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UNIT ONE
Math Review
A
n essential role of the nurse is providing safe medication administration to all clients.
To accurately perform dosage calculations, the nurse must have knowledge of basic
math, regardless of the problem-solving method used in calculation. Knowledge of basic
math is a necessary component of dosage calculation that nurses need to know to prevent
medication errors and ensure the safe administration of medications to all clients, regardless
of the setting. Serious harm to clients can result from a mathematical error during calculation and administration of a medication dosage. The nurse must practice and be proficient
in the basic math used in dosage calculations. Knowledge of basic math is a prerequisite for
the prevention of medication errors and ensures the safe administration of medications.
Although calculators are accessible for basic math operations, the nurse needs to be able
to perform the processes involved in basic math. Controversy still exists among educators
regarding the use of calculators in dosage calculation. Calculators may indeed be recommended for complex calculations to ensure accuracy and save time; the types of calculations requiring their use are presented later in this text. However, because the basic math
required for less complex calculations is often simple and can be done without the use of
a calculator, it is a realistic expectation that each practitioner should be competent in the
performance of basic math operations without its use. Performing basic math operations
enables the nurse to think logically and critically about the dosage ordered and the dosage
calculated.
Pre-Test
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Post-Test
Roman Numerals
Fractions
Decimals
Ratio and Proportion
Percentages
Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.
1
2
UNIT ONE Math Review
PRE-TEST
This test is designed to evaluate your ability in the basic math areas reviewed in Unit One.
The test consists of 72 questions. If you are able to complete the pre-test with 100% accuracy, you may want to bypass Unit One. Any problems answered incorrectly should be
used as a basis for what you might need to review. The purposes of this test and the review
that follows are to build your confidence in basic math skills and to help you avoid careless mistakes when you begin to perform dosage calculations.
Express the following in Roman numerals.
1. 9 _____________________________
1
4. 10 __________________________
2
2. 16 ____________________________
5. 22 ____________________________
3. 23 ____________________________
Express the following in Arabic numbers.
6. xiss ___________________________
9. xxiv __________________________
7. xii ____________________________
10. vi ____________________________
8. xviii __________________________
Reduce the following fractions to lowest terms.
14
11. ___________________________
21
24
14. ___________________________
30
25
12. __________________________
100
24
15. ____________________________
36
2
13. __________________________
150
Perform the indicated operations; reduce to lowest terms where necessary.
2
3
16. ____________________
3
9
1
1
23. 2 1 ____________________
6
4
3
17. 4 _____________________
4
3
24. 9 _______________________
5
2
1
18. _____________________
5
9
1
3
25. 4 1 ____________________
4
4
1
5
19. 7 2 ____________________
7
6
1
3
26. 7 1 ____________________
5
4
2
20. 4 4 ______________________
3
9
27. 7 ______________________
16
5
2
21. 3 5 ____________________
6
3
3
7
28. 3 1 __________________
10
10
6
5
22. 5 3 ____________________
7
7
Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.
Pre-Test
Change the following fractions to decimals; express your answer to the nearest tenth.
6
29. ____________________________
7
2
31. _____________________________
3
6
30. ___________________________
20
7
32. _____________________________
8
Indicate the largest fraction in each group.
3 4 7
33. , , _____________________
4 5 8
7 11 4
34. , , ___________________
12 12 12
Perform the indicated operations with decimals. Provide the exact answer; do not round
off.
35. 20.1 67.35 _________________
37. 4.6 8.72 ____________________
36. 0.008 5 ____________________
38. 56.47 8.7 ___________________
Divide the following decimals; express your answer to the nearest tenth.
39. 7.5 0.004 __________________
41. 84.7 2.3 ____________________
40. 45 1.9 _____________________
Indicate the largest decimal in each group.
42. 0.674, 0.659 ____________________
44. 0.25, 0.6, 0.175 __________________
43. 0.375, 0.37, 0.38 ________________
Solve for x, the unknown value.
45. 82 48x ____________________
1
1
47. x 15 _________________
10
2
46. x300 1150 _________________
48. 0.41 0.2x ___________________
Round off to the nearest tenth.
