© 2010 The McGraw-Hill Companies, Inc. All rights reserved 7-1 Math and Dosage Calculations for Health Care Third Edition Booth & Whaley Chapter 7: Methods.

© 2010 The McGraw-Hill Companies, Inc. All rights reserved

7-1

Math and Dosage Calculations for Health Care Third Edition

Booth & Whaley

Chapter 7: Methods for Dosage Calculations

McGraw-Hill


7-2

Learning Outcomes

7.1 Describe how the information on a physician’s order, medication administration record (MAR), or prescription, along with the drug label and package insert, are used to calculate the desired dose.

7.2 Convert the dosage ordered to the desired dose, using fraction proportion, ratio proportion, or dimensional analysis.

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7-3

Learning Outcomes (cont.)

7.3 Calculate the amount to administer of a drug, using any of the methods of dosage calculation – fraction proportion, ratio proportion, dimensional analysis, or formula.

7.4 Recognize common errors that occur during dose calculations.

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7-4

Introduction To calculate dosages you will use:

Basic math

Information from the physician’s order

Drug labels

Methods of converting quantities from one unit of measurement to another

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7-5

Dosages and Doses

Desired dose The amount of the drug to be

administered at a single time

To find the desired dose, you must have The dosage ordered The dose on hand

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7-6

Dosages and Doses (cont.)

Dosage ordered The amount of drug ordered and the

frequency of administration

Dosage strength Amount of drug per dosage unit Medication may be available in different

dosage strengths

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7-7

Dosages and Doses (cont.)

Dose on hand The amount of drug contained within a

dosage unit of medication If a medication has 250 mg of drug per

tablet, the dose on hand is 250 mg.

Dosage unit Tablet, capsule, mL, etc.

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Both can be found on the label


7-8

Calculating the Desired Dose Before calculating the amount to

administer, you must first determine the desired dose.

The dosage ordered may be in different units than found on the label. The dosage ordered must be converted

into a desired dose having the same units as the dose on hand.

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7-9

Dosage Calculation Dosage ordered = O

Desired dose = D

Dosage unit = Q

Dose on hand = H

Amount to administer = A

Dosage strength = H/Q


7-10

Calculating the Desired Dose (cont.)

Three methods to calculate desired dose Fraction proportion

Ratio proportion

Dimensional analysis

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Method used is a matter of choice


7-11

Calculating the Desired Dose (cont.)

Rule 7 - 1 Rule 7 - 1 The unit of measurement for the desired dose must be the same as the unit of measurement of the dose on hand before the amount to administer can be calculated.

The dose ordered must be converted into the same unit of measurement as the dose on hand.

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7-12

Fraction Proportion Method

Procedure Checklist 3-1Procedure Checklist 3-11.Write the conversion factor with the units

that you are converting to in the numerator and the units you are converting from in the denominator.

2.Write a fraction with the unknown [?] in the numerator and the number that you need to convert in the denominator.

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7-13

Fraction Proportion Method (cont.)

3. Set the two fractions up as a proportion.

4. Cancel units.

5. Cross multiply, then solve for the unknown value.

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7-14

Fraction Proportion Method (cont.)

The dosage ordered is 0.2 mg once a day.

The dosage strength is 100 mcg/tablet.Find the desired dose.

?/0.2 mg = 1000 mcg/1 mg?1000 = 0.2 ? = 200

Desired dose = 200 mcg

ExampleExample


7-15

Error Alert!In a fraction proportion, units from the

two fractions can be canceled only when they are the same portion of the fraction.

Units in the denominator of one fraction cannot be canceled with units found in the numerator of the other.

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Always include the units when performing calculations.


7-16

Ratio Proportion Method

Procedure Checklist 3-2Procedure Checklist 3-21. Write the conversion factor as a ratio A : B

so that A has the units of the value that you are converting (the dosage ordered) and B has the unit of value of the dose on hand.

2. Write a second C : D so that C is the missing value (desired dose) and D is the number that is being converted (the dosage ordered).

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7-17

Ratio Proportion Method (cont.)

3. Write the proportion in the form A : B :: C : D.Note: When using the ratio proportion method

to calculate the desired dose, C indicates the unknown value (desired dose).

4. Cancel units.

5. Solve the proportion by multiplying means and extremes.

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7-18

Ratio Proportion Method (cont.)

The order reads: ASA gr v PO daily. The drug label indicates 325

mg tablets.Find the desired dose using 1 gr = 65 mg

65mg:1gr:: C: 5 gr

1 × C = 65 × 5

C = 325

Desired dose is 325 mg

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ExampleExample


7-19

Error Alert!

In a ratio proportion, units can be canceled only when they are found in the same part of each of the ratios.

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7-20

Dimensional Analysis

Procedure Checklist 3-3Procedure Checklist 3-31. Determine the units of measure for the

answer and place it as the unknown on one side of the equation.

2. On the other side of the equation, write a conversion factor with the units of measure for the answer on top and the units you are converting from on the bottom.

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7-21

Dimensional Analysis (cont.)

3. Multiply the conversion factor by the number that is being converted over one.

4. Cancel units on the right side of the equation. The remaining unit of measure on the right side should match the unknown unit of measure on the left side.

5. Solve the equation.

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7-22

Dimensional Analysis (cont.)

Find the desired dose for the following:

Ordered: Nitrostat 800 mcg sublingually PRN chest pain

On hand: Nitrostat 0.4 mg sublingual tablets

D mg = 1mg/1000mcg x 800mcg/1

D mg = 800/1000

D mg = 0.8

Desired dose is 0.8 mg

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ExampleExample


7-23

Error Alert!

