Amt1 x %1 = Amt2 x %2 Amt1 = the quantity or amount of the ORIGINAL preparation.

%1 = the % strength of the ORIGINAL preparation expressed as a decimal or percent Amt2 = the quantity or amount of the WANTED preparation %2 = the % strength of the WANTED preparation expressed as a decimal or percent To solve concentration and dilution problems you need to identify the two preparations in the equation, convert ratio or percentage strengths to decimal expressions and convert to same systems of measurement. EXAMPLE: If 500 ml of a 15% solution are diluted to 1500 ml, what will be the percent strength? Amt1 x %1 = Amt2 x %2 Step 1: Identify the two preparations in the problem and assign values to appropriate terms. Step 2: Solve the equation by multiplying and solving for X.

500 ml x 15% = 1500 ml x X%

7500 = 1500X

7500/1500 = 1500X/1500

X = 5%

Step 3: Don’t forget to check the final answer for the correct units!!! CONCENTRATION AND DILUTION PRACTICE PROBLEMS 1. How many milliliters of a 25% solution can be prepared from 750ml of a 65% solution? 2. If 30gm of a 45% powder was diluted to make a 30% powder, how many grams will the new preparation weigh?



3. If you dilute 2 pints of a 65% solution to 30%, how many fl oz will the new preparation measure? 4. How many grams of a 10% phosphoric acid can be made from 1kg of 85% phosphoric acid? 5. If 20ml of a 1:200 solution of a chemical is diluted to 500ml, what is the ratio strength? 6. If 55ml of an 18% solution is diluted to 330ml, what will be the percentage strength? 7. How many milliliters of a 1:400 stock solution should be used to prepare 2L of a 1:2000 solution? 8. If 24 fl oz were prepared by diluting 1 pint of a 1:500 solution, what percentage strength would it be? 9. If 2 fl oz (apothecary) of a 25% solution is diluted to 5%, how many fluid ounces will the new solution measure? 10. How many pounds of a 1% cream can be made from 10,000gm of an 8.5% cream?



11. How many milliliters of a 15% solution can be made from a quart of a 60% solution? 12. How many liters of a 1/1,000 solution can be made form 200ml of a 0.1% solution? 13. How many milliliters of a 6% solution can be made from 2L of a 36% solution? 14. How many pints of a 6% solution can be made from 4 fl oz (apothecary) of a 15% solution? 15. How much of a 25% solution is needed to prepare 473 ml of a 10% solution? ANSWERS: (1) 1950 ml (2) 45 gm (3) 69.33 fl oz (4) 8500 gm (5) 1:5000 (6) 3% (7) 400 ml (8) 0.13% (9) 10 fl oz (10) 187.22 lbs (11) 3784 ml (12) 0.2 L (13) 12000 ml (14) 0.625 pts (15) 189.2 ml 8. Calculate the amounts of two stock preparations required to prepare a specified volume of a stated intermediate strength preparation when given the strengths of the two stock preparations. Alligations Alligation is a method used for calculating the average value of a mixture obtained by combining known quantities of two or more substances, the values of which are known quantities of two or more substances, the values of which are known. Step 1: Make a "tic-tac-toe" pattern. Step 2: Enter the percent strength of the stronger solution in the upper left



hand box. Step 3: Enter the percent strength of the weaker solution to be mixed in the lower left hand box. Step 4: Enter the desired percent strength of the solution in the center box. Step 5: Let x and y equal the unknown volume of the solutions to be mixed to obtain the desired mixture.

Have Want Parts Amount A Blank X R Blank C Z T B Blank Y S Procedure: 1. Subtract C from A to solve for Y. 2. Subtract B from C to solve for X. 3. X/Y = i.e. 20/25 = 4/5, which is interpreted as 4 parts to 5 parts, or a total of 9 parts. For every 4 parts of 95% alcohol, you must use 5 parts of 50% alcohol to attain 70% alcohol.

Alligation is often expanded to include calculations to determine the volume amount of each of the components to be combined to attain a given amount of a different strength solution.

EXAMPLE: As in the previous example, 4 parts of 5 parts will be used. This example, however, will be expanded to include a desired amount.

How much 95% alcohol and how much 50% alcohol will be needed to attain 450 ml of 70% alcohol?

