Transcript Med Math Power Point

Introduction to
Medication Math I
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Overall Objectives
• The student will be able to:
• Calculate appropriate conversion in the
metric system (by volume and by weight)
• Calculate drug dose
– Pills/capsules per dose (or per day)
– Milliliters per dose (or per day)
• Calculate flow rate
– Milliliters per hour (ml/hr)
• Calculate drop rate
– Drops per minute (gtts/min)
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The Metric System
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Example 4.5
If the prescriber ordered 1.5 liters of 5% dextrose
in water (D/W), how many milliliters were
ordered?
1.5 L = ? ml
5
You want to cancel the liters and obtain the
equivalent amount in milliliters.
? ml
1.5 L ´
= ? ml
?L
Since 1000 ml = 1 L (see Table 4.5), the fraction
you want is 1000 ml
1L
.
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1000 ml
1.5 L ´
=1500
? mlml
1L
So, 1500 cubic centimeters of 5% D/W were
ordered.
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Weight in the Metric System
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Example 4.6
The prescriber has ordered 500
micrograms of cyanocobalamin
(vitamin B12). How many milligrams in
this dose?
500 g = ? mg
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You want to cancel the micrograms and
obtain the equivalent amount in milligrams.
? mg
500 g 
 ? mg
? g
Because 1000 g = 1 mg, the fraction
you want is
1 mg
.
1000 g
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1
1 mg
1 mg
500 g 
 ? mg  0.5 mg
2
1000 g
2
So, 500 micrograms is the same as 0.5
milligram.
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Example 4.7
The order reads 0.016 gram of the
analgesic medication morphine sulfate.
How many milligrams would you
administer?
0.016 g = ? mg
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? mg
0.016 g 
 ? mg
?g
You want to cancel the grams and obtain the
equivalent amount in milligrams.
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1000 mg
0.016 g 
 16
? mg
mg
1g
So, 0.016 grams is the same as 16
milligrams, and you would administer 16
milligrams of morphine sulfate.
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• Dr. Lunic orders Navane 40 mg BID.
• How many capsules will you
dispense
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Figure 6.2:
Drug label
for
Navane.
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You want to convert 40 milligrams to
capsules.
40 mg = ?
cap
You want to cancel the milligrams and
calculate the equivalent amount in
capsules.
? cap
40 mg 
? mg
20
Because the label indicates that each capsule
contains 20 milligrams, you use the equivalent
fraction
1 cap
20 mg
.
2
1 cap
40 mg 
= 2 cap
20 mg
1
So, you would administer 2 capsules of navane
to the patient.
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Parenteral Medications
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Objectives:
• Do the calculations necessary to prepare
medications for injection from drugs
supplied in liquid form in vials and
ampules.
• Do the calculations necessary to prepare
medications for injection from drugs
supplied in powdered form in vials.
• Do calculations involving units.
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Figure 9.1: Ampules and vials.
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Parenteral Medications
Supplied as Liquids
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When parenteral medications are supplied in
liquid form, you need to calculate the volume
of liquid that contains the prescribed amount
of the drug. To do this, you will use the
dimensional analysis method you have been
using for all other calculations.
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The prescriber ordered 3 milligrams of
methadone hydochloride (Dolophine) sc.
Study the label in Figure 9.2. How many
milliliters would you administer to the patient?
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Figure 9.2: Drug label for methadone hydrochloride.
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Begin by finding out how many milliliters of
the liquid in the vial contains the
prescribed quantity of the drug (3
milligrams of methadone hydrochloride).
That is, you want to convert 3 milligrams
to an equivalent in milliliters.
3 mg = ? mL
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You cancel the milligrams and obtain the
equivalent quantity in milliliters.
? mL
3 mg 
 ? mL
? mg
The label reads 10 milligrams per milliliter,
which means 10 mg = 1 mL. So, the
equivalent fraction is 1 mL .
10 mg
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1 mL
3 mg 
 0.3
? mL
mL
10 mg
So, 0.3 milliliter contains 3 milligrams of
methadone, and you would administer 0.3
milliliter of the drug to your patient.
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The prescriber ordered 0.002 gram of
naloxone HCL (Narcan) IM. Read the label in
Figure 9.3, and calculate how many milliliters
of this narcotic antagonist you would
administer.
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Figure 9.3:
Drug label for
Narcan.
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The label shows Narcan in milligrams per
milliliter, so you want to convert 0.002 gram to
its equivalent in milligrams and then change
milligrams to milliliters.
0.002 g  ? mg  ? mL
Do this on one line as follows:
? mg
? mL
0.002 g 

