Transcript Intro_Chapter_6

Calculations
Chapter 6
Numbers

Knowing how to work with numbers is essential to the
proper handling of drugs and preparation of
prescriptions.

The amount of a drug in its manufactured or prescribed
form is always stated numerically (with numbers).
Roman Numerals

The Roman numerals are letters that represent
numbers.

They can be capital or lower case letters. (see handout)
ss = ½
I or i = 1
V or v = 5
X or x = 10
L = 50
C = 100
D = 500
M = 1000
Roman Numerals
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Two Rules:
Rule 1: When the second of the two letters has a value
equal to or smaller than the first, their values are added
together.
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xx = 20
DC = 600
lxvi = 66
10 + 10 = 20
500 + 100 = 600
50 + 10 + 5 + 1 = 66
Roman Numerals

Two Rules:
Rule 2: When the second of the two letters has a value
greater than the first, the value is subtracted from the
larger value.



iv = 4
xxxix = 39
xc = 90
1 subtracted from 5 = 4
30 + ( 1 – 10 ) = 39
10 subtracted from 100 = 90
Common Roman Numerals on
RX’s
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i=1
ii = 2
V=5
X = 10
C = 100
Fractions
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A fraction is a numerical representative indicating that
there is part of a whole.

Fractions have numerators and denominators.

The denominator is the bottom number of the fraction.
It tells us how many pieces the whole is divided into.

The numerator is the top number of the fraction. It
tells us how many pieces exist.
Fractions
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2
─
5
Example:
Numerator
we have 2 parts
Denominator
out of 5 total parts
Converting Fractions to Decimals

Fractions can be converted to decimals by dividing.
2
─
5
=
2 ÷ 5 = 0.4
Decimals

A decimal point is used to represent an amount
less than one (fraction).
0.1
0.01
0.001
0.0001
=
=
=
=
one tenth
one hundredth
one thousandth
one ten-thousandth
Reciprocals

Reciprocals are two different fractions that equal 1 when
multiplied together.
The reciprocal of
2
─
3
is
3
─
2
Reciprocals

When multiplied together, reciprocals equal 1
2
─
3
x
x
3
─
2
=
=
6
─
6
or 1
Adding & Subtracting Fractions

In order to add & subtract fractions, the fraction must
have the same common denominator.
1
─
4
2
─
5
+
1
─
4
-
1
─
5
=
2
─
4
=
1
─
5
or
1
─
2
Multiplying Fractions

Multiply each numerator, then multiply each denominator
2
─
3
x
24
─
1
=
48
─
3
or
16
Dividing Fractions

To divide a fraction, find the reciprocal of the fraction
(or invert the fraction), then multiply.

Example: 1/3 ÷ 1/2 =
1
─
3
x
2
─
1
=
2
─
3
Working with Decimals

The key to adding and subtracting with decimals is to
line up the decimal points, then work the problem as
you would a whole number equation.
45.6
+ 3.2
48.8
45.6
- 3.2
42.4
Multiplying with Decimals

To multiply with decimals, first multiply as if using whole
numbers. Count the total number of decimal places in the
equation. Insert the decimal point the total number of decimal
places, starting from the right.
47.2 (1 decimal place)
x 5.5 (1 decimal place)
2360
2360
25960
259.60 (2 decimal places)
Percentages

Percentages are fractions in which the denominator is
always 100.
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Percentages are expressed (using the % symbol) and
mean parts out of 100 units.
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Example:
25%
=
25
──
100
1
or
─
4
Basic Percentages
50% =
50
──
100
2% =
2
──
100
or
1
─
2
2% represents 2 parts
out of 100 parts
Significant Figures

4 Rules for significant figures:
1.
Digits other than zero are always significant. (1,2,3,4)
2.
Final zeros after a decimal point are always significant.
(1.20)
3.
Zeros between two other significant digits are always
significant. (1.05)
4.
Zeros used only to space the decimal are never significant.
(0.1)
Measurements

There are different systems of measurement used in
pharmacy: metric, English, apothecary & avoirdupois.

The major system of weights & measures in medicine is
the metric system.
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The different measurement units are related by
measures of ten.

