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Introduction to Medication Math I

Watch this ppt in slide show mode

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

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You want to cancel the liters and obtain the equivalent amount in milliliters.

Since 1000 ml = 1 L (see Table 4.5), the fraction you want is

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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 ? g ?

mg ? g 500

Because 1000 g = 1 mg, the fraction you want is

.g 1000

mg 1

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So, 500 micrograms is the same as 0.5 milligram.

mg ? g 1000

mg 1 g 500

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mg 1

1

2

mg 0.5

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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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You want to cancel the grams and obtain the equivalent amount in milligrams.

mg ? g ?

mg ? 016.0 g

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mg ? g 1

mg 1000 016.0 g mg 16

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.

mg ?

cap ? mg 40

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Because the label indicates that each capsule contains 20 milligrams, you use the equivalent fraction

.mg 20

cap 1

mg 20

cap 1mg 40

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1

= 2 cap

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 ? mg ?

mL ? mg 3

The label reads 10 milligrams per milliliter, which means 10 mg = 1 mL. So, the equivalent fraction is .

mg 10

mL 1

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So, 0.3 milliliter contains 3 milligrams of methadone, and you would administer 0.3 milliliter of the drug to your patient.

mL ? mg 10

mL 1 mg 3 mL 0.3

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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:

mL ? mg ?

mL ?

g ?

mg ? g 002.0

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The first equivalent fraction is .g 1

mg 1000

The label reads 1 milligram per milliliter, which means 1 mg = 1 mL. So, the second fraction is

.mg 1

mL 1

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You would administer 2 milliliters of naloxone HCL IM, which would contain 0.002 gram of naloxone HCL.

mL ? mg 1

mL 1

g 1

mg 1000 g 002.0 mL 2

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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 ? mg ?

mL ? mg 250

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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

.mg 100

mL 1

mL ? mg 100

mL 1 mg 250

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5mL 5.2

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 ? units ?

mL ? units 0005

The label on the vial reads 10,000 units per milliliter, so the equivalent fraction is .

units 10,000

mL 1

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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.

mL ? u 10,000

mL 1 u 0005

1

2

mL 5.0

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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 pre-scribed 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

mL ? mg ?

mL ?

g ?

mg ? g .250

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The first equivalent fraction is .g 1

mg 1000

Because the prepared solution is 1 mL = 500 mg, the second equivalent fraction is

.mg 500

mL 1

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So, 0.5 milliliter of the solution contains 0.25 gram of Fortaz.

mL ? mg 500

mL 1

g 1

mg 1000 g .250

1

2

mL 5.0