49. 0.43 __________________________
51. 1.47 ___________________________
50. 0.66 __________________________
Round off to the nearest hundredth.
52. 0.735 _________________________
54. 1.227 __________________________
53. 0.834 _________________________
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3
4
UNIT ONE Math Review
Complete the table below, expressing the measures in their equivalents where indicated.
Reduce to lowest terms where necessary.
Percent
Decimal
Ratio
Fraction
6%
__________
__________
__________
56. __________
__________
720
__________
57. __________
__________
__________
1
5
4
58. __________
0.015
__________
__________
55.
Find the following percentages. Express your answer to the hundredths place as indicated.
59. 5% of 95 ______________________
62. 20 is what % of 100 ______________
1
60. % of 2,000 ___________________
4
63. 30 is what % of 164 ______________
61. 2 is what % of 600 _______________
1
64. A client is instructed to take 1 teaspoons of a cough syrup three (3) times a day.
2
How many teaspoons of cough syrup will the client take each day?
_______________
65. A tablet contains 0.75 milligrams (mg) of a medication. A client receives three (3)
tablets a day for five (5) days. How many mg of the medication will the client
receive in five (5) days? ____________
66. A client took 0.44 micrograms (mcg) of a medication every morning and 1.4 mcg
each evening for five (5) days. What is the total amount of medication taken?
________________
67. Write a ratio that represents that every tablet in a bottle contains 0.5 milligrams
(mg) of a medication.__________________
68. Write a ratio that represents 60 milligrams (mg) of a medication in 1 milliliter (mL)
of a liquid. __________
69. A client takes 10 milliliters (mL) of a medication three (3) times a day. How long
will 120 mL of medication last? __________
70. A client weighed 275 pounds (lb) before dieting. After dieting, the client weighed
250 lb. What is the percent of change in the client’s weight? _____________
71. A client was prescribed 10 milligrams (mg) of a medication for a week. After a
week, the health care provider reduced the medication to seven (7) mg. What was
the percentage of decrease in medication? ________
72. A client received 22.5 milligrams (mg) of a medication in tablet form. Each tablet
contained 4.5 mg of medication. How many tablets were given to the client?
Answers on p. 5
Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.
Pre-Test
ANSWERS
3
1
21. 9 9 6
2
29. 0.9
42. 0.674
2. xvi, xvi, XVI
1
13. 75
30. 0.3
43. 0.38
3. xxiii, xxiii,
XXIII
4
14. 5
11
4
22. 8 9 7
7
31. 0.7
44. 0.6
4
2
15. 6
3
11
23. 12
32. 0.9
7
33. 8
45. x 12
4. xss, xss
16. 2
2
24. 8 5
11
34. 12
1
48. x 0.5 or 2
2
1
25. 2 2 4
2
35. 87.45
49. 0.4
36. 5.008
50. 0.7
9
26. 5 20
37. 40.112
51. 1.5
38. 47.77
52. 0.74
7
27. 6 16
39. 1,875
53. 0.83
40. 23.7
54. 1.23
6
3
28. 1 1 10
5
41. 36.8
1. ix, ix, IX
5. xxii, xxii, XXII
1
6. 11 2
7. 12
8. 18
9. 24
10. 6
2
11. 3
1
12. 4
1
17. 5 3
23
18. 45
13
19. 4 42
2
20. 18 3
46. x 2
47. x 3
Percent
Decimal
Ratio
Fraction
55. 6%
0.06
3 : 50
3
50
56. 35%
0.35
7 : 20
7
20
57. 525%
5.25
21 : 4
1
5
4
58. 1.5%
0.015
3 : 200
3
200
59. 4.75
63. 18.29%
1
64. 4 teaspoons
2
65. 11.25 milligrams
(mg)
67. 0.5 mg : 1 tablet
70. 9%
68. 60 mg : 1 mL
71. 30%
66. 9.2 micrograms
(mcg)
69. 4 days
72. 5 tablets
60. 5
61. 0.33%
62. 20%
Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.