 ? mL
?g
? mg
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1000
mg
The first equivalent fraction is
.
1g
The label reads 1 milligram per milliliter, which
means 1 mg = 1 mL. So, the second fraction is
1 mL
.
1 mg
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1000 mg
1 mL
mL
0.002 g 

 ?2 mL
1g
1 mg
You would administer 2 milliliters of naloxone
HCL IM, which would contain 0.002 gram of
naloxone HCL.
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Examine the label in Figure 9.7, and determine
the quantity of solution to be withdrawn from
the vial if the medication order reads 250
milligrams of 10% calcium chloride.
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Figure 9.7: Drug label for calcium chloride.
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You want to convert milligrams to
milliliters.
250 mg  ? mL
? mL
250 mg 
 ? mL
? mg
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The label “10% calcium chloride” means that
10 grams of calcium chloride are in 100
milliliters, or 100 milligrams of calcium chloride
are in 1 milliliter. So, the equivalent fraction is
1 mL
.
100 mg
5
1 mL
5 mL
250 mg 
 2?.mL
100 mg
2
So, you would withdraw 2.5 milliliters from the vial.
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Heparin
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The prescriber ordered:
Fragmin 5000 units sc q12h.
The label on the vial (Figure 9.9) reads
10,000 units per milliliter. How many milliliters
will you administer to the patient?
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Figure 9.9: Drug label for Fragmin.
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You want to convert units to milliliters.
5000 units = ? mL
You cancel the units and obtain the equivalent
amount in milliliters.
? mL
5000 units 
 ? mL
? units
The label on the vial reads 10,000 units per
milliliter, so the equivalent fraction is 1 mL .
10,000 units
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1
1 mL
5000 u 
 0?.5mL
mL
10,000 u
2
So, 0.5 milliliter contains 10,000 units of Fragmin
and you would administer 0.5 milliliter of Fragmin,
which is a low molecular weight heparin, to the
patient subcutaneously.
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Parenteral Medications
Supplied in Powdered Form
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Some parenteral medications are supplied in
powdered form in sealed vials (Figure 9.10).
The powder cannot be removed from these
vials. You must add sterile water or saline to
the vial and dissolve the powder to form a
solution. You then inject the liquid volume of
prepared solution that contains the proper
amount of the drug.
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Figure 9.10:
A sealed vial of Kefzol in powdered form with
label detail.
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The pharmaceutical manufacturer provides
instructions that specify the amount of sterile
liquid that must be injected into the vial of
powder to make a solution of a given strength.
After preparing the solution, you need to
calculate the volume that contains the prescribed amount of the drug.
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The prescriber has ordered 0.25 gram of the
antibiotic ceftazidime (Fortaz). The label on
the vial reads 500 milligrams per milliliter. How
many milliliters of the solution would contain
the prescribed dose?
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You want to convert 0.25 gram to milliliters.
This is a two-step problem.
0.25 g  ? mL  ? mL
? mg
? mL
0.25 g 

 ? mL
?g
? mg
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The first equivalent fraction is
1000 mg
.
1g
Because the prepared solution is 1 mL = 500 mg,
the second equivalent fraction is 1 mL
500 mg
.
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2
1000 mg
1 mL
5 mL
0.25 g 

 ?0.mL
1g
500 mg
1
So, 0.5 milliliter of the solution contains 0.25 gram
of Fortaz.
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