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Chapter 1, Numbering systems and mathematical review, provides a comprehensive review of fractions and decimals. When you have successfully completed Chapter 1, you will have mastered skills to be able to: Identify and determine the values of roman and arabic numerals; understand and compare the values of fractions in various formats; accurately add, subtract, multiply, and divide fractions and decimals;...
MathforthePharmacyTechnician: ConceptsandCalculations EglerãBooth Chapter1:NumberingSystems andMathematicalReview andMathematicalReview McGrawưHill â2010 by the McGraw-Hill Companies, Inc All Rights Reserved 12 Numbering Systems and Mathematical Review McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 13 Learning Outcomes When you have successfully completed Chapter 1, you will have mastered skills to be able to: Identify and determine the values of Roman and Arabic numerals Understand and compare the values of fractions in various formats Accurately add, subtract, multiply, and divide fractions and decimals Convert fractions to mixed numbers and decimals McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 14 Learning Outcomes (con’t) Recognize the format of decimals and measure their relative values Round decimals to the nearest tenth, hundredth, or thousandth Describe the relationship among percents, ratios, decimals, and fractions McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 15 Introduction Basic math skills are building blocks for accurate dosage calculations You must be confident in your math skills A minor mistake can mean major errors in the patient’s medication McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 16 Arabic Numbers Arabic numbers include all numbers used today. Numbers are written using the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. You can write whole numbers, decimals, and fractions by simply combining digits. McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 17 Arabic Numbers (con’t) Example Example The Arabic digits 2 and 5 can be combined to write: The whole number 25 The decimal 2.5 The fraction 2/5 The same two digits are used in each of the above Arabic numbers but each have different values McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 18 Roman Numerals Are used sometimes in drug orders You need to understand how to change Roman numeral into Arabic numbers in order to do dosage calculations McGrawHill Commonly used Roman numerals ss = ½ I = 1 V = 5 X = 10 They may be written in lower or uppercase ©2010 by the McGrawHill Companies, Inc All Rights Reserved 19 Combining Roman Numerals When reading a Roman numeral containing more than 1 letter, follow these two steps: If any letter with a smaller value appears before a letter with a larger value, subtract the smaller value from the larger value Add the value of all the letters not affected by Step 1 to those that were combined McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 110 Combining Roman Numerals (con’t) Example Example IX = 10 –1 = 9 XIV = 10 + (51) = 14 McGrawHill Roman numerals from 1 to 30 are the ones you are most likely to see in doctors’ orders Be familiar with these to read orders correctly ©2010 by the McGrawHill Companies, Inc All Rights Reserved 156 Converting Fractions into Decimals To convert a fraction to a decimal, divide the numerator by the denominator. For example: McGrawHill 0.75 1.6 ©2010 by the McGrawHill Companies, Inc All Rights Reserved 157 Converting Decimals into Fractions Write the number to the left of the decimal point as the whole number Write the number to the right of the decimal point as the numerator of the fraction Use the place value of the digit farthest to the right of the decimal point as the denominator Reduce the fraction part to its lowest term McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 158 Review and Practice Convert decimals to fractions or mixed number: 1.2 Answer 100.4 Answer McGrawHill 1 or 10 100 or 100 10 ©2010 by the McGrawHill Companies, Inc All Rights Reserved 159 Adding and Subtracting Decimals Write the problem vertically. Align the decimal points Add or subtract starting from the right. Include the decimal point in your answer 2.47 +0.39 2.86 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved Adding and Subtracting Decimals (con’t) Subtract 7.3 – 1.005 7.300 1.005 6.295 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 160 161 Review and Practice Add or subtract the following pair of numbers: 13.561 + 0.099 Answer 13.66 16.250 – 1.625 Answer 14.625 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 162 Multiplying Decimals First, multiply without considering the decimal points, as if the numbers were whole numbers Count the total number of places to the right of the decimal point in both factors To place the decimal point in the product, start at its right end and move the decimal point to the left the same number of places McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 163 Multiplying Decimals (con’t) Multiply 3.42 x 2.5 3.42 X 2.5 1710 684 8.550 There are three decimal places so place the decimal point between 8 and 5 (8.55) McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 164 Review and Practice A patient is given 7.5 milliliters of liquid medication 5 times a day. How many milliliters does she receive per day? Answer 7.5 x 5 7.5 X 5 37.5 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 165 Dividing Decimals Write the problem as a fraction Move the decimal point to the right the same number of places in both the numerator and denominator until the denominator is a whole number. Insert zeros Complete the division as you would with whole numbers. Align the decimal point of the quotient with the decimal point of the numerator, if needed McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 166 Review and Practice A bottle contains 32 ounces of medication. If the average dose is 0.4 ounces, how many doses does the bottle contain? Answer: 32 divided by 0.4 Take 0.4 into 32 Add a zero behind the 32 for each decimal place 320 divided by 4 = 80 or 80 doses McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 167 Review and Practice Convert the following mixed numbers to fractions: 18 39 Answer 18 9 10 99 10 McGrawHill Answer 13 ©2010 by the McGrawHill Companies, Inc All Rights Reserved 168 Review and Practice Round to the nearest tenth: 7.091 Answer 7.1 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 169 Review and Practice Add the following: 7.23 + 12.38 Answer 19.61 Multiply the following: 12.01 x 1.005 Answer 12.07005 McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved 170 Remember, you control the numbers! Always ask for assistance if you are uncertain, the only bad question is the one not asked. THE END McGrawHill ©2010 by the McGrawHill Companies, Inc All Rights Reserved ... Divide? ?the? ?numerator by? ?the? ?denominator 11 = 2 R3 (R3 means a remainder of 3) 3.Theresultisthewholenumber2witha remainderof3 4.Writetheremainderoverthewholeắ 5.Combinethewholenumberandthefraction2+ắ... 5x3 =? ?15 Add? ?the? ?product from Step? ?1? ?to? ?the? ?numerator of? ?the? ?fraction ? ?15 +1? ?=? ?16 McGrawHill ©2 010 by? ?the? ?McGrawHill Companies, Inc All Rights Reserved 1? ?20... ©2 010 by? ?the? ?McGrawHill Companies, Inc All Rights Reserved 1? ? 21 Review? ?and? ?Practice 17 What is? ?the? ?numerator in ? 10 0 Answer = 17 What is? ?the? ?denominator in ? 10 0 Answer = 10 0 Twelve patients are in? ?the? ?hospital ward. Four