5
CHAPTER 1
Roman Numerals
Objectives
After reviewing this chapter, you should be able to:
1. Recognize the symbols used to represent numbers in the Roman numeral system
2. Convert Roman numerals to Arabic numbers
3. Convert Arabic numbers to Roman numerals
T
he Roman numeral system dates back to ancient Roman times and uses letters to designate amounts. Roman numerals are used in the apothecary system of measurement
for writing medication dosages. Roman numerals do not use commas.
gr x
↓
↑
[
[
Example:
Apothecary measure
(unit of weight)
Roman numeral
(Arabic equivalent 10)
Roman numerals are also still used on objects that indicate time (e.g. watches, clocks).
Roman numerals are used in other instances, for example, the Super Bowl (e.g., Super
Bowl XXVII), movie sequels (e.g., the Rocky series), and car styles (e.g., Mach V).
Roman numerals are also seen on the labels of medications that are considered to be
controlled substances (medications which can lead to abuse or dependence). The roman
numeral is usually written using capital letters and has a large “C” (control) encircling it.
Roman numerals one through five (I–V) are used to indicate the potential for abuse. This
will be discussed in more detail in Chapter 13, Reading Medication Labels.
The label for the controlled substance Vicodin (hydrocodone bitartrate and acetaminophen) shown in Figure 1-1 indicates it is a Schedule III medication, as indicated by
CIII on the label.
6
Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.
CHAPTER 1 Roman Numerals
Figure 1-1 Vicodin label.
SAFETY ALERT!
Misinterpretation of the symbol for a controlled substances can lead to a medication error.
Roman numerals are also used to identify different clotting factors found in a person's
blood. For example, Factor I (Fibrinogen) and Factor III (Thromboplastin).
In the Arabic system, numbers, not letters, are used to express amounts. The Arabic system also uses fractions (1⁄2) and decimals (0.5).
Most medication dosages are ordered using metric measurements and Arabic numbers;
however, on rare occasions, medication orders may include a Roman numeral.
Example:
Aspirin gr x, which is correctly interpreted as aspirin 10 grains
To calculate medication dosages and assist in the prevention of medication errors, nurses
need to know both Roman numerals and Arabic numbers. Lowercase letters are usually used
to express Roman numerals in relation to medications. The Roman numerals you will see
most often in the calculation of dosages are built on the basic symbols i, v, and x. To prevent
errors in interpretation a line is sometimes drawn over the symbol. If this line is used, the
lowercase “i” is dotted above the line, not below.
Example 1: 10 grains gr x
Example 2: 2 ii
SAFETY ALERT
Correctly identifying Roman numerals will assist in preventing medication errors. According to the Institute for Safe Medication Practices (ISMP), abbreviations increase the risk for occurrence of medication errors. Although some health care providers may still use Roman numerals and the apothecary system, the
ISMP recommends using the metric system.
RULE
As illustrated in the example, with apothecary measures, the label grains when abbreviated (gr) precedes the Roman numeral.
When the symbol for 1⁄2 (ss) is used in conjunction with Roman numerals, the symbol is
placed at the end.
1
Example 1: 3 iiiss or iiiss
2
1
Example 2: 1 grains gr iss or gr iss
2
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7
8
UNIT ONE Math Review
NOTE
Larger Roman numerals, such
as L(l) 50, C(c) 100, and
larger, are usually not used in relation to medications.
Box 1-1 lists the common Arabic equivalents for Roman numerals (review them if necessary). They are often expressed with lowercase letters. Review this list before proceeding
to the rules pertaining to Roman numerals as shown on p. •. You will most commonly see
Roman numerals up to the value of 30 when they are used in relation to medications. It is
recommended to use uppercase letters when smaller numbers are part of a number over 30,
for example, 60 LX not lx.
BOX 1-1 Arabic Equivalents for Roman Numerals
Arabic Number
1
⁄2
1
2
3
4
5
6
7
8
Roman
Numeral
Arabic Number
ss or ss
i or i, I
ii or ii, II
iii or iii, III
iv or iv, IV
v or v, V
vi or vi, VI
vii or vii, VII
viii or viii, VIII
9
10
15
20
30
50
100
500
1,000
Roman
Numeral
ix or ix, IX
x or x, X
xv or xv, XV
xx or xx, XX
xxx or xxx, XXX
L(l)
C(c)
D(d)
M(m)
Although the Roman numerals for 50, 100, 500, and 1,000 are not used in relation to
medications, a well-known mnemonic: “Lovely Cats Don't Meow,” can help you to remember the order and value of the Roman numerals (L, C, D, M) for 50, 100, 500, and
1,000 (Box 1-2).
