1. Calculations Chapter 6

2. Numbers Knowing how to work with numbers is essential to the proper handling of drugs and preparation of prescriptions. Knowing how to work with numbers is essential to the proper handling of drugs and preparation of prescriptions. The amount of a drug in its manufactured or prescribed form is always stated numerically (with numbers). The amount of a drug in its manufactured or prescribed form is always stated numerically (with numbers).

3. Roman Numerals The Roman numerals are letters that represent numbers. The Roman numerals are letters that represent numbers. They can be capital or lower case letters. (see handout) They can be capital or lower case letters. (see handout) ss = ½L = 50 ss = ½L = 50 I or i = 1C = 100 V or v = 5D = 500 X or x = 10M = 1000

4. Roman Numerals Two Rules: Two Rules: Rule 1: When the second of the two letters has a value equal to or smaller than the first, their values are added together. xx = 2010 + 10 = 20 xx = 2010 + 10 = 20 DC = 600500 + 100 = 600 DC = 600500 + 100 = 600 lxvi = 6650 + 10 + 5 + 1 = 66 lxvi = 6650 + 10 + 5 + 1 = 66

5. Roman Numerals Two Rules: Two Rules: Rule 2: When the second of the two letters has a value greater than the first, the value is subtracted from the larger value. iv = 41 subtracted from 5 = 4 iv = 41 subtracted from 5 = 4 xxxix = 3930 + ( 1 – 10 ) = 39 xxxix = 3930 + ( 1 – 10 ) = 39 xc = 9010 subtracted from 100 = 90 xc = 9010 subtracted from 100 = 90

6. Common Roman Numerals on RX’s i = 1 i = 1 ii = 2 ii = 2 V = 5 V = 5 X = 10 X = 10 C = 100 C = 100

7. Fractions A fraction is a numerical representative indicating that there is part of a whole. A fraction is a numerical representative indicating that there is part of a whole. Fractions have numerators and denominators. Fractions have numerators and denominators. The denominator is the bottom number of the fraction. It tells us how many pieces the whole is divided into. The denominator is the bottom number of the fraction. It tells us how many pieces the whole is divided into. The numerator is the top number of the fraction. It tells us how many pieces exist. The numerator is the top number of the fraction. It tells us how many pieces exist.

8. Fractions Example: Example: 2 Numerator we have 2 parts ─ 5Denominator out of 5 total parts

9. Converting Fractions to Decimals Fractions can be converted to decimals by dividing. Fractions can be converted to decimals by dividing.2 ─ = 2 ÷ 5 = 0.4 5

10. Decimals A decimal point is used to represent an amount less than one (fraction). A decimal point is used to represent an amount less than one (fraction). 0.1=one tenth 0.01=one hundredth 0.001=one thousandth 0.0001=one ten-thousandth

11. Reciprocals Reciprocals are two different fractions that equal 1 when multiplied together. Reciprocals are two different fractions that equal 1 when multiplied together. The reciprocal of 2 is 3 ── 32

12. Reciprocals When multiplied together, reciprocals equal 1 When multiplied together, reciprocals equal 1 2 x 3=6 ───or 1 3 x2=6

13. Adding & Subtracting Fractions In order to add & subtract fractions, the fraction must have the same common denominator. In order to add & subtract fractions, the fraction must have the same common denominator. 1121 ─ +─=─or ─ 4442 211 ─ -─=─ 555

14. Multiplying Fractions Multiply each numerator, then multiply each denominator Multiply each numerator, then multiply each denominator 22448 ─ x─=─or 16 313

15. Dividing Fractions To divide a fraction, find the reciprocal of the fraction (or invert the fraction), then multiply. To divide a fraction, find the reciprocal of the fraction (or invert the fraction), then multiply. Example: 1/3 ÷ 1/2 = Example: 1/3 ÷ 1/2 = 122 ─x─=─ 313

16. Working with Decimals The key to adding and subtracting with decimals is to line up the decimal points, then work the problem as you would a whole number equation. The key to adding and subtracting with decimals is to line up the decimal points, then work the problem as you would a whole number equation. 45.645.6 45.645.6 + 3.2 - 3.2 + 3.2 - 3.2 48.8 42.4

