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c h a p t e r9Basic Pharmacy.MathChapter Overview.A basic understanding of mathematics is necessary for the.material covered in this and subsequent chapters involving calculations. This chapter will demonstrate basic mathematics as a.review, but will mainly focus on the problem solving seen on.the pharmacy technician exams. To complete this chapter, you.will need a basic calculator that adds, subtracts, divides, and.multiplies.KEY TERMS.Arabic numbers.common fraction.complex fraction.concentration.decimal fraction.decimal number.denominator.extremesfraction.improper fraction.lowest common denominator.means.metric system.mixed fraction.numerator.proper fractionproportion.ratio.Roman numerals.rounding.solute.solution.solvent135PharmExam3E_09_135-152.indd 1354/6/17 11:43 AM.–BASIC PHARMACY MATH–Fundamentals of Calculations.Calculations in the pharmacy setting require you to.have a basic understanding of Roman numerals,.Arabic numbers (1, 2, 3, 4, 5, 6, 7, 8, 9, 10, etc.), and.critical thinking (the ability to look at a problem and.figure out the steps necessary to solve it).Roman Numerals.In pharmacy practice, we may use Roman numerals.to denote quantities ordered on prescriptions or.when compounding, especially when using the.apothecary system of weights and measuresA numeral is a word or sign, or a group of words.or signs, which express a number. The easiest way to.note a number is to make that many marks—little I’sThus I would mean 1, II would mean 2, III would.mean 3, and so on. However, this system becomes.awkward and clumsy for larger numbersIn the Roman system of counting, letters are.used to designate numbers. Upper and lowercase letters signify the same values (e.g., i = I). There are.seven letters which represent Roman numerals: I, V,.X, L, C, D, and MArabic and Roman Numeral.Equivalents.Arabic Number.Roman Numeral.1.__.2ss1I or i*2II or ii3III or iii4IV or iv5V or v6VI or vi7VII or vii8VIII or viii9IX or ixArabic and Roman Numeral.Equivalents.Arabic Number.Roman Numeral.10X or x20XX or xx30XXX or xxx40XL or xl50L or l100C or c500D or d1,000M or m* All lowercase Roman numerals may be written with a line above them.In general, Roman numerals can be converted to.Arabic numbers mathematically by simply assigning a.numerical value to each letter and calculating a totalAlthough the historical practice has varied, the modern convention is to arrange the letters from left to.right, in order of decreasing value; the total is then.calculated by adding the numerical values of all the.letters in the sequence. For example, the Roman.numeral MDCLXXXVIII would be equal to:.1,000 + 500 + 100 + 50 + 10 + 10 + 10 + 5 +.1+ 1+ 1 = 1,688.Using this notation, Roman numerals can get.quite long—and so the Romans began to use contractions, called the subtraction principle, in which a.smaller letter appears before a larger letter to indicate.a smaller number: IV = one from five = 4 or CM = one.hundred from one thousand = 900There is one additional “Roman” numeral used.in pharmacy practice, but was never used by the.Romans: ss = __12 . You should be aware of this notation,.but avoid its use. It is easily confused with the number.55 when handwritten and could lead to significant.medication errorsA simple set of rules governs the Roman system.of notation in pharmacy practice. The position of one136PharmExam3E_09_135-152.indd 1364/6/17 11:43 AM.–BASIC PHARMACY MATH–letter to another is very important and determines the.value of the Roman numeral. Repeating a Roman.numeral twice doubles its value; repeating a Roman.numeral three times triples its value:.I = 1 and II = 2.x = 10 and xxx = 30.However, Roman numerals are not repeated.more than three times in succession:.III = 3 is a correct notation, but IIII = 4 is.incorrectWhen you place the same or a smaller Roman.numeral after a larger Roman numeral, you add the.Roman numerals