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Ratios, Proportions, Percents Ratios Show the relationship between two entities. apples to oranges apples to total fruit men to women total people to women medication to saline solution medication to total amount Can be written: a b a:b a to b Most common used in pharmacy. The strength is a measure of the concentration of the drug per solid unit or the concentration of the drug in a solution. Solids – tablets, ointments, creams, powders Tablets and capsules - the ratio will always be the amount of medication per one (meaning per one tablet), even though tablets can be cut in half. (examples: 1000mg/tablet, 100 : 1, 1000mg/capsule) Ointments, crams, powders – expressed in units per weight (examples: 50mg per 10g, 15 : 1) Liquids – “how much of the drug (in weight or volume) per volume of liquid (mL) into which the drug is mixed” (examples: 5mg : 1L, 15mL : 1L) Example 1 from text: “Dispense Demeclomycin 250mg tablet per dose. Pharmacy stocks 500mg tablets.” 500mg this ratio represents what the pharmacy HAS 1tablet 250mg this ratio represents what you NEED dose(? tablets ) The question is how many tablets are needed for the 250mg dose? 500mg 250mg called a "proportion", now solve for "x " 1tablet x tablets 500 x 250 1 500 x 250 500 x 250 500 500 x 0.5 tablet or 1/2 tablet This can also be done using a conversion chain. The question rephrased is, “ A drug comes in 500mg tablets. I need 250mg for 1 dose. How many tablets will it take for that one dose?” 1tablet 250 mg 0.5tablets / dose 1dose 500 mg 1 or tablet per dose 2 In this case I think the proportion is easier. You will need to know both ways. Practice Problems 3.1 (21-25) Let’s discuss these. 21. 750mg tablet of clarithromycin 22. 10mg capsule of dicyclomine 23. 125mg of amoxicillin in 5mL 24. 300mg of ranitidine in 2mL 25. 20mg of diphenhydramine in 1g Proportions Two ratios that are equal to each other. Different ways to express this type of relationship. 3 9 most common 8 24 Use cross multiplication or reducing to 3 9 :: check for equivalency. 8 24 3 : 8 9 : 24 3 : 8 :: 9 : 24 Parts of the proportion have names. In our example above: 3 and 24 are called the ______________________ 8 and 9 are called the ______________________ Example of solving proportions: “A patient needs 300mg of medication. The pharmacy stocks 250mg/5mL strength.” 250mg 300mg start with what you know, include units 5mL x mL 250 x 5 300 250 x 1500 1500 250 x 6mL x include the units If asked, show the answer is correct by multiplying the means, multiplying the extremes, and showing they are the same. Percents Mean out of 100, per 100, for every 100. What are the rules? What are the short cuts? Percent to Fractions 15% 15.2% 0.05% Fractions to Percents 1/8 0.5/100 220/100 Percents to Decimals 2% 216% 0.2% Decimals to Percents 0.5 50 60.8 Discussion (p32 in your text) SOMETHING YOU SHOULD KNOW The percent is used most often to express the concentration of intravenous (IV) solutions and topical medications (creams and ointments). This can also be called a percent strength. It describes the amount of drug contained in a specific volume (liquid or solid). An IV solution containing 5% dextrose has 5g of dextrose for every 100mL of solution. It could also be translated as 5g/100mL, 0.05, or5:100. An ointment that contains 0.1% triamcinolone has 0.1g of triamcinolone for every 100g of ointment. This translates to 0.1g/100mL, 0.001, or 0.1:100 as a fraction, decimal, or ratio respectively. Homework for Chapter 3: (remember, the calculator is to be used for checking, not for doing the work) Chapter 3 Quiz (in text), you are to do every odd problem. 1-5 (1st section) Copy the problem, change to a fraction, give simplified fraction. 1-5 (2nd section) Copy the problem, change to a ratio using a colon without changing the numbers, simplify if possible. 1-5 (3rd section) Copy the problem, change to a ratio without changing the numbers, give the simplified ratio if possible 1-5 (4th section) Copy the problem, change to a fraction or decimal, then change to a percent (show any work you can’t do in your head). 1-5 (5th section) Copy the problem, change to a fraction or decimal, change to a percent (show work) 1-5 (6th section) Copy the problem, change to a fraction (or decimal), then give the simplified fraction (show any work you can’t do in your head). 1-5 (7th section) Copy the problem, solve algebraically in a top down manner. Each problem should have at least 3 lines (equations). 1-10 (last section, word problems) Answer each question by setting up a proportion and solving in a top down manner. Units must be included both in the problem and with the answer. Each answer should be justified.