In dimensional analysis, units can be canceled only when they are found in both the numerator and the denominator of the fraction.

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7-24

Practice

Determine the desired dose. Ordered: Penicillin VK 0.25 gOn hand: Penicillin VK 500 mg/tablet

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Desired dose: 250 mg


7-25

Calculating the Amount to Administer

Once the desired dose is calculated, the amount to administer must be calculated.

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7-26

Calculating the Amount to Administer (cont.)

Rule 7–2Rule 7–2 To calculate the amount of medication to administer (A), the following information must be known:

The desired dose (D) or the amount of drug to be given at a single time. This is the dosage ordered converted to the same units as the dose on hand.

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7-27


Rule 7 - 2 Rule 7 - 2 (cont.)

The dosage strength or the dose on hand (H) per the dosage unit (Q) The dose on hand (H) is the amount of drug

contained in a dosage unit.

The dosage unit (Q) is the unit by which you will measure the medication-tablets, capsules, milliliters, teaspoons, etc. (Find this on the medication label).

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7-28


Procedure 7-1 Procedure 7-1 Calculating the Amount to Administer by Fraction Proportion:

1. Set up the proportion as follows: dosage unit amount to administer dose on hand desired dose

2. Cancel units.

3. Cross multiply, then solve for the unknown value.

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DHQ A


7-29

Ordered: 250 mg IM Dosage strength available:

0.5 g/mLFind the amount to administer.Convert 0.5 gm to milligrams

500 x A = 1mL x 250 500mL250

500500A

mg250A

mg500mL1


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Example Example

A 500 = 250mL

Amount to administer= 0.5mL


7-30

Procedure 7-2Procedure 7-2 Calculating the Amount to Administer by Ratio Proportion:

1. The proportion will be set up as follows:dosage unit : dose on hand :: amount to administer :

desired dose

or Q : H :: A : D

2. Cancel units.

3. Multiply the means and extremes then solve for the missing value.


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7-31

The dosage ordered is Erythromycin 500 mg PO q 6h

On hand: Erythromycin 250 mg tabsFind the amount to administer.D = 500mg Q = 1 tablet H = 250mg

1 tablet : 250mg :: A : 500mg

A = 1 tablet x 2

250mg500tablet1

250A250


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Example Example

Amount to administer = 2 tablets


7-32


Procedure 7-3Procedure 7-3 Calculating the Amount to Administer by Dimensional Analysis:With dimensional analysis you will not need to calculate the desired dose and amount to administer separately.

You will place your unknown (amount to administer) on one side of the equation then multiply a series of factors on the right side of the equation.

Canceling units will help you determine the equation has been set up correctly.

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7-33


Procedure 7-3Procedure 7-3 (cont.):1. Determine the units of measure for the

answer and place it as the unknown on one side of the equation.

2. On the right side of the equation, write a conversion factor with the unit of measure for the desired dose on top and the unit of measure for the dosage ordered on the bottom. If units are different than the dose on hand.

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7-34


Procedure 7-3Procedure 7-3 (cont.):3. Multiply the conversion factor by a

second factor – the dosage unit over the dose on hand.

4. Multiply by a third factor - dose ordered over the number one.

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7-35


Procedure 7-3Procedure 7-3 (cont.):5. Cancel units on the right side of the

equation. The remaining unit of measure on the right side of the equation should match the unknown unit of measure on the left side of the equation.

6. Solve the equation.

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7-36


The order reads: Prozac Liquid 40mg daily

On hand: Prozac 20 mg/5 mLFind the amount to administer.D = 40 mg Q = 5 mL H = 20 mg

A mL = 200/20

Amount to administer = 10 mL

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Example Example

1mg40

mg20mL5

AmL


7-37


Procedure 7-4 Procedure 7-4 Calculating Amount to Administer Using the Formula Method:

1. Determine the desired dose. Determine the dose on hand (H) and dosage unit (Q)

2. Fill the formula• D for the desired dose • H for the dose on hand • Q for the dosage unit in the formula • A for the unknown or the amount to

administer

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7-38


Procedure 7-4Procedure 7-4 (cont.):

3. Cancel the units.

4. Solve for the unknown.

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AxQHD


7-39


The dosage ordered is Famvir 500 mg PO q 8 h

On hand: Famvir 250 mg/tabsFind the amount to administer.D = 500 mg H = 250 mg Q = tablet

2 x 1 tablet = A

2 tablets = Amount to administerMcGraw-Hill

Example Example

Atablet1mg 250mg 500


7-40

Apply Your Knowledge

The amount of the drug to be administered at a single time is called the:a. dosage orderedb. dosage unitc. desired dosed. dosage strength

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7-41


True or FalseIf a medication has 300 mg of drug per tablet, the dose on hand is 300 mg.

Answer True

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7-42


The MAR reads Glucotrol 10 mg PO qd.

The desired dose is ____ mg.

Answer 10 mg

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7-43


Calculate the amount to administer.Ordered: Prednisone 10 mg PO qidOn hand: Prednisone 5 mg tablets

Answer (Using ratio proportion)5 mg : 1 tablet : : 10 mg : ? tablet1 x 10 = 5 x ?? = 2Amount to administer: 2 tablets

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7-44

End of Chapter 7

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Each problem

that I solved

became a rule,

which served

afterwards to

solve other

problems.

-- Rene

Descartes

© 2010 The McGraw-Hill Companies, Inc. All rights reserved 7-1 Math and Dosage Calculations for Health Care Third Edition Booth & Whaley Chapter 7: Methods.

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