17. Multiplying with Decimals To multiply with decimals, first multiply as if using whole numbers. Count the total number of decimal places in the equation. Insert the decimal point the total number of decimal places, starting from the right. To multiply with decimals, first multiply as if using whole numbers. Count the total number of decimal places in the equation. Insert the decimal point the total number of decimal places, starting from the right. 47.2(1 decimal place) x 5.5 (1 decimal place) x 5.5 (1 decimal place) 2360 2360 25960 25960 259.60 (2 decimal places)

18. Percentages Percentages are fractions in which the denominator is always 100. Percentages are fractions in which the denominator is always 100. Percentages are expressed (using the % symbol) and mean parts out of 100 units. Percentages are expressed (using the % symbol) and mean parts out of 100 units. Example: Example: 25% = 251 ──or─ 1004

19. Basic Percentages 501 501 50%=──or ─ 1002 2 2%=── 2% represents 2 parts 100 out of 100 parts

20. Significant Figures 4 Rules for significant figures: 4 Rules for significant figures: 1. Digits other than zero are always significant. (1,2,3,4) 2. Final zeros after a decimal point are always significant. (1.20) 3. Zeros between two other significant digits are always significant. (1.05) 4. Zeros used only to space the decimal are never significant. (0.1)

21. Measurements There are different systems of measurement used in pharmacy: metric, English, apothecary & avoirdupois. There are different systems of measurement used in pharmacy: metric, English, apothecary & avoirdupois. The major system of weights & measures in medicine is the metric system. The major system of weights & measures in medicine is the metric system. The different measurement units are related by measures of ten. The different measurement units are related by measures of ten. Metric measures apply to both liquids and solids. Metric measures apply to both liquids and solids.

22. Liquids Liquids (including lotions) are measures by metric volume. The most common being liters (L) or milliliters (ml). Liquids (including lotions) are measures by metric volume. The most common being liters (L) or milliliters (ml). Unit Symbol Liquid Conversion liter L 1L = 1000 ml milliliter ml 1ml = 0.001 L **cc’s (cubic centimeters) are often used in place of ml

23. Solids Solids (pills, granules, ointments) are measured by weight. Solids (pills, granules, ointments) are measured by weight. UnitsSymbolSolid Conversion_ kilogram kg1kg = 1000 g gram g1g = 1000 mg =0.001 kg milligrams mg1mg = 1000 mcg =0.001 g microgram mcg1mcg =0.001 mg

24. Ounces, Pounds & Grains UnitsSymbolConversion poundlb1 lb = 16 oz. poundlb1 lb = 16 oz. ounceoz1 oz = 437.5 gr ounceoz1 oz = 437.5 gr graingr1 gr = 64.8 mg graingr1 gr = 64.8 mg **grains are often rounded up to 65mg or down to 60mg in the pharmacy practice.

25. Apothecary Measurements UnitSymbolConversion gallongal1 gal = 4 qt gallongal1 gal = 4 qt quartqt1 qt = 2 pt quartqt1 qt = 2 pt pintpt1 pt = 16 fl oz pintpt1 pt = 16 fl oz ouncefl oz1 oz = 30 ml ouncefl oz1 oz = 30 ml

26. Household Measures Teaspoons, tablespoons & cups are common household measures. Teaspoons, tablespoons & cups are common household measures. UnitSymbolConversion 15 dropsgtts15gtts = 1ml Teaspoontsp1 tsp = 5ml Tablespoontbsp1 tbsp = 15 ml = 3 tsp Cupcup1 cup = 8 oz

27. Conversions 1L = 33.8 fl oz 1 pt = 473.167 ml (473 or 480ml) 1 fl oz = 29.57 ml (30ml) 1 kg = 2.2 lbs 1 lb = 453.59 g (454g) 1 oz = 28.35 g (30g) 1 g = 15.43 gr (15gr) 1gr = 64.8 mg (65mg)

28. Dose Measurements Not all doses doctor’s write prescriptions for are available from the manufacturer…so what do you do? Not all doses doctor’s write prescriptions for are available from the manufacturer…so what do you do? Tablets can be doubled up: for example, the RX is written for 250mg, and only 125mg is made, the result is the dose taken by the patient is 2 tablets together to equal 250mg. Tablets can be doubled up: for example, the RX is written for 250mg, and only 125mg is made, the result is the dose taken by the patient is 2 tablets together to equal 250mg. A tablet can also be cut in half, or even a quarter to provide the adequate dose for the patient. A tablet can also be cut in half, or even a quarter to provide the adequate dose for the patient.

