1. CHAPTER 6 : DILUTIONS
1.1. Stock Solutions/Solids
1.1.1. Stock solutions or solids are generally concentrated solutions or solids that are used to prepare weaker ones. Stock solutions or solid concentrations are often expressed as ratio strengths w/ or w/w (1:400 w/v) but can also be expressed as a percent strength w/v or w/w (50% w/v). Dilution of these concentrated solutions or solids creates a smaller concentration in a higher volume that will allow for easier, more accurate measurement of a desired dose. A solution that has a concentration 50% (50 g/100 mL) and has the volume doubled now has a concentration of 25% (25 g/100 mL). The amount of medication (or solute) in the solution did not change, only the volume of the liquid (dilu-ent). This means that the same amount of solute is now in twice as much diluent, creating a weaker solution. The same would be true for a solid product (ointment or creams). A cream with a percent strength of 18% (18 g/100 g) and a weight of 20 g that is combined with an additional 20 g of cream base would now have a percent strength of 9% (9 g/100 g). When performing calculations to create a more dilute product, the shortest route is not always the best. It is more important to be accurate, so that may mean more steps in the calculation. Remembering two key rules can help simplify the
1.1.2. 1. Ratio strengths should be converted to percent strengths for easier calcula- tions. The ratio strength 1:500 = 0.2%. 2. Proportions (20:5) or fractions (6/30 should be simplified to their lowest form. The ratio 20:5 = 4:1 and the fraction 30 = 3.;
1.2. Liquid Dilutions
1.2.1. Diluting liquids changes the concentration of that liquid. Since three of the four components are already known, the concentration of the new solution can be determined by using the proportion rule. This procedure can also be used to determine how much product (weaker strength) can be made from a known amount of a higher concentration.
1.3. Solid Dilutions
1.3.1. The dilution of solid products (creams and ointments) reduces their concentration also. They can be represented as ratio strengths or percent strengths just like solutions. They are diluted with an ointment or cream base with no active ingredient. The calculations are done the same way as solution dilutions. The proportion rule or quantity/concentration formula can be used
1.4. Alligations
1.4.1. Alligations is a method used to calculate the percent strength when combining multiple strengths of the same ingredient. It can also be used when the volume of each of two different strengths of the same ingredient must be determined in order to make a new strength. This new strength must be in-between the two strengths that are being combined. Alligations medial is the method used to determine the new percent strength when combining multiple strengths of the same ingredient and the volumes are known. There are two different ways to do this calculation.
2. CHAPTER 7 : DOSING
2.1. Geriatrics
2.1.1. gGeriatric patients are generally classified as persons over 60 years of age. This is relative because some patients may have geriatric symptoms at 50 years of age or even younger. As we age, our physiologic functions start to decline. Kidney function and liver function are two major concerns when dosing medications in elderly patients. These both affect the absorption and elimination of medications. When medications remain in the body longer, they accumulate in the blood and tissues creating increased drug levels, which cause toxicity. Drugs are often dosed using body surface area (BSA). Some medications have guidelines for reduced dosing based on the patients weight and age. Renal (kid-ney) function can also play a role in dosing a medication. If the kidneys are not functioning properly, reduced doses are often prescribed. Creatinine clearance is the lab value physicians and pharmacists use to determine kidney function and appropriate dosing for elderly patients. Medications will have dosing guidelines for reduced kidney function to prevent toxicity. BSA is the calculation we focus on in this book. It is used for geriatric, pediat-ric, and chemotherapy dosing. The formula is the same for all three applications. There is a preprinted nomogram that can be used to determine a patient's BSA by knowing his or her height and weight. Many reference books have this chart included. Most pharmacy computer programs have this calculation in its formula banks, which eliminates manual calculating and potential error.
2.2. Pediatrics
2.2.1. They should be dosed based on their weight or BSA. Accuracy in dosing pediatric patients is very important. Toxicity can occur at much smaller doses. There are several formulas that can be used if the BSA is not known or if the drug does not require a BSA to determine the dose. While age does play a role, weight is still the best way to dose when the BSA is not known. When dosing by weight, the drug product tells you the dosing guidelines (50 mg/kg/dose).
