1. Week 1
Roman Numerals and Fractions

2. Uses of Roman Numerals in Pharmacy
• Roman numerals were once used frequently in
pharmacy; now you will only see them
occasionally
• Sometimes prescribers will use them on written
prescriptions to indicate a quantity

3. Make sure you know these
• I = 1 (you may also see “i”)
• V = 5 (you may also see “v”)
• X = 10 (you may also see “x”)
• L = 50
• C = 100
• D = 500
• M = 1000

4. The symbol for 1, 10, 100 or 1000 can
be repeated up to 3 times to make
larger numbers.
• C = 100
• CC = 200
• CCC = 300
• M = 1000
• MM = 2000
• MMM = 3000

5. Smaller valued symbols AFTER a larger
valued symbol are ADDED
• X = 10
• XI = 10 + 1 = 11
• XII = 10 + 1 + 1 = 12
• XIII = 10 + 1 + 1 + 1 = 13
• XV = 10 + 5 = 15
• XVI = 10 + 5 + 1 = 16
• XXXIII = 10 + 10 + 10 + 1 + 1 + 1 = 33
• MCX = 1000 + 100 + 10 = 1110

6. Smaller valued symbols BEFORE a
larger valued symbol are SUBTRACTED
• V = 5
• IV = 5 – 1 = 4
• X = 10
• IX = 10 – 1 = 9
• L = 50
• XL = 50 – 10 = 40
• C = 100
• XC = 100 – 10 = 90

7. Most of the Roman numerals you
encounter in pharmacy will be the
basic ones
Example from a prescription:
Percocet 5/325 XX
Sig: ii bid
This means: fill a prescription for 20 (XX) Percocet
tabs, with 2 (ii) tabs to be taken twice daily (bid).
Percocet is a combination drug; each tab contains
5mg oxycodone and 325mg acetaminophen (5/325).

8. To Remember
• Memorize the basic symbols: I, V, X, L, C, D, M
• The following symbols can be repeated up to 3
times to make numbers: I, X, C, M
• Smaller valued symbols that come AFTER larger
valued ones are ADDED, for example
VI = 5 + 1 = 6
• Smaller valued symbols that come BEFORE
larger valued ones are SUBTACTED, for example
IV = 5 – 1 = 4

9. Test Yourself
• C = ?
• 100
• XVIII = ?
• 10 + 5 + 1 + 1 + 1 = 18
• IV = ?
• 5 – 1 = 4
• XLII = ?
• (50 – 10) + 1 + 1 = 42
• MCXXX = ?
• 1000 + 100 + 10 + 10 + 10 = 1130

10. Uses of Fractions in Pharmacy
• Fractions are used all day, every day in
pharmacy and are very important to master
• For example, drug concentrations are expressed
as fractions
• On this drug label “40 mg/ml” is a fraction that
tells you the concentration of the drug
tobramycin in the vial

11. Fractions
• Fractions express parts of a whole and can be
written many different ways.
• 3 parts out of 4 = 3 / 4 = 3 out of 4 = 3 : 4
• = 3 per 4
• The first (top) number in a fraction is called the
numerator
• The second (bottom) number in a fraction is
called the denominator

12. Fractions
• ANYTIME zero is the numerator of a fraction,
the fraction is equal to 0
• For example 0 / 2 = 0 0 / 11,143 = 0
• ANYTIME the number one is the denominator of
a fraction, the fraction is equal to the numerator
• For example 3 / 1 = 3 0 / 1 = 0 6.6 / 1 = 6.6
• Zero cannot be the denominator of a fraction
• For example 450 / 0 is “undefined”

13. Fractions
• Any fraction where the numerator and
denominator are the same is equal to 1.
• For example, 9 / 9 = 1 4 / (3+1) = 1
• If two fractions are equal, they are called
equivalent fractions
• These 4 fractions are equivalent and are all ways
of writing 1 / 2 or one half.

14. Test Yourself
• Express 5 per 6 as a fraction
• 5 / 6
• 16 / 0 = ?
• This is undefined (division by 0 is not possible)
• 55.5 / 1 = ?
• 55.5 (any number over 1 = itself)
• 0 / 734 = ?
• 0 (zero over any number = zero)
• 3/3 = ?
• 1 (any number over itself is = 1)
• Are these equivalent? ¾ and 1/3
• No, because they are not equal

15. Simplifying Fractions
• When you do calculations with fractions, the
answer should be “in simplest terms”. To
simplify fractions, you need to first factor the
numerator and the denominator, then cross out
like terms (because any number over itself = 1)
4 2 x 2 2 x 2 2
_ = ___ = ___ = _
6 2 x 3 2 x 3 3

16. Simplifying Fractions
• Other examples of simplifying fractions:
15 3 x 5 3 x 5 5
__ = _____ = ______ = ___ = 5 / 9
27 3 x 3 x 3 3 x 3 x 3 3 x 3
250 5 x 5 x 5 x 2 5 x 5 x 5 x 2 5
__ = _______ = ________ = _ = 5
50 5 x 5 x 2 5 x 5 x 2 1

17. Test Yourself
Simplify:
4
_ = ?
24
4 2 x 2
_ = ________
24 2 x 2 x 2 x 3

18. Test Yourself
Simplify:
4 2 x 2 1 1
_ = ________ = ___ = __
24 2 x 2 x 2 x 3 2 x 3 6

19. To Remember
• Any number over itself = 1
• Any number over 0 is undefined
• Any number over 1 = itself
• Any fraction with 0 in the numerator = 0
• Answers to fractions calculations should be
simplified
• To simplify, factor the numerator and
denominator completely and cross out like terms
on top and bottom.

