Arithmetic Review
Chapter 1 Pre-Test: Arithmetic Review
Name _________________________________ | Date _____________ |
Converting Between Arabic Numbers and Roman Numerals
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1. 7 = __________
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2. XI = __________
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3. 17 = __________
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4. XVI = __________
Multiplying and Dividing Fractions
Converting Fractions to Decimals
Multiplying and Dividing Decimals
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15. 2.75 × 1.25 =
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16. 0.25 ÷ 0.4 =
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17. 4.50 × 0.75 =
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18. 10.50 ÷ 4.5 =
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19. 1.2 × 2 =
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20. 1.5 ÷ 0.75 =
Objectives
After completing this chapter, you will successfully be able to:
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Express Arabic numbers as Roman numerals.
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Express Roman numerals as Arabic numbers.
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Identify the numerator and denominator in a fraction.
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Multiply and divide fractions.
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Multiply and divide decimals.
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Convert fractions to decimals.

Every nurse must know and practice the six rights of medication administration including the
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Right drug
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Right dose
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Right route
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Right time
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Right patient
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Right documentation
Although the right drug, route, time, patient, and documentation may be readily identified, the right dose requires arithmetic skills that may be difficult for you. This chapter reviews the basic arithmetic skills (multiplication and division) necessary for calculating medication dosage problems using the problem-solving method of dimensional analysis. Calculating the right dose of medication to be administered to a patient is one of the first steps toward preventing medication errors.
Arabic Numbers and Roman Numerals
Most medication dosages are ordered by the physician or the nurse practitioner in the metric and household systems for weights and measures using the Arabic number system with symbols called digits (ie, 1, 2, 3, 4, 5). Occasionally, orders are received in the apothecaries’ system of weights and measures using the Roman numeral system with numbers represented by symbols (ie, I, V, X). The Roman numeral system uses seven basic symbols, and various combinations of these symbols represent all numbers in the Arabic number system.
Table 1.1 includes the seven basic Roman numerals and the corresponding Arabic numbers.
The combination of Roman numeral symbols is based on three specific principles:

Correctly identifying Roman numerals will assist in preventing medication errors. Some medication orders may include a Roman numeral.
Example: Administer X gr of aspirin, which is correctly interpreted as administer 10 gr of aspirin.
However, according to the Institute for Safe Medication Practices (ISMP), abbreviations increase the risk of medication errors. Additionally, while some health care providers may still use roman numerals and the apothecaries’ system, the ISMP recommends using the metric system.
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1. Symbols are used to construct a number, but no symbol may be used more than three times. The exception is the symbol for five (V), which is used only once because there is a symbol for 10 (X) and a combination of symbols for 15 (XV).
Example 1.1
III = (1 + 1 + 1) = 3
XXX = (10 + 10 + 10) = 30
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2. When symbols of lesser value follow symbols of greater value, they are added to construct a number.
Example 1.2
VIII = (5 + 3) = 8
XVII = (10 + 5 + 1 + 1) = 17
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3. When symbols of greater value follow symbols of lesser value, those of lesser value are subtracted from those of higher value to construct a number.
Example 1.3
IV = (5 – 1) = 4
IX = (10 – 1) = 9
Table 1.1 Seven Basic Roman Numerals | ||||||||||||||||
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Exercise 1.1 Arabic Numbers and Roman Numerals (See page 23 for answers)
Express the following Arabic numbers as Roman numerals.
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1. 1 = ______
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2. 2 = ______
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3. 3 = ______
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4. 4 = ______
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5. 5 = ______
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6. 6 = ______
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7. 7 = ______
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8. 8 = ______
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9. 9 = ______
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10. 10 = ______
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11. 11 = ______
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12. 12 = ______
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13. 13 = ______
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14. 14 = ______
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15. 15 = ______
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16. 16 = ______
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17. 17 = ______
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18. 18 = ______
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19. 19 = ______
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20. 20 = ______
Although medication orders rarely involve Roman numerals higher than 20, for additional practice, express the following Arabic numbers as Roman numerals.
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21. 43 = ______
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22. 24 = ______
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23. 55 = ______
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24. 32 = ______
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25. 102 = ______
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26. 150 = ______
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27. 75 = ______
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28. 92 = ______
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29. 64 = ______
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30. 69 = ______
Express the following Roman numerals as Arabic numbers.
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31. II = ______
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32. IV = ______
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33. VI = ______
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34. X = ______
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35. VIII = ______
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36. XIX = ______
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37. XX = ______
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38. XVIII = ______
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39. I = ______
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40. XV = ______
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41. III = ______
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42. V = ______
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43. IX = ______
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44. VII = ______
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45. XI = ______
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46. XIV = ______
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47. XVI = ______
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48. XII = ______
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49. XVII = ______
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50. XIII = ______
To increase your abilities to use either system, convert the following Arabic numbers or Roman numerals.
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51. 19 = ______
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52. XII = ______
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53. 7 = ______
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54. IX = ______
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55. IV = ______
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56. 11 = ______
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57. VIII = ______
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58. 16 = ______
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59. XX = ______
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60. 5 = ______
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61. I = ______
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62. 18 = ______
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63. VI = ______
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64. 2 = ______
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65. III = ______
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66. 10 = ______
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67. XIII = ______
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68. 14 = ______
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69. XV = ______
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70. 17 = ______
Fractions
Medication dosages with fractions are occasionally ordered by the physician or used by the pharmaceutical manufacturer on the drug label. A fraction is a number that represents part of a whole number and contains three parts:
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Numerator—the number on the top portion of the fraction that represents the number of parts of the whole fraction.
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Dividing line—the line separating the top portion of the fraction from the bottom portion of the fraction.
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Denominator—the number on the bottom portion of the fraction that represents the number of parts into which the whole is divided.


Understanding fractions will assist in preventing medication errors. A medication order may include a fraction.
Example: Administer 1/150 gr of nitroglycerin.
To solve medication dosage calculation problems using dimensional analysis, you must be able to identify the numerator and denominator portion of the problem. You also must be able to multiply and divide numbers, fractions, and decimals.
Multiplying Fractions
The three steps for multiplying fractions are:
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Multiply the numerators.
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