2.3. Chemotheraphy
2.3.1. Chemotherapy agents are medications that are used for cancer. They are very potent, hazardous chemicals that cause cell death. Because these agents are so hazardous, dosing them correctly is critical. These medications are normally dosed based on BSA and take into consideration kidney (renal) function. The measure of kidney function is the serum creatinine lab value. This value is then used in a formula to determine the patient's creatinine clearance that is then used to determine dosing of certain medications. Creatinine is a product of creatine phosphate from muscle metabolism. The normal value for serum creatinine used by most laboratories is 0.7-1.5 mg/dL.. If this value is above 1.5, the patient has decreased renal function. Decreased renal function means the medication dose must be reduced. Likewise, if the creatinine is lower than 0.7, the patient has increased renal function. The medication may need to be dosed higher so the medication can remain in the body long enough to elicit a therapeutic effect. While technicians do not do this calculation often, it is good to know how and where the values are used. Pharmacy computer programs usually have this calculation in their system, but when computers fail, knowing how to determine creatinine clearance manually can allow patient dosing to continue. Manufacturers of these hazardous medications provide detailed dosing information regarding BSA, renal function, and many other lab values that might create the need to alter a dose for a patient. They may suggest a specific dose or a percent reduction of a standard dose.
3. CHAPTER 8 : IV ADMIXTURE CALCULATIONS
3.1. Intravenous Medications
3.1.1. An intravenous (IV) medication is a drug that is in a liquid, or liquid-like, state that is administered with a syringe and needle. It may be given just under the skin (subcutaneous (SQ]), directly into a muscle (intramuscular [IM]), directly into a vein (intravenous push [IVPJ), or slowly infused into the vein through dilution in an IV fluid (parenteral IV infusion). Many of these medications come in bulk packaging, which requires either dilution, or simple calculations to determine the volume needed for a patient dose. Most medications are dosed in milligrams or grams. These are common measures and have been utilized throughout this text. There are two other measures seen in IV medications: milliequivalents (mEq) and units.
3.2. Milliequivalents
3.3. Units
3.3.1. unit is a measurement used in insulin, some vitamins, heparin, penicillin, me blood products, and various other medications. The unit is a measure of particular medication's activity based on a test system for that specific agent. hese test systems are biological assays designed to define a specific medication's unit" of activity. A unit of insulin is not measured the same as a unit of heparin • a unit of vitamin E. Insulin is based on its affect on glucose in the bloodstream. eparin is based on its anticoagulation effect in the bloodstream. Insulin is measured by its units with syringes available that are designed pecifically for measuring insulin doses. The standard concentration of insulin is 00 units per 1 mL or 100 units/mL. Physicians order insulin by the unit based on he patient's blood glucose level. They may have multiple doses ordered 10 units efore breakfast, 20 units before dinner.
3.4. TPN Solutions
3.4.1. Total parenteral solution (TP) is an IV that provides nutrition to patients who not eat normally. They have multiple additives that are customized to the patient's nutritional needs. These Is have a dextrose solution and an amino acid solution as the base that represents the sugar (carbohydrate) and proteins portions. of a traditional diet. Additives often include potassium, sodium, calcium, and mul-tivitamins. They can also include insulin, trace elements, heparin, and an H, antagonist (reduces the production of stomach acid). The quantities of each additive are determined by lab values that are drawn daily in the beginning and then weekly if the patient is on TPN therapy for a length of time.