20. Adding and Subtracting Fractions
• If the denominators are the same, simply add or
subtract the numerators and keep the same
denominator
• For example 1 / 4 + 2 / 4 = (1 + 2) / 4 = 3 / 4
• Remember to simplify your answer if needed (in the
above example, 3 / 4 is already in simplest terms).
• If your answer has a numerator greater than the
denominator, the answer can also be simplified
• For example 2 / 3 + 2 / 3 = 4 / 3 which is the same
as 1 1/3.

21. Adding or Subtracting Fractions
• If the denominators are NOT the same, one or more
of the fractions in the problem will have to be
converted into an equivalent fraction so that all of
the fractions have the same (common) denominator.
• For example:
1 1
_ + _ = ? You can’t simply add numerators,
2 4 since the denominators are
different.
For the new denominator, choose a number that both
old denominators will divide into.

22. Adding Fractions
1 1
_ + _ = ?
2 4
Both 2 and 4 will divide into 4, so choose 4 for the
new denominator. To convert ½ to fourths,
multiply both top and bottom by 2.
1 (2) 1 2 1 3
___ + _ = _ + _ = _
2 (2) 4 4 4 4

23. Adding and Subtracting Fractions
• Another example:
3 2
_ - _ = ?
4 3
4 and 3 can both be divided into 12
Multiply ¾ by 3/3 to convert to 12ths. Multiply 2/3 by
4/4 to convert to 12ths.
3 2 3 (3) 2 (4) 9 8 1
_ - _ = ___ - ___ = _ - _ = _
4 3 4 (3) 3 (4) 12 12 12

24. Test Yourself
2 1
_ + _ = ?
5 2
5 and 2 can both be divided into 10
Multiply 2/5 by 2/2 to convert to 10ths. Multiply
½ by 5/5 to convert to 10ths.
2 (2) 1 (5) 4 5 9
____ + ___ = _ + _ = _
5 (2) 2 (5) 10 10 10

25. To Remember
• When adding or subtracting fractions, if the
denominators are the same, you can simply add or
subtract the numerators and keep the same
denominator.
• If the denominators of the two fractions you are
adding or subtracting are not equal, you must
convert them to fractions with the same common
denominator.
• Find a number that both denominators will divide
into, and use that as the new denominator.

26. Multiplying Fractions
• Multiplying fractions is actually easier than adding
or subtracting them!
• Simply multiply the numerators together, and then
then the denominators, then simplify if needed.
Example:
1 1
_ x _ = ?
2 3
1 1 1 x 1 1
_ x _ = ____ = _
2 3 2 x 3 6

27. Multiplying Fractions
• Another example:
4 1 4 x 1 4 2 x 2 2 x 2 2
_ x _ = ____ = _ = ____ = ___ = _
5 6 5 x 6 30 2 x 15 2 x 15 15

28. Test Yourself
3 1
_ x _ = ?
7 4
3 1 3 x 1 3
_ x _ = ____ = _ (already simplest terms)
7 4 7 x 4 28

29. Dividing Fractions
• To divide two fractions, you take the reciprocal
of the second fraction, then multiply.
• What is a reciprocal?
• You simply “flip” the fraction over (swap
numerator and denominator)
• For example, the reciprocal of 2/3 is 3/2.
• The reciprocal of ¼ is 4/1 or 4.
• The reciprocal of 61 is 1/61 (since 61 = 61/1).

30. Dividing Fractions
• Division example:
1 1 1 8 1 x 8 8 2 x 2 x 2
_ ÷ _ = _ x _ = ___ = _ = _____ =
2 8 2 1 2 x 1 2 2
2 x 2 x 2 4
______ = _ = 4
2 1

31. Dividing Fractions
• Another example:
3 2 3 3 3 x 3 9
_ ÷ _ = _ x _ = ___ = _
5 3 5 2 5 x 2 10

32. Test Yourself
The reciprocal of 1/12 is ?
12/1 or 12
The reciprocal of 7/8 is ?
8/7
To divide two fractions, multiply the first fraction
by the reciprocal of _____?
The second fraction

33. Test Yourself
1 3
_ ÷ _ = ?
17 2
1 3 1 2 1 x 2 2
_ ÷ _ = _ x _ = ____ = _
17 2 17 3 17 x 3 51

34. Remember
• To multiply fractions, multiply the numerators
and the denominators together and simplify the
answer.
• To divide fractions, multiply the first fraction by
the reciprocal of the second fraction.
• To find the reciprocal of a fraction, swap the
numerator and the denominator.

35. Using Fractions in Pharmacy
• Look closely at this drug label
• Note the concentration of the drug highlighted in the red bar:
“ 500mg PE/10 ml”. The concentration is expressed as a
fraction.
• Underneath that you will see another fraction ---
“50mgPE/ml”. This fraction is equivalent to the first and is
the simplified version of the first fraction.
500 5 x 5 x 5 x 2 x 2 5 x 5 x 5 x 2 x 2 5 x 5 x 2
___ = ___________ = __________ = ______ = 50
10 5 x 2 5 x 2 1

36. Next steps
• Do the homework problems and check your
answers using the back of the textbook.
• Complete your discussion board assignment.
Also post any observations or questions you may
have about the powerpoint and the homework.
• Review this powerpoint as well as the homework
problems before taking the weekly quiz.