CHAPTER
1
Review of Basic Math
Fundamentals
Payal Agarwal, PhD
Learning Objectives
After successful completion of this chapter, the student should be able to:
1.Recognize Arabic and Roman numerals
2.Explain and differentiate between common and decimal fractions
3.Solve problems based on ratio and proportion
4.Describe significant figures and explain the concept’s importance in pharmacy
Key Terms
Arabic numerals
Common fraction
Decimal fraction
Proportion
Ratio
Roman numerals
1.1 Introduction to Arabic and Roman Numerals
T
© Stockbyte/Thinkstock
he most common form of numbers that we use today is Arabic numerals. The origin
of these numbers is not very well known. The use of Roman numerals can be seen
in some older prescriptions. In our current system of prescription writing, use of Roman
numerals is minimal, but it can still be seen occasionally on current prescriptions. Roman
numerals are used either to specify the quantity of the ingredient in the apothecary system
or units of dosage to be dispensed. They are also used to represent different schedules of
controlled substances (for example, Schedule I, II, III, IV, and V).
A mathematical algebraic number (currently described as an Arabic number) in the
Roman system of numbers is designated by a letter, as given in Table 1.1. This table
shows various stem numbers that are used in the Roman system of number writing. Other
numbers in the Roman system are generated from these stem numbers; for example, 15 is
expressed as XV (10 1 5 5 15).
1
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2 Chapter 1 / Review of Basic Math Fundamentals
Table 1.1 Roman system of numbers
Arabic Number
Roman Designation
1
I or i
5
V or v
10
X or x
50
L
100
C
500
D
1,000
M
The following section demonstrates how to read Roman numerals.
1.1.1 How to Read Roman Numerals
Rule 1: Addition
When a lower number is right after a higher number, add all the numbers together:
XII 5 10 1 1 1 1 5 12
Similarly, VI 5 5 1 1 5 6.
Rule 2: Subtraction
When a lower number precedes a higher number, the lower number is subtracted from the
higher number:
IV 5 1 and 5. Because 1 , 5 and 1 precedes 5, 1 is subtracted from 5. So, IV 5 4;
similarly, IX 5 9.
Rule 3: Smaller number between two larger numbers
XIX represents 19; X 5 10, I 5 1, and X 5 10. Because I precedes X, it is calculated as
10 2 1 5 9 and 10 1 9 5 19.
I t can be easily misunderstood as 21, which is 11 1 10 5 21. However, that is incorrect.
Twenty-one in Roman form is expressed as XXI.
Rule 4: Avoid the repetition of more than three occurrences of the same letter
For example, 7 is written as VII, not as IIIIIII.
Rule 5: Use the largest value numeral
In accordance with Rule 4, when required, the largest value numeral should be used. For
example, 99 is written as XCIX, not as XXXXXXXXXIX.
Rule 6: Power of 10
The smaller number must be a power of 10, and cannot precede a number more than
10 times its value. For example, 99 cannot be expressed as IC 5 100 2 1 5 99. The correct way is XCIX. Similarly, 49 is correctly expressed as 40 1 9 5 XLIX and not as IL.
Rule 7: Use only one preceding smaller number
There cannot be more than one small number in front of a larger number. For example,
IIX is an invalid Roman numeral. It should be VIII.
Rule 8: Using a bar
A bar placed on top of a letter increases the numeral’s value 1,000 times (XII 5 12, XII 5
12,000).
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1.2 / Common and Decimal Fractions 3
Test Yourself 1.1
1.Express the following numerals in Arabic numbers:
a. XXIV
b.MDXLIII
c. XCII
d.LXXI
e. MMXX
2.Express the following numbers in Roman numerals:
a. 35
b.407
c. 198
d.1,020
e. 2,487
1.2 Common and Decimal Fractions
Common fractions (CF) are proportions of whole numbers. These are expressed as 4/3,
1/2, 3/7, and so on. In contrast, a decimal fraction (DF) is a fraction whose denominator
is 10n, and n ≥ 1. A decimal fraction is expressed in terms of decimals and not as a CF;
for example, 4/100 is expressed decimally as 0.04 and 55/10 as 5.5. Rules for how to perform mathematical operations, such as addition, subtraction, multiplication, and division,
in common fractions along with the conversion rules are demonstrated in Table 1.2.