29. Dose Measurements Example 1: Example 1: Rx: Flagyl 125mg po bid x 7 days Rx: Flagyl 125mg po bid x 7 days On hand is 500mg tablets, how would you accommodate the patients needs? On hand is 500mg tablets, how would you accommodate the patients needs? 500mg/125mg = 4 500mg/125mg = 4 Take ¼ tablet (=125mg) by mouth two times a day for 7 days. Take ¼ tablet (=125mg) by mouth two times a day for 7 days.

30. Dose Measurements How many tablets would you dispense to last the patient the duration of the treatment? How many tablets would you dispense to last the patient the duration of the treatment? ¼ + ¼ = 2/4 or ½ tablet daily ¼ + ¼ = 2/4 or ½ tablet daily ½ X 7 days = 3.5 **always round up on quantity to dispense, ***not dose ½ X 7 days = 3.5 **always round up on quantity to dispense, ***not dose 4 tablets would be dispensed; and that would equal a 7 day supply. 4 tablets would be dispensed; and that would equal a 7 day supply.

31. Dose Measurements Example 2: Example 2: Rx: Amoxicillin 500mg po tid X 10 days Rx: Amoxicillin 500mg po tid X 10 days On hand Amox 250mg/5ml On hand Amox 250mg/5ml 250mg = 5ml 250mg = 5ml Take 2 teaspoonfuls (=500mg) by mouth three times a day for 10 days Take 2 teaspoonfuls (=500mg) by mouth three times a day for 10 days What is the quantity you will dispense to cover the duration of the therapy? What is the quantity you will dispense to cover the duration of the therapy?

32. Dose Measurements 2 tsp = 10 ml / dose 2 tsp = 10 ml / dose 10ml X 3 = 30ml / day 10ml X 3 = 30ml / day 30 ml x 10 days = 300 ml / 10 days 30 ml x 10 days = 300 ml / 10 days

33. Equations & Variables In pharmacy calculations, there is often an unknown variable that needs to be determined. In pharmacy calculations, there is often an unknown variable that needs to be determined. We solve for the unknown value by setting up mathematical equations. We solve for the unknown value by setting up mathematical equations. In equations, this is usually represented by the letter “x”. In equations, this is usually represented by the letter “x”.

34. Equations & Variables Example: How many ounces is equal to 120ml? Example: How many ounces is equal to 120ml? total ml total ml x (oz) = ──────────── ml to oz conversion ml to oz conversion 120ml 120ml x (oz) = ────────x (oz) = 4 30ml 30ml

35. Equations & Variables Example: Calculate the quantity for an Rx with a sig of 1 tid x 7. Example: Calculate the quantity for an Rx with a sig of 1 tid x 7. x (qty) = (1 cap per dose) x (3 times a day) x (7 days) x (qty) = 1 x 3 x 7 x (qty) = 21

36. Dose Equation D/A X Q = dose quantity D/A X Q = dose quantity D = desired D = desired A = Available on hand A = Available on hand Q = Quantity (dose) on hand Q = Quantity (dose) on hand

37. Dose Equation Example: Example: A prescription calls for 200mg of a drug that you have in a 10mg/15ml concentration. How many ml of the liquid do you need? A prescription calls for 200mg of a drug that you have in a 10mg/15ml concentration. How many ml of the liquid do you need? Desired = 200mg Desired = 200mg Available = 10mg Available = 10mg Quantity (dose) on hand = 15ml Quantity (dose) on hand = 15ml