BOX 1-2 Mnemonic Device: Note the pattern:
50-100-500-1,000
L 50
Lovely
C 100
Cats
D 500
Don't
M 1,000 Meow
RULE
Rules Relating to the Roman System of Notation
1. The same Roman numeral is never repeated more than three times.
a. Example: Convert the Arabic number 4 to a Roman numeral.
i. Right: 4 iv
ii. Wrong: 4 iiii
b. Example: Convert the Arabic number 9 to a Roman numeral.
i. Right: 9 ix
ii. Wrong: 9 viiii
2. When a Roman numeral of a lesser value is placed after one of equal or greater value, the numerals are
added.
a. Example: Convert the Arabic number 25 to a Roman numeral.
i. Right: 25 xxv (10 10 5 25)
b. Example: Convert the Roman numeral xvi to an Arabic number.
i. Right: xvi 16 (10 5 1 16)
3. When a Roman numeral of a lesser value is placed before a numeral of greater value, the numerals are
subtracted.
a. Example: Convert the Roman numerals ix and xxiv to Arabic numbers.
i. Right: ix 9 (10 1 9)
ii. Right: xxiv 24 [10 10 (5 1) 24]
b. Example: Convert the Arabic numbers 19 and 14 to Roman numerals.
i. Right: 19 xix [10 (10 1) 19]
ii. Right: 14 xiv [10 (5 1) 14]
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CHAPTER 1 Roman Numerals
9
PRACTICE PROBLEMS
Write the following as Roman numerals.
Write the following as Arabic numbers.
1. 15 ____________________________
9. xiv ___________________________
2. 13 ____________________________
10. xxix __________________________
3. 28 ____________________________
11. iv ____________________________
4. 11 ____________________________
12. xix ___________________________
5. 17 ____________________________
13. xxxiv _________________________
6. 65 ____________________________
14. CC ___________________________
7. 1,001 _________________________
15. MVIII _________________________
8. 69 ____________________________
Answers on p. 1
CHAPTER REVIEW
Write the following Arabic numbers as Roman numerals.
1. 6 _____________________________
7. 20 ____________________________
2. 30 ____________________________
8. 3 _____________________________
1
3. 1 ___________________________
2
9. 21 ____________________________
4. 27 ____________________________
10. 26 ____________________________
5. 12 ____________________________
11. 150 ____________________________
6. 18 ____________________________
12. 999 ___________________________
Write the following Roman numerals as Arabic numbers.
13. viiss __________________________
20. xvi ___________________________
14. xix ___________________________
21. v _____________________________
15. xv ____________________________
22. xxvii __________________________
16. xxx ___________________________
23. XC ____________________________
17. ss ____________________________
24. LXXV __________________________
18. iii ____________________________
25. DXIV _________________________
19. xxii ___________________________
Answers on p. 10
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For additional practice problems, refer to the Mathematics Review section of the
Drug Calculations Companion, Version 5, on Evolve.
10
UNIT ONE Math Review
ANSWERS
Answers to Practice
Problems
1. xv, xv, XV
Answers to Chapter
Review
9. 14
1. vi, vi, VI
10. xxvi, xxvi, XXVI
18. 3
11. CL
19. 22
20. 16
2. xiii, xiii, XIII
10. 29
3. xxviii, xxviii, XXVIII
11. 4
2. xxx, xx
x
, XXX
3. iss, iss, iss
4. xi, xi, XI
12. 19
4. xxvii, xxvii, XXVII
5. xvii, xvii, XVII
13. 34
5. xii, xii, XII
12. IM
1
13. 7 2
6. LXV
14. 200
6. xviii, xviii, XVIII
14. 19
23. 90
7. MI
15. 1,008
7. xx, xx, XX
15. 15
24. 75
8. iii, iii, III
16. 30
1
17. 2
25. 514
8. LXIX
9. xxi, xxi, XXI
21. 5
22. 27
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