Solved Examples
1.Convert the following common fractions to decimal fractions:
a. 2/4
2/4 5 1/2 5 0.5
b.1/10
1/10 5 0.1
c. 24/30
24/30 5 4/5 5 0.8
d.6/12
6/12 5 1/2 5 0.5
e. 18/5
18/5 5 3.6
2.Convert the following decimal fractions to the lowest common fractions:
a. 0.234
0.234 5 234/1000 5 117/500
b.62.5
62.5 5 625/10 5 125/2
c. 10.5
10.5 5 105/10 5 21/2
d.25.2
25.2 5 252/10 5 126/5
e. 0.001
0.001 5 1/1000
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4 Chapter 1 / Review of Basic Math Fundamentals
Table 1.2 Rules for performing mathematical operations with common fractions and decimal fractions
Rule
Examples
Conversion
Common fraction to decimal fraction
Divide the denominator into the
numerator.
20
2
5 5 0.5
40
4
1
5 0.04
25
Decimal fraction to common fraction
Express the decimal as a ratio and
reduce it to the lowest possible common
fraction.
257
1000
15
3
1.5 5
5
10
2
0.257 5
Addition
Fractions with the same denominator
Simply add the numerators and divide
the result by the denominator.
Reduce the fraction to its simplest form.
1
5
3
1 1
4
4
4
11 5 1 3
9
5
4
4
9/4 5 Lowest fraction
Fractions with different denominators
Find the least common multiple (LCM)
for the denominator.
Convert the individual fractions to reflect
the LCM denominator.
Add the numerators.
Reduce the fraction to its simplest form.
2
3
7
1 1
6
1
2
LCM 5 6
2/6 5 2/6
3/1 5 18/6
7/2 5 21/6
2 1 18 1 21 41
5
6
6
41/6 5 Lowest fraction
Subtraction
Fractions with the same denominator
Simply subtract the numerators and
divide the result by the denominator.
Reduce the fraction to its simplest form.
25/7 2 4/7
25 2 4
21
5
7
7
21 3
5 5 Lowest fraction
7
1
Fractions with different denominators
Find the LCM for the denominator.
Convert the individual fractions to reflect
the LCM denominator.
Subtract the numerators.
Reduce the fraction to its simplest form.
3
2
2
6
1
LCM 5 6
3/1 5 18/6
2/6 5 2/6
2
16
8
18
5
2 5
6
6
6
3
8/3 5 Lowest fraction
Multiplication
Multiply the numerators.
Multiply the denominators.
Write the new fraction.
Reduce it to its simplest form.
4
2
8
3 5
5
30
6
8
4
5
30
15
4/15 5 Lowest fraction
Division
Invert the divisor.
Apply the rules for multiplication.
9
3
4
4
2
Divisor 5 3/4
Invert the divisor 5 4/3
9
4
36
3 5
2
3
6
36/6 5 6/1 5 Lowest fraction
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1.2 / Common and Decimal Fractions 5
3.Perform the necessary mathematical operations and report the final answer.
a. 14/5 1 6/3 1 10/9
Find the LCM for the denominator: 45.
Convert each fraction to have a common denominator:
14 3 9 126
14
5
5
5
539
45
6 3 15
6
90
5
5
3
3 3 15
45
10 3 5
10
50
5
5
9
935
45
Perform the operation:
126
90
50
266
1
5
1
45
45
45
45
The lowest fraction is 266/45.
b.2/3 2 1/3
The denominators are the same, so
2 21 1
5
3
3
c. 14/5 2 4/2
This has different denominators.
Find the LCM for the denominator: 10.
Convert each fraction to have a common denominator:
14 3 2
14
28
5
5
5
532
10
435
4
20
5
5
2
235
10
Perform the operation:
28
20
8
2
5
10
10
10
Reduce to the lowest fraction:
8
4
5
10
5
Answer 5 4/5
d.6/5 3 5/2
635
30
5
532
10
Reduce to the lowest fraction:
30
3
5
10
1
Answer 5 3/1
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6 Chapter 1 / Review of Basic Math Fundamentals
e. 15/1 ÷ 3/5
15 3 5
75
5
133
3
Reduce to the lowest fraction:
75
25
5
3
1
Answer 5 25/1
Test Yourself 1.2
Express the results of the following problems in common fractions and decimal fractions:
1.
4
2
1 11
2
9
2.
2
1
2
8
11
3.
6
1
2
2
2
4.
3
1
3
5
8
1.3 Ratio and Proportion
Ratio can be defined as the relationship of two or more things in a quantitative manner.