3.5. IV Floe Rates
3.5.1. IV solutions are ordered they must have a rate of administration. It might run over a specific time-20 min, or at a continual rate-100 mL/hr. A general e is that an IV solution with 250 mL or less is considered a "piggyback" and used through a main IV line over a set period of time. Large volumes are con-ered 500 mL or more and are run at a continual rate. Knowing the rate of administration will help the technician determine how ny IV bags need to be prepared for a patient. Most hospital pharmacies prepare for a 24-hr period. If an IV is running at 125 mL/hr and the order is for 1000 ,
3.6. Drop Sets
3.6.1. IV solutions are administered using IV tubing sets. These sets are called drip sets, drop sets, or microdrip sets. Each one delivers a set number of drops in 1 mL. This information can be used to determine the rate at which an IV is administered. While nursing generally performs these calculations, pharmacy staff should be able to assist as a double check. The most common sets have a drip rate of 10, 15, 20, and 60 drops per milliliter (gtts/mL). The 60 gtts/mL tubing is often called a microdrip set. To convert a rate from mL/hr to gtts/min, the following formula can be used:
4. CHAPTER 9 : BUSINESS MATH
4.1. Iventory
4.1.1. All saleable items found in a pharmacy are considered inventory. Inventory is one of the largest costs in a pharmacy. Pharmacies want to turn over their inventory as often as possible. If an item sits on a shelf, it is costing the pharmacy money. The turnover rate is the total number of times the pharmacy's inventory has been replaced in one year: Turnover rate = annual inventory purchased + average inventory The annual inventory is the sum of the year's invoices. The average inventory is the value of the inventory maintained on a daily basis. If the annual invoices total $100,000 and the average inventory is $20,000, then the turnover rate is five (100,000 + 20,000). A good turnover rate is four or more.
4.2. Profit
4.2.1. The amount of money made on the sale of an item is the profit. The two types of profit are gross profit and net profit. The gross profit is the difference in the selling price and the purchase price. The net profit is the selling price minus all costs associated with the dispensing of the product. These costs might include pharmacy supplies (e.g., labels, bottles), personnel time, and shipping fees.
4.3. Selling price
4.3.1. The selling price of a prescription is based on several factors. The pharmas charge enough to cover the cost of the drug, the cost of acquiring the dr the time invested in dispensing the drug. The average wholesale price (A used to determine the selling price of medications. The AWP is the averag charged by wholesalers for that product. Most wholesalers offer a discoun on volume or contracting with large chains.Pharmacies add a markup percent or flat rate and sometimes a dispensing fee, compounding fee, or professional fee to the cost they pay for a medication to determine the selling price. The markup percent or flat rate is set by the individual pharmacy or pharmacy chain. Sometimes the percent or flat rate is tiered based on the cost of the drug. The compounding fee and professional fee are based on time or a flat rate.
4.4. Insurance Reimbursement
4.4.1. Insurance companies reimburse pharmacies for prescriptions dispensed to their clients based on the AWP pricing of medications. The AWP is the average price charged by wholesalers for a medication. Insurance companies will pay the AWP minus a percentage plus a dispensing fee. Every insurance company has a different pricing structure.Insurance companies reimburse pharmacies for prescriptions dispensed to their clients based on the AWP pricing of medications. The AWP is the average price charged by wholesalers for a medication. Insurance companies will pay the AWP minus a percentage plus a dispensing fee. Every insurance company has a different pricing structure.
4.4.2. Some insurance companies reimburse using a system called capitation. These insurance companies pay a flat fee every month to a pharmacy no matter how many of its clients frequent that pharmacy. The fee is set by contract and is usually renegotiated annually. A pharmacy might receive $5000 monthly from Insurance A. If the pharmacy submits $4000 in claims, they will still receive $5000. On the other hand, if they submit $6000, they will receive only $5000. The goal of the pharmacy and the insurance company is to try and break even at the end of the year. Averages from previous years are used to determine the monthly fee.
5. Both methods produce the same answer. As mentioned earlier, the simplest way is not always the best way. Confidence in calculations is important, so the method used (when more than one is possible) depends on the person. Alligations alternate is the method used to determine the volume necessary for each ingredient combined (i.e., same ingredient, different percent strength) to produce a new percent strength. This new percent strength must be in-between the two being combined. This method uses a grid to complete the calculations. It resembles a tic-tac-toe board and provides a great visual for calculating. The answers obtained will be the ratio in which the ingredients should be combined. The ratio should always be simplified to it smallest form.