38. Dose Equation 200mg / 10mg X 15ml 200mg / 10mg X 15ml 200 / 10 = 20 (the mg are canceled) 200 / 10 = 20 (the mg are canceled) 20 X 15ml = 300 ml 20 X 15ml = 300 ml

39. Ratio & Proportion Understanding ratios & proportions is important for pharmacy technicians so they can perform the calculations necessary for the job. Understanding ratios & proportions is important for pharmacy technicians so they can perform the calculations necessary for the job. Ratio: A ratio states a relationship between two quantities. Ratio: A ratio states a relationship between two quantities.a It can be stated as: a : b or ─ It can be stated as: a : b or ─b

40. Ratio & Proportion Proportion: Two equal ratios form a proportion. Proportion: Two equal ratios form a proportion. ac ─=─ bd 12 ─=─ 24 1/2 & 2/4 are equivalent ratios, therefore the equation is a proportion. 1/2 & 2/4 are equivalent ratios, therefore the equation is a proportion.

41. Ratio & Proportions Proportion Example: If one person has 1 bottle containing 5 tablets, and another has 3 bottles containing a total of 15 tablets, it is still an equivalent ratio. (5:1) Proportion Example: If one person has 1 bottle containing 5 tablets, and another has 3 bottles containing a total of 15 tablets, it is still an equivalent ratio. (5:1) 515 ─=─ It is not the quantity, but the 13 relationship between the quantity that we are looking for.

42. Solving Ratio & Proportion Equations There are 3 conditions for using ratio & proportion equations: There are 3 conditions for using ratio & proportion equations: 1. Three of the four values must be known. 2. The numerators must have the same units. 3. The denominators must have the same units.

43. Solving Ratio & Proportion Equations Example: You receive an Rx for Ktabs 1 bid x 30. How many tablets are needed to fill the Rx? Example: You receive an Rx for Ktabs 1 bid x 30. How many tablets are needed to fill the Rx? Define the unknown variable: x = total tablets needed. Establish the known ratio: 2 tablets per day Establish the unknown ratio: x tablets/30 days x tabs 2 tabs ─────=───── = x = 60 ─────=───── = x = 60 30 days 1 day We need 60 tablets to fill the Rx.

44. Percents & Solutions Percents are used to indicate the amount or concentration of something in a solution. Percents are used to indicate the amount or concentration of something in a solution. Concentrations are indicated in terms of weight to volume or volume to volume. Concentrations are indicated in terms of weight to volume or volume to volume. Weight to volume = grams per 100 milliliters ( g/ml ) Weight to volume = grams per 100 milliliters ( g/ml ) Volume to volume = milliliters per 100 milliliters (ml/ml) Volume to volume = milliliters per 100 milliliters (ml/ml)

45. Percents & Solutions Example: You have a 70% dextrose solution. How many grams in 20mls of solution? Example: You have a 70% dextrose solution. How many grams in 20mls of solution? 70gx g ─ =─ =1400 = 100x(g) = 14g 100ml 20ml 100ml 20ml

46. Calculations for Business Terms: Terms: Usual & customary price (U&C) is the lowest price for a customer paying cash on that day for that drug. Usual & customary price (U&C) is the lowest price for a customer paying cash on that day for that drug. Average wholesale price (AWP) is the average wholesale price for that drug. Average wholesale price (AWP) is the average wholesale price for that drug. Professional fee or fee for service: the charge for service. Professional fee or fee for service: the charge for service.

47. Calculations for Business Prescription prices are determined by a variety of formulas. The easiest is AWP + professional fee = the selling price. Prescription prices are determined by a variety of formulas. The easiest is AWP + professional fee = the selling price. To calculate the retail price, you must first calculate the AWP for the specific quantity of tablets then apply the appropriate professional fee. To calculate the retail price, you must first calculate the AWP for the specific quantity of tablets then apply the appropriate professional fee.