For example, Jen has $1,000 to spend on a night out, whereas Emily has $200. Therefore,
we can say that Jen has 5 times more dollars than Emily to spend for the night.
In terms of ratio, 1000 dollars/200 dollars 5 5/1 5 5 to 1 or 5:1.
A ratio can be expressed in different ways, for example, a / b, a:b, or a to b, where a
and b can be whole numbers, decimals, fractions, or a combination of any of them.
When two or more ratios can be expressed with an equals sign, then the two ratios are
said to be in proportion. For example, a:b 5 c:d, where a, b, c, and d can be whole numbers, decimals, fractions, or a combination of any of them.
As another example, a / b 5 c / d, where a and d are extreme values and b and c are
mean values. In any given proportion, when two ratios are equal, the product of extreme
values is equal to the product of mean values, which means if a / b 5 c / d, then a 3 d 5
b 3 c.
Therefore, using this rule, an unknown value can be determined if any of the three
values are known in a given proportion.
Rules to Remember About Numerators and Denominators
■■
■■
■■
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Numerators should have the same units.
Denominators should be of same units.
Three out of four variables should be known.
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1.3 / Ratio and Proportion 7
1.3.1Setting Up the Right Ratio and Proportion
If the cost of 10 prescription bottles for Drug A is $25, what would be the cost of 6 prescription bottles for the same drug?
To use a ratio, we have to establish a relationship between prescription bottles and
dollars. As mentioned in the problem statement:
10 bottles 5 25 dollars
6 bottles 5 ? dollars
Set the ratio:
10 bottles
6 bottles
5
25 dollars
x dollars
According to the rule of proportion, 10 3 x 5 25 3 6.
x 5 150 / 10 5 15 dollars
Ratio and proportion have a wide range of applications. You will use them often.
1.3.2 Dimensional Analysis
Dimensional analysis, also known as unit factor method, is another way to solve problems. This system is very useful when one unit of measurement has to be converted into
a different unit of measurement. This method can also be easily used in place of ratio and
proportion to solve problems. Dimensional analysis is based on the fact that any number
or unit can be multiplied by one without changing its value. Use the following steps to
perform dimensional analysis:
1. Write the desired unit on the right side of the page and line up all the available data with
the units on the left side of the page.
2. Include the conversions that pertain to the units given in the data.
3. Invert the dimensions as needed.
4. Cross out the units that appear in the numerator and denominator of the dimensions,
leaving only the desired unit.
5. Check: If all the other units are crossed out, leaving the desired unit, it means the problem has been set up with correct dimensions.
6. Perform the calculation.
Solved Examples
4.Convert 2 lb to g.
1.Write the desired unit on the right side and line up all the available data with the
units on the left side.
g
2 lb
2.and 3. Include the conversions that pertain to the units given in the data, and invert if
required.
2 lb
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1 kg
2.2 lb
1,000 g
1 kg
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8 Chapter 1 / Review of Basic Math Fundamentals
4.Cross out the units that appear in the numerator and denominator of the dimensions,
leaving only the desired unit.
1 kg
1,000 g
2.2 lb
1 kg
2 lb
5.Check: If all the other units are crossed out, leaving the desired unit, it means the
problem has been set up with correct dimensions.
Yes, every other unit is crossed out, leaving g.
6.Perform the calculation.
2 3 1 3 1000
5 909.1g
2.2
5.Convert 1 week into seconds.
1.Write the desired unit on the right side and line up all the available data with the
units on the left side.
seconds
1 week
2.and 3. Include the conversions that pertain to the units given in the data and invert if
required.
1 week
7 days
1 week
24 hrs
1 day
60 min
1 hr
60 sec
1 min
4.Cross out the units that appear in the numerator and denominator of the dimensions,
leaving only the desired unit.
1 week
7 days
24 hrs
60 min
60 sec
1 week
1 day
1 hr
1 min
5.Check: If all the other units are crossed out, leaving the desired unit, it means the
problem has been set up with correct dimensions.
Yes, every other unit is crossed out, leaving seconds.
6.Perform the calculation.
7 3 24 3 60 3 60
5 604,800 seconds
1
6.Convert 2.6 meters to centimeters.
2.6 m
100 cm
1m
5 260 cm
Or,
2.6 m 3
100 cm
5 260 cm.
1 m
Or, 2.6 m 5 260 cm.
