, Solution manual for Pharmaceutical Calculations
for Pharmacy Technicians A Worktext, 3rd Edition
Jahangir Moini
Notes
1- The file is chapter after chapter.
2- We have shown you 10 or five pages.
3- The file contains all Appendix and Excel
sheet if it exists.
4- We have all what you need, we make
update at every time. There are many
new editions waiting you.
5- If you think you purchased the wrong file
You can contact us at every time, we can
replace it with true one.
Our email:
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
Solution and Answer Guide
MOINI, PHARMACEUTICAL CALCULATIONS FOR PHARMACY TECHNICIANS, ISBN: 9780357765975; CHAPTER
1: FUNDAMENTALS OF MATH
TABLE OF CONTENTS
Answer Key with Rationales for End-of-Chapter Questions...................................................1
Test Your Knowledge ................................................................................................................ 1
Critical Thinking ....................................................................................................................... 30
ANSWER KEY WITH RATIONALES FOR END-OF-CHAPTER
QUESTIONS
TEST YOUR KNOWLEDGE
Convert the following Arabic numbers to Roman numerals.
1. 5
Answer:
Solution: The Arabic number 5 is represented by the uppercase letter or the lowercase in
Roman numerals.
2. 18
Answer:
Solution: To convert the Arabic number 18 to Roman numerals, first split 18 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
3. 9
Answer:
Solution: To convert the Arabic number 9 to Roman numerals, first split 9 to its constituent parts
that have an equivalent letter in Roman numerals. Letters are never used more than three times
in a row.
In this case, splitting to will exceed the use of the letter three times in
a row. Therefore, the subtraction method is to be used, with the lower-valued letter then placed
before the higher-valued letter:
4. 16
Answer:
Solution: To convert the Arabic number 16 to Roman numerals, first split 16 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
5. 19
Answer:
Solution: To convert the Arabic number 19 to Roman numerals, first split 19 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter three
times in a row. Therefore, a combination of addition and subtraction is to be used with a lower-
valued letter placed between two higher-valued letters:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
6. 22
Answer:
Solution: To convert the Arabic number 22 to Roman numerals, first 22 to its constituent parts
that have an equivalent letter in Roman numerals. Letters are never used more than three times
in a row. Then, substitute each constituent part with its equivalent letter in Roman numerals:
7. 24
Answer:
Solution: To convert the Arabic number 24 to Roman numerals, first split 24 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
8. 27
Answer:
Solution: To convert the Arabic number 27 to Roman numerals, first split 27 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
9. 29
Answer:
Solution: To convert the Arabic number 29 to Roman numerals, first split 29 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the
letter three times in a row. Therefore, a combination of addition and subtraction is to be used
with a lower-valued letter placed before the final higher-valued letter:
10. 30
Answer:
Solution: To convert the Arabic number 30 to Roman numerals, first split 30 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
11. 45
Answer:
Solution: To convert the Arabic number 45 to Roman numerals, first split 45 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter three times
in a row. Therefore, a combination of addition and subtraction is to be used with a lower-valued
letter placed before a higher-valued letter:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 4
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
12. 89
Answer:
Solution: To convert the Arabic number 89 to Roman numerals, first split 89 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
13. 112
Answer:
Solution: To convert the Arabic number 112 to Roman numerals, first split 112 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
14. 155
Answer:
Solution: To convert the Arabic number 155 to Roman numerals, first split 155 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 5
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
15. 198
Answer:
Solution: To convert the Arabic number 198 to Roman numerals, first split 198 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the
letter three times in a row. Therefore, a combination of addition and subtraction is to be used
with a lower-valued letter placed before a higher-valued letter:
16. 202
Answer:
Solution: To convert the Arabic number 202 to Roman numerals, first split 202 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
17. 506
Answer:
Solution: To convert the Arabic number 506 to Roman numerals, first split 506 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 6
website, in whole or in part.
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
18. 534
Answer:
Solution: To convert the Arabic number 534 to Roman numerals, first split 534 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
19. 1000
Answer:
Solution: The Arabic number 1000 is represented by the uppercase letter or the lowercase
in Roman numerals.
20. 1025
Answer:
Solution: To convert the Arabic number 1025 to Roman numerals, first split 1025 to its
constituent parts that have an equivalent letter in Roman numerals. Letters are never used more
than three times in a row. Then, substitute each constituent part with its equivalent letter in
Roman numerals:
Convert the following Roman numerals to Arabic numbers.
21.
Answer: 4
Solution: Roman numerals are read by adding or subtracting the value of the letters. If a lower-
valued letter is placed before a higher-valued letter, the lower-valued letter is subtracted from the
higher-valued letter:
22.
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 7
website, in whole or in part.
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
Answer: 7
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears twice in a row, the value of the letter is counted twice. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
23.
Answer: 9
Solution: Roman numerals are read by adding or subtracting the value of the letters. If a lower-
valued letter is placed before a higher-valued letter, the lower-valued letter is subtracted from the
higher-valued letter:
24.
Answer: 13
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears three times in a row, the value is counted three times. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
25.
Answer: 14
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
Roman numeral of smaller value comes between two other Roman numerals with larger values,
subtract the smaller numeral from the one to its right. Then, add the remaining values:
26.
Answer: 18
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears three times in a row, the value is counted three times. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
27.
Answer: 19
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 8
website, in whole or in part.
for Pharmacy Technicians A Worktext, 3rd Edition
Jahangir Moini
Notes
1- The file is chapter after chapter.
2- We have shown you 10 or five pages.
3- The file contains all Appendix and Excel
sheet if it exists.
4- We have all what you need, we make
update at every time. There are many
new editions waiting you.
5- If you think you purchased the wrong file
You can contact us at every time, we can
replace it with true one.