4 95 20 70 9 50 25 5 Step 1. What is the desired product? c = _____ What is the greater strength? a = _____ What is the lesser strength? b = _____



Step 2. Place these values in the grid Step 3. The difference between B and C. _____ The difference between A and C. _____ Step 4. Reduce the proportion to lowest terms. (Blocks X and Y, i.e. 20/25 reduced to 4/5) Step 5. Find Z by adding blocks X and Y. Step 6. Looking at the right half of this grid, you should recognize two ratio and proportion problems that are set up. By solving these simple problems you will find out exactly how much of each ingredient is necessary. 4 X 9 450 ml 9 450 ml 5 X 9 X = 4 x 450 9 X = 5 x 450 9 X = 1800 9 X = 2250 X = 200 ml X = 250 ml of 95 % alcohol of 50 % alcohol ALLIGATION PRACTICE PROBLEMS 1. How many grams of sulfathiazole should be added to 3400gm of a 10% sulfathiazole cream to prepare a cream containing 15% sulfathiazole? Have Want Parts Amount 100% Blank ? gm Blank 15% 10% Blank 3400gm 2. In what proportions should be 95% alcohol be mixed with 30% alcohol to make 70% alcohol? Have Want Parts Amount 95 % Blank ?



Blank 70% 30% Blank ? 3. How many grams of 20% precipitated sulfur ointment and 5% precipitated sulfur ointments should be used to make 908gm of 8% ointment?

Have Want Parts Amount 20% Blank ? gm Blank 8% 908gm 5% Blank ? gm 4. How many grams of coal tar solution (LCD) should be added to 2700gm of an ointment base to prepare a 10% coal tar ointment? 5. How many grams of coal tar should be added to 925gm of zinc oxide paste to prepare a 6% coal tar ointment? 6. In what proportions should solutions of 12% and 4% be mixed to make a 5% solution? 7. How many grams of petrolatum should be added to 250gm of 20% sulfathiazole ointment to make a 5% sulfathiazole ointment? 8. How many milliliters of 95% isopropyl alcohol must be mixed with purified water to obtain 7568ml of 70% isopropyl alcohol?



9. How many milliliters of water should be added to a quart of 75% solution to make 25% solution? 10. How many grams of sulfur should be mixed with some 1:400 sulfur to make 2 ounces (AV) of 1:25 sulfur ointment? 11. How many grams of coal tar should be added to 908gm of zinc oxide paste to prepare a 9% coal tar ointment? 12. How many milligrams of petrolatum should be added to 340gm of a 35% sulfur ointment to make 10% sulfur ointment? 13. How many milliliters of water should be added to some 50% isopropyl alcohol to make 2 gallons of 40%? 14. How many milliliters of water should be added to a liter of 1:250 solution to make a 1:4000 solution? 15. How many milliliters of 8% solution can be made if 1 liter of 30% solution is mixed with water?



16. How many liters of water should be added to a gallon of 80% solution to make 50% solution? 17. How many milliliters of 90% alcohol and 60% alcohol should be added together to make 4 pints of 75% alcohol? 18. How many milliliters of alcohol should be mixed with 1.5 quarts of 30% alcohol to make some 70% alcohol? 19. In what proportions should 90% acetone be mixed with 40% acetone to make 65% acetone? 20. How many milliliters of water should be added to a liter of 75% alcohol to make some 45% ANSWERS: (1) 200 gm (2) 8, 5 (3) 181.6 gm, 726.4gm (4) 300 gm (5) 59.04 gm (6) 1 : 7 (7) 750 gm (8) 5,576.42 ml (9) 1,892 ml (10) 2.13 gm (11) 89.8 gm (12) 850,000 mg (13) 1,513.6 ml (14) 15,000 ml (15) 3,750 ml (16) 2.27 ml (17) 946 ml, 946 ml (18) 1,892 ml (19) 1 : 1 (20) 666.6 ml 9. Calculate the appropriate dose for a patient when given the reecommended dosage of that drug and the patient’s weight in either pounds or kilograms. Dosage Calculations - medications may be dosed by one of at least three different ways: body weight, body surface area, and age. Body weight and surface area are the most accurate. In any case, the appropriate patient information will need to be provided. When medications are prescribed, there is often an acceptable dosage range the patient may receive. Pharmacy's duty is to make sure the prescription's dosage falls within the acceptable range. When checking a dose, first check the reference to see how the recommended dose is expressed, then you will know how to proceed with checking the prescription