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1.3 / Ratio and Proportion 9
7.Convert 2.6 km to mm.
2.6 km
1,000 m
100 cm
10 mm
1 km
1m
1 cm
Or,
2.6 km 3
1000 m 100 cm 10 mm 3
3
5 2,600,000 mm.
1 km
1m 1 cm Or, 2.6 km 5 2,600,000 mm.
8.Convert 110 liters to milliliters.
1,000 mL
110 L
1L
110 3 1000 mL
5 110,000 mL
1
Or, 110 L 5 110,000 mL.
9.Determine the ratio of the following:
a. 8 to 24
8 to 24 5 8/24 5 1/3, which means 8 is one third of 24.
b.21 to 7
21 to 7 5 21/7 5 3/1, which means 21 is 3 times 7.
10. Find the unknown value in the given proportion:
a. 2/3 5 x/10
a/b 5 c/d
a3d5c3b
2 3 10 5 x 3 3
20 5 3 3 x
Or, x 5 20/3 5 6.66.
b.5/25 5 10/x
a/b 5 c/d
a3d5c3b
5 3 x 5 25 3 10
5 3 x 5 250
Or, x 5 250/5 5 50.
11. Drug A is available in both generic and brand forms. The generic version costs three
fourths of the branded product. If the price of the generic form is $16, calculate the price
of the branded product.
Generic product 5 16 dollars
Generic product 5 3/4 of branded product
Let the cost of branded product 5 $x
Therefore, cost of generic product 5 3/4 of x
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10 Chapter 1 / Review of Basic Math Fundamentals
16 dollars 5 3/4 of x
16
3/4
5
x
1
x5
16
3/4
x 5 21.33 dollars
Test Yourself 1.3
1.If 1 tablet of acetaminophen contains 250 mg of the active ingredient, how many tablets
can be prepared from 1,500 mg of the drug?
2.If 2.6 g of dye is required to prepare 3 liters of a solution, what quantity of the dye will
be required for preparing 1 liter of the same solution?
3.A vial of drug X contains 30 mg of drug in 1 mL of the solution. In order to dispense
15 mg of the drug, what volume of the solution will be required?
4.A patient purchases a prescription drug bottle of 200 tablets for $65. What would be the
cost for 70 tablets?
1.4 Significant Figures
The number of significant figures in a result is simply the number of figures that are
known with some degree of reliability.
1.4.1 Rules for Deciding the Number of Significant Figures in a Measured Quantity
Table 1.3 shows rules along with examples to determine the number of significant figures
in any given number. To express and handle numbers that are very large or very small, exponential notation can be used. The powers of 10 are used to express numbers exponentially.
For example, a very large number such as 1,004,567,000 can be represented as 1.0 3 109,
14,600 can be represented as 1.46 3 104, and 23,506,001 as 2.35 3 107. Similarly, small
numbers such as 0.0045 can be written as 4.5 3 1023 or 0.0000611 as 6.11 3 1025.
Table 1.3 Rules for deciding the number of significant figures in a measured quantity
Rule
Examples
All nonzero digits are significant.
a. 1.234 g has 4 significant figures.
b. 1.2 g has 2 significant figures.
Any zeroes between nonzero digits are significant.
a. 1,002 kg has 4 significant figures.
b. 3.07 mL has 3 significant figures.
Leading zeros to the left of the first nonzero digits are not
significant; such zeroes indicate the position of the decimal
point.
a. 0.0043 has 2 significant figures.
b. 0.01 has 1 significant figure.
Trailing zeroes that are also to the right of a decimal point in a
number are significant.
a. 0.0230 mL has 3 significant figures.
b. 0.20 g has 2 significant figures.
When a number ends in zeroes that are not to the right of a
decimal point, the zeroes are not necessarily significant.
a. 230 miles may be 2 or 3 significant figures.
b. 21,400 calories may be 3, 4, or 5 significant figures.
To be explicit about the number of significant figures in this
situation, it is a good practice to express the number in terms of
scientific notation.
For example:
a. 230 5 23 3 101 5 2 significant figures
b. 21,400 5 214 3 102 5 3 significant figures
c. 21,400 5 2.14 3 104 5 3 significant figures
d. 2.140 3 104 5 4 significant figures
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1.4 / Significant Figures 11
Table 1.4 Rules for rounding off numbers
Digit to Be Dropped
Rule
Example
Digit to be dropped . 5
The last retained digit is increased
by 1.