Metric measures apply to both liquids and solids.
Liquids

Liquids (including lotions) are measures by metric
volume. The most common being liters (L) or milliliters
(ml).
Unit
liter
milliliter
Symbol
L
ml
Liquid Conversion
1L = 1000 ml
1ml = 0.001 L
**cc’s (cubic centimeters) are often used in place of ml
Solids

Solids (pills, granules, ointments) are measured by weight.
Units
Symbol
kilogram
kg
gram
g
milligrams mg
microgram mcg
Solid Conversion_
1kg = 1000 g
1g = 1000 mg =0.001 kg
1mg = 1000 mcg =0.001 g
1mcg
=0.001 mg
Ounces, Pounds & Grains
Units
Symbol
Conversion
pound
ounce
grain
lb
oz
gr
1 lb = 16 oz.
1 oz = 437.5 gr
1 gr = 64.8 mg
**grains are often rounded up to 65mg or down to 60mg in
the pharmacy practice.
Apothecary Measurements
Unit
gallon
quart
pint
ounce
Symbol
gal
qt
pt
fl oz
Conversion
1 gal = 4 qt
1 qt = 2 pt
1 pt = 16 fl oz
1 oz = 30 ml
Household Measures

Teaspoons, tablespoons & cups are common household
measures.
Unit
Symbol
15 drops
gtts
Teaspoon
tsp
Tablespoon
tbsp
Cup
cup
Conversion
15gtts = 1ml
1 tsp = 5ml
1 tbsp = 15 ml = 3 tsp
1 cup = 8 oz
Conversions
1L
=
1 pt =
1 fl oz =
1 kg =
1 lb =
1 oz =
1g =
1gr =
33.8 fl oz
473.167 ml (473 or 480ml)
29.57 ml
(30ml)
2.2 lbs
453.59 g
(454g)
28.35 g
(30g)
15.43 gr
(15gr)
64.8 mg
(65mg)
Dose Measurements
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Not all doses doctor’s write prescriptions for are
available from the manufacturer…so what do
you do?
Tablets can be doubled up: for example, the RX is
written for 250mg, and only 125mg is made, the
result is the dose taken by the patient is 2 tablets
together to equal 250mg.
 A tablet can also be cut in half, or even a quarter to
provide the adequate dose for the patient.
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Dose Measurements
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Example 1:
Rx: Flagyl 125mg po bid x 7 days
On hand is 500mg tablets, how would you
accommodate the patients needs?
 500mg/125mg = 4
 Take ¼ tablet (=125mg) by mouth two times a day
for 7 days.
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Dose Measurements
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How many tablets would you dispense to last
the patient the duration of the treatment?
¼ + ¼ = 2/4 or ½ tablet daily
½ X 7 days = 3.5 **always round up on quantity
to dispense, ***not dose
4 tablets would be dispensed; and that would
equal a 7 day supply.
Dose Measurements
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Example 2:
Rx: Amoxicillin 500mg po tid X 10 days
On hand Amox 250mg/5ml
 250mg = 5ml
 Take 2 teaspoonfuls (=500mg) by mouth three times
a day for 10 days
 What is the quantity you will dispense to cover the
duration of the therapy?
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Dose Measurements
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2 tsp = 10 ml / dose
10ml X 3 = 30ml / day
30 ml x 10 days = 300 ml / 10 days
Equations & Variables
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In pharmacy calculations, there is often an unknown
variable that needs to be determined.

We solve for the unknown value by setting up
mathematical equations.

In equations, this is usually represented by the letter
“x”.
Equations & Variables

Example: How many ounces is equal to 120ml?
total ml
x (oz) = ────────────
ml to oz conversion
120ml
x (oz) = ────────
30ml
x (oz) = 4
Equations & Variables

Example: Calculate the quantity for an Rx with a sig of
1 tid x 7.
x (qty) = (1 cap per dose) x (3 times a day) x (7 days)
x (qty) = 1 x 3 x 7
x (qty) = 21
Dose Equation
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D/A X Q = dose quantity
D = desired
A = Available on hand
Q = Quantity (dose) on hand
Dose Equation
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Example:
A prescription calls for 200mg of a drug that
you have in a 10mg/15ml concentration. How
many ml of the liquid do you need?
Desired = 200mg
Available = 10mg
Quantity (dose) on hand = 15ml
Dose Equation
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200mg / 10mg X 15ml
200 / 10 = 20 (the mg are canceled)
20 X 15ml = 300 ml
Ratio & Proportion

Understanding ratios & proportions is important for
pharmacy technicians so they can perform the
calculations necessary for the job.