48. Calculations for Business Example: What is the retail price for #30 glyburide 5mg tablets (AWP 480.15/M) and a professional fee of $4.00? Example: What is the retail price for #30 glyburide 5mg tablets (AWP 480.15/M) and a professional fee of $4.00? 1. Calculate AWP per tablet: 480.15/1000 =.48 per tab. 2. Multiply # of tablets by price per tablet = 30 x.48 = 14.40. 3. Add professional fee = 14.40 + 4.00 = 18.40 retail price.

49. Discounts Pharmacies sometimes give a discount to certain groups of patients (such as senior citizens). Pharmacies sometimes give a discount to certain groups of patients (such as senior citizens). To begin, calculate the retail price of a prescription as we did on the previous slide, then we calculate the discount. To begin, calculate the retail price of a prescription as we did on the previous slide, then we calculate the discount.

50. Discounts Example: The glyburide Rx is for a senior citizen, who qualifies for a 10% discount. (retail was 18.40). Example: The glyburide Rx is for a senior citizen, who qualifies for a 10% discount. (retail was 18.40). 18.40 x.10 = 1.84 18.40 – 1.84 = 16.56 The customer would pay 16.56 as the discounted price. The customer would pay 16.56 as the discounted price.

51. Practice What would a customer pay for Verapamil SR #30 (AWP 135.85/C) with a $5.00 professional fee and a 10% senior discount? What would a customer pay for Verapamil SR #30 (AWP 135.85/C) with a $5.00 professional fee and a 10% senior discount? AWP per tab = 135.85/100 = 1.36 Cost per 30 tablet = 1.36 x 30 tabs = 40.80 Professional fee = 40.80 + 5.00 = 45.80 10 % Discount = 45.80 x.10 = 4.58 Retail price = 45.80 – 4.58 = 41.22 Answer: $ 41.22

52. Gross Profit & Net Profit Gross profit is the difference between the selling price and the acquisition cost. Gross profit is the difference between the selling price and the acquisition cost. To calculate gross profit, there is no consideration for any of the other expenses associated with filling a prescription. To calculate gross profit, there is no consideration for any of the other expenses associated with filling a prescription. In its simplest form, cash prescriptions, it is the difference between the selling price and the cost paid for the item In its simplest form, cash prescriptions, it is the difference between the selling price and the cost paid for the item

53. Gross Profit Gross profit = selling price – acquisition cost Gross profit = selling price – acquisition cost Example: An Rx for Amoxil 250mg # 30 has a U & C of 8.49. The acquisition cost is 2.02. What is the gross profit? Example: An Rx for Amoxil 250mg # 30 has a U & C of 8.49. The acquisition cost is 2.02. What is the gross profit? GP = 8.49 – 2.02 GP = 6.47 Answer: $ 6.47

54. Net Profit The net profit is the difference between the selling price and the sum total of all the costs associated with filling the prescription. The net profit is the difference between the selling price and the sum total of all the costs associated with filling the prescription. Costs associated with filling an Rx: Costs associated with filling an Rx: Cost of the medication Cost of the medication Cost of the vials, lids, labels, caution labels Cost of the vials, lids, labels, caution labels Cost of labor: pharmacy tech, pharmacist, clerk, etc. Cost of labor: pharmacy tech, pharmacist, clerk, etc. Costs of operations: rent, utilities Costs of operations: rent, utilities These are often grouped together and called a dispensing fee. These are often grouped together and called a dispensing fee.

55. Net Profit Net profit = selling price – acquisition cost – dispensing fee Net profit = selling price – acquisition cost – dispensing feeor Net profit = Gross profit – dispensing fee Net profit = Gross profit – dispensing fee Example: Amoxil 250mg #30 (U&C 8.49) with an acquisition cost of 2.02 and a dispensing fee of 5.50. What is the net profit? Example: Amoxil 250mg #30 (U&C 8.49) with an acquisition cost of 2.02 and a dispensing fee of 5.50. What is the net profit? selling price acquisition dispensing fee NP = 8.49 – 2.02 – 5.50 NP =.97

56. The End Read Chapter 6 Read Chapter 6 Do Practice Problems Throughout Chapter Do Practice Problems Throughout Chapter Take Self Test Take Self Test Study Review Pages Study Review Pages