39.6 is rounded to 40.
Digit to be dropped , 5
The last retained digit is not
changed.
39.4 is rounded to 39.
Digit to be dropped 5 5
If the digit following 5 is not zero, the
last retained digit is increased by 1.
39.351 is rounded to 39.4.
12.2502 is rounded to 12.3.
If all the digits following 5 are zero,
the last retained digit is unchanged.
39.500 is rounded to 39.
40.125 is rounded to 40.12.
Table 1.5 Rules for performing mathematical operations and reporting the
end value with the correct number of significant figures
Addition and Subtraction
Report the final value with the same
number of decimal places as the
measurement with the least number
of decimal places.
104.3 (1 decimal place) 1 23.643 (3 decimal
places)
Calculator answer 5 127.943
Correct answer 5 127.9 (round to 1 decimal place)
Multiplication and Division
When two or more numbers are
approximate numbers
Report the final value with the
same number of significant figures
as in the component with the least
number of significant figures.
3.0 (2 significant figures) 3 12.60 (4 significant
figures)
Calculator answer 5 37.8000
Correct answer 5 38 (2 significant figures)
When one of the numbers is an
absolute number
Report the final value with the same
number of significant figures as in
the approximate number.
21 (absolute number, with 2 significant figures)
3 3.542 (approximate number with 4 significant
figures)
Calculator answer 5 74.382
Correct answer 5 74.38 (4 significant figures)
1.4.2 Rules for Rounding Off Numbers
Table 1.4 shows rules to be used for rounding off numbers.
1.4.3 Rules for Mathematical Operations
In carrying out calculations, the general rule is that the accuracy of a calculated result is
limited by the least accurate measurement involved in the calculation. This is explained
with examples in Table 1.5.
Solved Examples
12. Determine the number of significant figures in the following:
a. 2.567
2.567 5 4
b.7,002
7,002 5 4
c. 6,400
6,400 5 2, 3, or 4
d.92.50
92.50 5 4
e. 0.211
0.211 5 3
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12 Chapter 1 / Review of Basic Math Fundamentals
f. 0.0014
0.0014 5 2
g.1.0
1.0 5 2
h.0.01 3 102
0.01 3 102 5 1
i. 0.001
0.001 5 1
13. Give the exact numerical result for the following, and then express it with the correct
number of significant figures:
a. 47.76 1 1.507 1 103.2
b.25 2 6.23 1 3.19
c. 3.05 3 5.0
d.400.0 / 3.2002
e. (2.0)3
f. 12 1 0.5
g.38 1 2.125
h.48 3 25
i. 12 1 111.5
j. 10.01 1 4.0552
Solutions
Problem
Calculator Answer
Answer with the Correct
Number of Significant Figures
47.76 1 1.507 1 103.2
152.467
152.5
25 2 6.23 1 3.19
21.96
22
3.05 3 5.0
15.25
15
400.0 / 3.2002
124.992188
125.0
(2.0)3
8
8.0
12 1 0.5
12.5
12
38 1 2.125
40.125
40
48 3 25
1,200
12 3 102
12 1 111.5
123.5
123
10.01 1 4.0552
14.0652
14.07
Test Yourself 1.4
1.Determine the number of significant figures in the following:
a. 2.366
b.1.002
c. 2.00
d.3.45
e. 0.15 3 103
f. 0.0050
g.890
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1.5 / Application of Math Fundamentals to Pharmaceutical Calculations 13
2.Give the exact numerical result for the following, and then express it with the correct
number of significant figures:
a. 23.04 1 11 1 0.002 5
b.527.15 2 2.614 5
c. 34 3 2 5
d.12 2 3.03 1 0.19 5
e. 3.05 3 5.0 5
f. 400.0 / 3.2002 5
g.2.0132 3 198 5
h.(5.0)3 5
i. 0.326 3 (72 2 12.4) 5
j. Find the average of 0.23, 0.260, 0.1155, 1.242, and 2.1.
1.5 Application of Math Fundamentals to
Pharmaceutical Calculations
As mentioned earlier in this chapter, Roman numerals were used in ancient prescription
writing, and their use is still evident in many current prescriptions. This section will provide some examples related to compounding and dispensing of pharmaceutical products
covering the concepts discussed in previous sections of this chapter.
Use the information you have learned throughout this chapter to work on the following prescriptions.