Example 1: An adult male has a prescription that reads - penicillin 250mg, qid, dispense 40

1. First, check the dose in a reference: according to Facts and Comparisons,

the dosage for adults and children over 12 years of age ranges from 125mg

bid, to 500mg qid

2. According to that information, this dose is appropriate

Example 2: cephadrine 250mg/5ml suspension, 150mg qid x10d, dispense

150ml, patient weight, 20 kg, age 6 y/o

1. First, check the dose in a reference: according to Facts and Comparisons,

the dose for children over 9 months of age is 25-50mg/kg/day in divided

doses every 6 or 12 hours

2. To compare, determine how much the patient is receiving per day: 150mg

x qid = 600mg/day

3. Next divide the total amount of medication by the body weight: 600mg /

20 kg = 30mg/kg, which is between 25 and 50mg

Example 3: chloral hydrate syrup 500mg/5ml, 1 tbsp prior to surgery

appointment for sedation, patient weight 15 kg, 3 y/o

1. First check dose in reference: according to Facts and Comparisons, as a

sedative for children, 25mg/kg/day, up to 500mg per dose

2. Change any units to metric: 1 tbsp = 15ml



3. Determine how much the patient is to receive per the prescription: ratio

and proportion is useful here:

500 mg x mg

5 ml 15 ml

4. Multiply 15 ml x 500 mg = 7500 mg/ml divided by 5ml = 1500 mg

5. 1500 mg exceeds the recommended one-time dose of 500 mg, prompting

a call to the provider

Given the following dosage guidelines, determine if the prescriptions below are dosed appropriately. Answer "OK" for appropriate doses, "over" for doses over the recommendation, and "under" for doses under the recommendation. ***These guidelines are "For Training Purposes Only" and not to be used on the job.*** Acetaminophen Adults (> 12 yrs) - 325mg-650mg every 4-6 hours, or 1 gm 3-4 times/day - do not exceed 4 gm/day Children (< 12 yrs) - 10-15 mg/kg per dose, not to exceed 5 doses in 24 hours Amikacin Adults, children and infants - 15mg/kg/day in 2-3 divided doses Amoxicillin Adults (> 12 yrs) - 750-1,000mg/day in 2 or 3 divided doses Children (< 12 yrs) - 20-40mg/kg/day in 3 divided doses Ampicillin Children (< 12 yrs) - 50-400mg/kg/day in 4 divided doses Adults (> 12 yrs) - 1-12 gm in 4 divided doses Gentamycin 5-7mg/kg/day in 2-3 divided doses Ibuprofen Children (6 mos to 12 yrs) - 5-10mg/kg/dose, 3-4 times/day, not to exceed 40mg/kg/day Adults - do not exceed 3.2 gm/day Nafcillin Children (< 12 yrs) - 100-200mg/kg/day in 4 divided doses



Adults (> 12 yrs) 500-1000gm every 4-6 hours Penicillin V (oral) Children (2-12 yrs) - 30-50mg/kg/day in 4 divided doses Adults (> 12 yrs) - 250-500mg every 6-8 hours Theophylline Maximum daily doses for ages: (1-9 yrs 24mg/kg/day) (9-12 yrs 20mg/kg/day) (12-16 yrs 18mg/kg/day) (> 16 yrs 13mg/kg/day) Vancomycin Adults (> 12 yrs) - 500mg-2 gm/day in 3 or 4 divided doses Children (< 12 yrs) - 40mg/kg/day in 3 or 4 divided doses Abbreviations: y/o = years old, wt. = weight, < =less than, > = greater than 1. Patient - 8 y/o, wt. 70 lbs Rx - Nafcillin 1.2 gm IV, q6h 2. Patient - 4 y/o, wt. 24 kg Rx - Amikacin 140mg IV q8h 3. Patient - 14 y/o, wt. 130 lb Rx - Theophylline 200mg tabs, 2 tabs po tid 4. Patient - 28 y/o, wt. 82 kg Rx - Ibuprofen 800mg tabs, 1 tab po q4h 5. Patient - 6 y/o, wt. 27 kg Rx - Acetaminophen 160mg/5ml, 1 tsp po q6h 6. Patient - 17 y/o, wt. 150 lb Rx - Amoxicillin 250mg caps, 2 caps po qid 7. Patient - 11 y/o, wt. 75 lb Rx - Penicillin 250mg/5ml, 3ml po qid 8. Patient - 32 y/o, wt. 125 lb Rx - Vancomycin, 1gm IV q6h 9. Patient - 3 y/o, wt. 16 kg Rx - Gentamycin 32mg IV q8h 10. Patient - 7 y/o, wt. 65 lb Rx - Ibuprofen 100mg/5ml, 3 tsp po q8h