6. CHAPTER 1 : fundamental of maths
6.1. Arabic numerals
6.1.1. system uses the numerals 1,2,3,4,5,6,7,8,9 and zero .Also know as demical number .A demical point separates whole numbers or units from fractional numbers or fractional units
6.2. roman numerals
6.2.1. System does not utilize numberals and putting together of alpha characters that follow specific rules represents each numbers.Roman numeral system not used to do calculation
6.2.2. in orders calculation roman numerals have to be converted to arabic number
6.3. metric system
6.3.1. The measurement system in place for pharmacy are metric, avoirdupois, apotheraphy
6.3.2. apothecary systems used the base of grains and minims. apothecary systems are drams , ounces , and pounds. The most common units used for volume in pharmacy are the liter , milliliter , and microliter
6.3.3. it only takes a portion of a large part to equal a smaller part
6.4. metric conversions
6.4.1. the most common used by people outside the medical ans scientific community are the household measurements ( eg, tsp,tbsp,ounce,quart,gallon).Some common conversions that should be commited to memory
7. CHAPTER 2 : Fractions and Demicals
7.1. fractions
7.1.1. fraction is made up of two components the numerator and denominator .A proper fractioms is one that has a smaller number on top(numerator) this represents a number that is less then one
7.1.2. an improper fraction is a fraction that has a larger number on top (numerator) . This number would represent a whole plus a portion of another whole .A mixed number is a whole number with a fraction and it make this number into an improper fraction in order to perform any calculations
7.2. Addition and Subtraction
7.2.1. Adding and subtracting fraction requires a few rules in order to obtain the correct answer and add or subtract fractions must have the same denominator or common denominator . To find a common denominator need to determine a number that both denominators have in common (common denominator)
7.3. Multiplication and division
7.3.1. Multiplying fractions is one of the simpler calculations to perform and do not need to worry about common denominators.The numerators are multiplied together and the answer is then simplified to its lowest term
7.4. Decimal
7.4.1. Demical is another way to represent fractional parts of a whole unit to convert a fraction to a demical and simply divide the numerator by the denominator
7.5. Decimal Addition and Subtraction multiplication and division
7.5.1. Addition and Subtraction of decimals has one basic rule always line up the decimals points when adding or subtracting . multiplication decimals is the same as multiplying any others whole number once the answer is determined insert the decimal according to the total number of position taken by all the decimals in the origin number counting from right to left . Division in order divide decimals must make them whole numbers before dividing them . move the decimal point to the right until a whole number is made.
7.6. Decimal Rounding and Significant figures
7.6.1. When multiplying and dividing decimal your answer may have more decimal digits the answer may have more decimal digits than your original numbers for measurement of liquids will generally round to the nearest tenth . Number to the immediate right of the one you wish to round . Significant Figures A significant figure is a digit of known value in a number that can be accurately measured. A number usually consists of one or several significant figures, or digits, plus one more digit that cannot be considered accurate but is needed to hold a position in the number. 1. All leading zeros are not significant. 2. All zeros within (surrounded by digits are significant. 3. Count all digits from left to right excluding leading zeros. 4. Zeros at the end of a digit may or may not be significant depending on the accuracy of the measuring tool.
8. CHAPTER 3 : RATIO, PROPORTIONS AND PERCENTS
8.1. relationship between two numbers. Another way to di comparison of the magnitude of two like values (3:5; 2:7). They ar olon in between the two values. The ratio of 3:5 is read as follows parts. This ratio means that for every three parts of one value, five value will be needed. Ratios are also written as fractions. In phar is the most common form of ratios.
8.2. A proportion is defined as an expression of two equal ratios. A ratio can be expressed in whole numbers separated by a colon or as a fraction. A proportion, therefore, can be expressed as two ratios (numerals or fractions) separated by two colons. It can also be expressed with an equal sign instead of the two colons.
8.3. The word percent means "per 100." When a number is represented as a percent (%), it is a relationship between that number and 100. In other words, a percent is a part, or fraction, of a whole. Percents are represented in many different forms.