Solved Examples
14. Interpret the correct quantities of different ingredients in the following prescriptions:
a.
B. Pajamo, M.D.
4701 Main St.
Baltimore, MD 12345
Name John Smith
DOB 6/7/69
Address 51 Broadway Blvd
Date 1/25/14
Acetaminophen
65 mg
Lactose q.s. ad
300 mg
Disp: Capsule XXX
Sig: take 1 cap po bid
Refills 0
B. Pajamo M.D.
The formula is given for one capsule; dispense XXX means dispense 30 such capsules. Also calculate the amount of lactose required for 30 capsules.
Quantity of acetaminophen required for 30 capsules: 65 3 30 5 1,950 mg
Lactose q.s. ad means the quantity of lactose sufficient to make the total weight of
the individual capsule equal to 300 mg. (Refer to Chapter 2.)
Amount of lactose in one capsule 5 300 mg 2 65 mg5 235 mg.
For 30 capsules 5 235 3 30 5 7,050 mg.
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14 Chapter 1 / Review of Basic Math Fundamentals
b.
B. Pajamo, M.D.
4701 Main St.
Baltimore, MD 12345
Name John Smith
DOB 6/7/69
Address 51 Broadway Blvd
Date 4/30/14
Zinc oxide
parts vi
Camphor
parts ii
White petrolatum
parts liii
Disp: ounces xv
Sig: Apply on the affected
area as directed bid
B. Pajamo M.D.
Refills 0
Zinc oxide: 6 parts
Camphor: 2 parts
White petrolatum: 53 parts
Dispense: 15 ounces
1 ounce 5 30 g (Refer to Chapter 3.)
So, 15 ounces 5 450 g.
Use the concepts of ratio and proportion.
Add the total parts of the individual ingredients in the prescription.
6 parts 1 2 parts 1 53 parts 5 61 parts
To prepare 61 g of ointment:
6 g of zinc oxide
2 g of camphor
53 g of white petrolatum
To prepare 450 g of ointment:
6 g of zinc oxide
x g of zinc oxide
5
61 g of ointment
450 g of ointment
x 5 44.26 g of zinc oxide
2 g of camphor
x g of camphor
5
61 g of ointment
450 g of ointment
x 5 14.75 g of camphor
53 g of white petrolatum
x g of white petrolatum
5
61 g of ointment
450 g of ointment
x 5 391 g of white petrolatum
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1.5 / Application of Math Fundamentals to Pharmaceutical Calculations 15
15. Calculate the quantity of drug X in 30 mL of the following prescribed solution:
B. Pajamo, M.D.
4701 Main St.
Baltimore, MD 12345
Name Laya Griffin
DOB 8/20/88
Address 51 Broadway Blvd
Date 6/14/14
Drug X
2.5 g
Purified water qs
100 mL
Disp: 30 mL
Sig: Take 2 tsp qid for 5 days
Refills 0
B. Pajamo M.D.
2.5 g of drug is required to make 100 mL of solution. For 30 mL of solution, set the
ratio and use the proportion:
x g of drug X
2.5 g of drug X
5
100 mL of solution
30 mL of solution
0.75 g of drug X is present in 30 mL of the solution.
Answers to Test Yourself
Test Yourself 1.1
1.
a. 24
b.1,543
c. 92
d.71
e. 2,020
2.
a. XXXV
b.CDVII
c. CXCVIII
d.MXX
e. MMCDLXXXVII
Test Yourself 1.2
1.29/9, 3.2
2.7/44, 0.159
3.5/2, 2.5
4.3/40, 0.075
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16 Chapter 1 / Review of Basic Math Fundamentals
Test Yourself 1.3
1.6
2.0.866 g
3.0.5 mL
4.$22.75
Test Yourself 1.4
1.
a. 4
b.4
c. 3
d.3
e. 2
f. 2
g.2 or 3
2.
a. 34.042, 34
b.524.536, 524.54
c. 68, 68
d.9.16, 9
e. 15.25, 15
f. 124.992188, 125.0
g.398.6136, 398.61
h.125, 1.3 3 102
i. 19.4296, 19.4
j. 0.7895, 0.78950
References
1. Ansel CH. Pharmaceutical Calculations. 13th ed. Philadelphia, PA: Lippincott Williams & Wilkins; 2009.
2. Khan MA, Reddy IK. Pharmaceutical and Clinical Calculations. 2nd ed. New York, NY: CRC Press;
2000.
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