Our email:
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
Solution and Answer Guide
MOINI, PHARMACEUTICAL CALCULATIONS FOR PHARMACY TECHNICIANS, ISBN: 9780357765975; CHAPTER
1: FUNDAMENTALS OF MATH
TABLE OF CONTENTS
Answer Key with Rationales for End-of-Chapter Questions...................................................1
Test Your Knowledge ................................................................................................................ 1
Critical Thinking ....................................................................................................................... 30
ANSWER KEY WITH RATIONALES FOR END-OF-CHAPTER
QUESTIONS
TEST YOUR KNOWLEDGE
Convert the following Arabic numbers to Roman numerals.
1. 5
Answer:
Solution: The Arabic number 5 is represented by the uppercase letter or the lowercase in
Roman numerals.
2. 18
Answer:
Solution: To convert the Arabic number 18 to Roman numerals, first split 18 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 1
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
3. 9
Answer:
Solution: To convert the Arabic number 9 to Roman numerals, first split 9 to its constituent parts
that have an equivalent letter in Roman numerals. Letters are never used more than three times
in a row.
In this case, splitting to will exceed the use of the letter three times in
a row. Therefore, the subtraction method is to be used, with the lower-valued letter then placed
before the higher-valued letter:
4. 16
Answer:
Solution: To convert the Arabic number 16 to Roman numerals, first split 16 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
5. 19
Answer:
Solution: To convert the Arabic number 19 to Roman numerals, first split 19 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter three
times in a row. Therefore, a combination of addition and subtraction is to be used with a lower-
valued letter placed between two higher-valued letters:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 2
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
6. 22
Answer:
Solution: To convert the Arabic number 22 to Roman numerals, first 22 to its constituent parts
that have an equivalent letter in Roman numerals. Letters are never used more than three times
in a row. Then, substitute each constituent part with its equivalent letter in Roman numerals:
7. 24
Answer:
Solution: To convert the Arabic number 24 to Roman numerals, first split 24 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
8. 27
Answer:
Solution: To convert the Arabic number 27 to Roman numerals, first split 27 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 3
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
9. 29
Answer:
Solution: To convert the Arabic number 29 to Roman numerals, first split 29 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the
letter three times in a row. Therefore, a combination of addition and subtraction is to be used
with a lower-valued letter placed before the final higher-valued letter:
10. 30
Answer:
Solution: To convert the Arabic number 30 to Roman numerals, first split 30 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
11. 45
Answer:
Solution: To convert the Arabic number 45 to Roman numerals, first split 45 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter three times
in a row. Therefore, a combination of addition and subtraction is to be used with a lower-valued
letter placed before a higher-valued letter:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 4
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
12. 89
Answer:
Solution: To convert the Arabic number 89 to Roman numerals, first split 89 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
13. 112
Answer:
Solution: To convert the Arabic number 112 to Roman numerals, first split 112 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
14. 155
Answer:
Solution: To convert the Arabic number 155 to Roman numerals, first split 155 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 5
website, in whole or in part.
,Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
15. 198
Answer:
Solution: To convert the Arabic number 198 to Roman numerals, first split 198 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the
letter three times in a row. Therefore, a combination of addition and subtraction is to be used
with a lower-valued letter placed before a higher-valued letter:
16. 202
Answer:
Solution: To convert the Arabic number 202 to Roman numerals, first split 202 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
17. 506
Answer:
Solution: To convert the Arabic number 506 to Roman numerals, first split 506 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row. Then, substitute each constituent part with its equivalent letter in Roman
numerals:
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 6
website, in whole or in part.
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
18. 534
Answer:
Solution: To convert the Arabic number 534 to Roman numerals, first split 534 to its constituent
parts that have an equivalent letter in Roman numerals. Letters are never used more than three
times in a row.
In this case, splitting to will exceed the use of the letter
three times in a row. Therefore, a combination of addition and subtraction is to be used with a
lower-valued letter placed before the final higher-valued letter:
19. 1000
Answer:
Solution: The Arabic number 1000 is represented by the uppercase letter or the lowercase
in Roman numerals.
20. 1025
Answer:
Solution: To convert the Arabic number 1025 to Roman numerals, first split 1025 to its
constituent parts that have an equivalent letter in Roman numerals. Letters are never used more
than three times in a row. Then, substitute each constituent part with its equivalent letter in
Roman numerals:
Convert the following Roman numerals to Arabic numbers.
21.
Answer: 4
Solution: Roman numerals are read by adding or subtracting the value of the letters. If a lower-
valued letter is placed before a higher-valued letter, the lower-valued letter is subtracted from the
higher-valued letter:
22.
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 7
website, in whole or in part.
, Solution and Answer Guide: Moini, Pharmaceutical Calculations for Pharmacy Technicians, Third Edition, ISBN: 9780357765975;
Chapter 1: Fundamentals of Math
Answer: 7
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears twice in a row, the value of the letter is counted twice. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
23.
Answer: 9
Solution: Roman numerals are read by adding or subtracting the value of the letters. If a lower-
valued letter is placed before a higher-valued letter, the lower-valued letter is subtracted from the
higher-valued letter:
24.
Answer: 13
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears three times in a row, the value is counted three times. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
25.
Answer: 14
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
Roman numeral of smaller value comes between two other Roman numerals with larger values,
subtract the smaller numeral from the one to its right. Then, add the remaining values:
26.
Answer: 18
Solution: Roman numerals are read by adding or subtracting the value of the letters. When a
letter appears three times in a row, the value is counted three times. If a lower-valued letter
follows a larger-valued letter, the letter values should be added:
27.
Answer: 19
© 2023 Cengage. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible 8
website, in whole or in part.