Ratio: A ratio states a relationship between two
quantities.
a
It can be stated as: a : b
or
─
b
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Ratio & Proportion

Proportion: Two equal ratios form a proportion.
a
c
─
=
─
b
d
1
─
2

=
2
─
4
1/2 & 2/4 are equivalent ratios, therefore the equation
is a proportion.
Ratio & Proportions

Proportion Example: If one person has 1 bottle
containing 5 tablets, and another has 3 bottles containing
a total of 15 tablets, it is still an equivalent ratio. (5:1)
5
─ =
1
15
─
3
It is not the quantity, but the
relationship between the
quantity that we are looking for.
Solving Ratio & Proportion Equations
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There are 3 conditions for using ratio & proportion
equations:
1.
Three of the four values must be known.
2.
The numerators must have the same units.
3.
The denominators must have the same units.
Solving Ratio & Proportion Equations
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Example: You receive an Rx for Ktabs 1 bid x 30. How many
tablets are needed to fill the Rx?
Define the unknown variable:
Establish the known ratio:
Establish the unknown ratio:
x tabs
─────
30 days
=
2 tabs
─────
1 day
We need 60 tablets to fill the Rx.
x = total tablets needed.
2 tablets per day
x tablets/30 days
= x = 60
Percents & Solutions

Percents are used to indicate the amount or
concentration of something in a solution.

Concentrations are indicated in terms of weight to
volume or volume to volume.

Weight to volume = grams per 100 milliliters ( g/ml )

Volume to volume = milliliters per 100 milliliters (ml/ml)
Percents & Solutions

Example: You have a 70% dextrose solution. How
many grams in 20mls of solution?
70g
─ =
100ml
xg
─
=
20ml
1400 = 100x(g)
= 14g
Calculations for Business
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Terms:

Usual & customary price (U&C) is the lowest price for a
customer paying cash on that day for that drug.

Average wholesale price (AWP) is the average wholesale
price for that drug.
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Professional fee or fee for service: the charge for service.
Calculations for Business
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Prescription prices are determined by a variety of
formulas. The easiest is AWP + professional fee = the
selling price.
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To calculate the retail price, you must first calculate the
AWP for the specific quantity of tablets then apply the
appropriate professional fee.
Calculations for Business
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Example: What is the retail price for #30 glyburide 5mg
tablets (AWP 480.15/M) and a professional fee of $4.00?
1.
Calculate AWP per tablet: 480.15/1000 = .48 per tab.
2.
Multiply # of tablets by price per tablet = 30 x .48 =
14.40.
3.
Add professional fee = 14.40 + 4.00 = 18.40 retail price.
Discounts

Pharmacies sometimes give a discount to certain groups
of patients (such as senior citizens).

To begin, calculate the retail price of a prescription as
we did on the previous slide, then we calculate the
discount.
Discounts

Example: The glyburide Rx is for a senior citizen, who
qualifies for a 10% discount. (retail was 18.40).
18.40 x .10 = 1.84
18.40 – 1.84 = 16.56
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The customer would pay 16.56 as the discounted price.
Practice
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What would a customer pay for Verapamil SR #30
(AWP 135.85/C) with a $5.00 professional fee and a
10% senior discount?
AWP per tab = 135.85/100 = 1.36
Cost per 30 tablet = 1.36 x 30 tabs = 40.80
Professional fee = 40.80 + 5.00 = 45.80
10 % Discount = 45.80 x .10 = 4.58
Retail price = 45.80 – 4.58 = 41.22
Answer: $ 41.22
Gross Profit & Net Profit

Gross profit is the difference between the selling price
and the acquisition cost.

To calculate gross profit, there is no consideration for
any of the other expenses associated with filling a
prescription.

In its simplest form, cash prescriptions, it is the
difference between the selling price and the cost paid
for the item
Gross Profit

Gross profit = selling price – acquisition cost

Example: An Rx for Amoxil 250mg # 30 has a U & C
of 8.49. The acquisition cost is 2.02. What is the gross
profit?
GP = 8.49 – 2.02
GP = 6.47
Answer: $ 6.47
Net Profit

The net profit is the difference between the selling price
and the sum total of all the costs associated with filling
the prescription.
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Costs associated with filling an Rx:
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Cost of the medication
Cost of the vials, lids, labels, caution labels
Cost of labor: pharmacy tech, pharmacist, clerk, etc.
Costs of operations: rent, utilities
These are often grouped together and called a dispensing
fee.
Net Profit



Net profit = selling price – acquisition cost – dispensing fee
or
Net profit = Gross profit – dispensing fee
Example: Amoxil 250mg #30 (U&C 8.49) with an
acquisition cost of 2.02 and a dispensing fee of 5.50. What is
the net profit?
selling price
acquisition
dispensing fee
NP = 8.49 – 2.02 – 5.50
NP = .97
The End

Read Chapter 6

Do Practice Problems Throughout Chapter
Take Self Test
Study Review Pages
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