11. Patient - 15 y/o, wt. 64 kg Rx - Amikacin, 1gm IV q12h 12. Patient - 10 y/o, wt. 38 kg Rx - Ampicillin, 350 mg IV q6h 13. Patient - 14 y/o, wt. 130 lb Rx - Theophylline 300 mg tabs, 1 tab po tid 14. Patient - 23 y/o, wt. 165 lb Rx - Ampicillin 250mg caps, 1 cap qid 15. Patient - 27 y/o, wt. 77 kg Rx - Acetaminophen 500mg tabs, 2 tabs po q4h 16. Patient - 12 y/o, wt. 100 lb Rx - Vancomycin 600 mg IV q8h 17. Patient - 2 y/o, wt. 14 kg Rx - Penicillin 250mg/5ml, 1 tsp po qid 18. Patient - 8 y/o, wt. 25 kg Rx - Ibuprofen 100mg/5ml, 2.5 tsp po q6h 19. Patient - 14 y/o, wt. 135 lb Rx - Ampicillin 250mg caps, 1 cap qid 20. Patient - 13 y/o, wt. 95 lb Rx - Amikacin, 70mg IV q8h 21. Patient - 18 y/o, wt. 170 lb Rx - Acetaminophen 325mg, 3 tabs q6h 22. Patient - 13 y/o, wt. 125 lb Rx - Amoxicillin 250mg caps, 1 cap q8h 23. Patient - 4 y/o, wt. 20 kg Rx - Gentamycin, 60 mg q8h 24. Patient - 6 y/o, wt. 24 kg Rx - Nafcillin, 450mg IV q8h 25. Patient - 24 y/o, wt. 115 lb Rx - Theophylline 200mg tabs, 1 tab tid



26. Patient - 17 y/o, wt. 66 kg Rx - Amikacin, 330mg IV q8h 27. Patient - 10 y/o, wt. 36 kg Rx - Penicillin V 250mg/5ml, 9ml po qid 28. Patient - 23 y/o, wt. 110 lb Rx - Ibuprofen 400mg tabs, 1-2 tabs q4-6h (determine maximum amount able to be taken and compare to recommended dose) Answers: (1) OK - 150mg/kg/d (2) Over - 17.5mg/kg/d (3) Over - 20.3mg/kg/d (4) Over - 4.8 gm/d (5) Under - 5.9 mg/kg/dose (6) Over - 2g/d & qid (7) Under - 17.6mg/kg/d (8) Over - 4 gm/d (9) OK - 6 mg/kg/d (10) OK - 30.5mg/kg/d (11) Over 31.25mg/kg/d (12) Under 36.8 mg/kg/d (13) OK 15.2 mg/gkg/d (14) OK 1gm/d (15) Over - 6 gm/d (16) OK - 39.6 mg/kg/d (17) over - 71 mg/kg/d (18) OK - 40 mg/kg/d (19) OK - 1 gm/d (20) Under - 4.8 mg/kg/d (21) OK - < 4gm/d (22) OK - 750 mg/d (23) Over - 9 mg/kg/d (24) Under - 56.3 mg/kg/d (25) OK - 11.5 mg/kg/d (26) OK - 15 mg/kg/d (27) OK - 50 mg/kg/d (28) Over - 4.8 g/d 10. Calculate the appropriate drop factors for patients receiving IV therapy. FLOW RATES

Using flow rates, you can calculate the volume of fluid and amount of drug a patient will be receiving over a certain time period.

General Formula:

ml to be infused = ml hours to be infused 1 hour ml = ml 60 minutes 1 min Drop factor X ml/min = gtts/min

EXAMPLE: Calculate the flow rate when 200mg of aminophylline is administered in 1000ml of 0.9% Sodium Chloride over 6 hours, with a 20gtt/ml IV set.