8.4. The percent is the most common way to represent drug strength or concen tion. This means you sometimes need to convert a ratio, fraction, or decimal percent.The format of a ratio is the drug (solute) in relation to the solvent (liquid or solu-tion). Therefore, the position of the numbers is important. A ratio of 5:1 is not the same as a ratio of 1:5. A ratio of 5:1 means that there are five parts of drug to one part of solute.
9. CHAPTER 4 : LIQUID MEASURES
9.1. Density is described as the mass per unit of volume of a particular substance. It is normally written as grams/cc (mL). The standard, or constant, that it is measured against is the mass of 1 mL of water at 4°C. This means that the density of water is 1 g/mL. The density for substances, usually chemicals, is found on the label. IV solutions also have the density listed. This may be used to calibrate IV admixture machines. Some of these machines determine the necessary volume of an IV solution based on its density. Some use the specific gravity. The formula for calculating density is mass divided by volume. mass
9.2. pecific gravity is the ratio of the weight of a liquid or solid in relation to the weight if an equal volume or mass of water. It is expressed as a decimal. If this ratio is less han one (0.82), then the substance is lighter than water. If this ratio is more than one. The liquid with the smallest specific gravity number is on top, and the liquid with the highest specific gravity number is on the bottom. Gases also have specific gravity, and their ratio is determined by using hydrogen as the standard instead of water. In pharmacies with a high volume of total parenteral nutrition (TPN) solu-tions, specific gravity is used to measure the multiple ingredients' volumes. TPNs have multiple additives, and two to three main solutions are combined to provide intravenous nutrition to patients. These pharmacies have an IV admixture compounding machine that operates by combining set volumes of fluid based on the known specific gravity of the solutions and additives needed.
10. CHAPTER 5 : CONCENTRATIONS
10.1. Weight / weight
10.1.1. The concentration of a medication that is listed as % w/w is a proportion of the active ingredient (solute) in relation to the inactive ingredient, or carrier (solvent). It is most often used to describe solid or semisolid products because they are measured based on their mass or weight. Ointments, creams, gels, lotions, and some tablets or capsules will have their dosage strength listed in % w/w form. The expression of % w/w on a drug label means x g/100 g of solute to sol-vent, or medication in a carrier. When you see percent (%) used to describe the strength of a solid or semisolid product, it carries the same meaning as % w/w. Bacitracin ointment 0.5% has 0.5 g of active ingredient, bacitracin, in every 100 g of ointment. This is important to understand. This information can help determine the total amount of active drug in any given quantity dispensed.
10.2. volume/volume
10.2.1. Volume/volume concentration (% v/v) describes the concentration of a liquid dissolved in another liquid. An example might be diluting chlorine (bleach) in water--liquid in a liquid. Acetic acid is another liquid that is often diluted in either water or saline. Alcohol is yet another liquid dissolved into another liquid. A concentration of 12% /v of phenol means that there is 12 mL of phenol in every 100 mL of solution. Again, as in the % w/w designation, this is often seen only on chemical reagents. These are concentrated solutions used for the sole purpose of dilution or addition to other products.
10.3. weight/volume
10.3.1. Weight/volume concentration describes the concentration of a solid dissolved in a liquid. IV solutions are an example of weight/volume concentration. They are expressed as % w/v, or × g/100 mL. An IV solution of D5%W (5% w/v) has 5 g/100 mL of dextrose.
10.4. Ratio strenght
10.4.1. Ratio strength represents the concentration of weak solutions. It is expressed in ratio form (x:y). A percent strength can be converted to a ratio strength and vice versa. Calculations can be performed in ratio format or converted to percent strength. When writing ratio strengths, the first number should be 1, so you need to reduce the ratio to its smallest denomination. The rules are similar to those of % w/w, % w/v, and % v/v. If the product is a solid, then a ratio of 1:1000 would mean there is 1 g of solute to 1000 g of solvent/ carrier. If the product is a liquid, it represents either a solid in liquid or a liquid in liquid.