1000ml = 166.6ml 6 1 hour 166.6ml/hr = 2.77ml 60 minutes 1 min



20gtt/ml X 2.77ml/min = 55.4gtt/min

EXAMPLE: If 1000ml must be infused over an 8 hour period, what will be the flow using a 60gtt/ml IV set?

1000ml = 125ml = 125ml = 2.08ml 8 hr 1 hour 60 min 1 min 60gtt/ml X 2.08ml/min = 124.9gtt/min

(Can’t have part of a drop so you have to round up or down, in this case round up.) 125gtt/min NOTE: : Number of ml/hr = number of microgtts/min. Microdrip sets deliver 60 gtts/ml. So in this case 125ml/hr = 125 microgtts/min.

FLOW RATE PRACTICE PROBLEMS 1. What is the flow rate, in ml/hr, if 1 liter of 5% Dextrose in Water with 20mEq of KCl is given over 12 hours? 2. Calculate the flow rate when 200mg of aminophylline is administered in 1000ml of 0.9% Sodium Chloride over 6 hours, with a 20gtt/ml IV set. 3. An IV order calls for 100mg of hydrocortisone to be added to 1000ml of NaCl every 6 hours. What will be the flow rate using a 15gtt/ml administration set? 4. Using a 10gtt/ml IV set, what will be the flow rate, if 500ml of solution is infused every 4 hours? 5. The physician order is for 1000ml of D5W to be administered in 5 hours. If a 20gtt/ml set is used, what is the flow rate in ml/hr and gtts/min?



6. If an IV infusion of 100ml must be absorbed in 12 hours, what should be the flow rate for: a. 20 gtt/ml set _______ b. 15 gtt/ml set _______ c. 10 gtt/ml set _______ d. 60 gtt/ml set _______ 7. If an IV infusion of 500ml must be run over 12 hours, what should be the rate of flow using the following administration sets? 20 gtts/ml ______ 15 gtts/ml ______ 10 gtts/ml ______ 60 gtts/ml ______ 8. Determine the flow rate of an IV infusion for an adult if the physician ordered 1000ml to be given in 2 hours with a drop factor of 10. 9. What is the flow rate if 500ml of D5W is infused over 4 hours using micro-drip tubing? 10. What is the flow rate in ml/min if 1 liter of solution is infused over 6 hours using a 15gtt/ml set? 11. Determine the flow rate to be used to infuse 1000ml, of dextrose 5% in water over 12 hours if the set delivers 10 drops per ml. 12. Determine the flow rate to be used to infuse 250ml, of Sodium Chloride 0.9% over 4 hours using a 20gtt/ml set.



ANSWERS: (1) 83.3 ml/hr (2) 55.4 gtt/min (3) 41.55 gtt/min (4) 20.8 gtt/min (5) 66.6 gtt/min (6) a-2.8 gtt/min b.-2.1 gtt/min c-1.4 gtt/min d-8.4 gtt/min (6) 13.8 gtt/min, 10.35 gtt/min, 6.9 gtt/min, 41.4 gtt/min (7) 83 gtt/min (8) 125 gtt/min (9) 2.77 ml/min (10) 13.8 gtt.min (11) 20.8 gtt/min 11. Describe methods for double-checking calculations.

We have discussed a variety of calculations that you will use to perform your duties as a pharmacy technician. Before we end this discussion, lets look at a few preventative measures you can take to prevent an error in calculation, thus preventing a medication error.

• Never leave a decimal point naked. Always place a zero before a decimal expression less than one. Example: .25mg may be read as 25 mg. The correct way is to write 0.25 mg.

• Never place a decimal point and a zero after a whole number. The decimal may not be seen and result in a tenfold overdose. Example: 5.0 mg may be read as 50 mg. The correct way is to write 5 mg.

• Avoid using decimals whenever whole numbers can be used as alternatives. Example: 0.5 g should be expressed as 500 mg.

• Whenever possible, use the metric system rather than grains or drams.

Developing a working knowledge of pharmaceutical calculations is crucial for success in your career as a pharmacy technician. Your customer's health depends on your accuracy each time you calculate a dose or make a pharmaceutical preparation. Another important aspect of your job, especially when making those pharmaceutical preparations, is pharmaceutical chemistry. In the next unit, we will cover basic concepts of chemistry and properties of pharmaceuticals. But first, answer the following questions to see if you have developed that working knowledge of pharmaceutical calculations.


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