217Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.

CHAPTER 14Dosage Calculation Using

the Ratio and Proportion Method

ObjectivesAfter reviewing this chapter, you should be able to:1. State a ratio and proportion to solve a given dosage calculation problem2. Solve simple calculation problems using the ratio and proportion method

Several methods are used for calculating dosages. The most common methods are ratioand proportion and use of a formula. After presentation of the various methods, students

can choose the method they find easiest and most logical to use. First, let’s discuss calcu-lating by using ratio and proportion. If necessary, review Chapter 4 on ratio and proportion.

Use of Ratio and Proportion in Dosage CalculationWhen you know three of the four values of a proportion, you can solve the proportion todetermine the unknown quantity. In dosage calculation, it is often necessary to find onlyone unknown quantity. As you recall from Chapter 4 (ratio and proportion), the proportioncan be set up stating the terms using colons (ratio format) or as a fraction. Recall that aproportion is a relationship comparing two ratios. Remember, in addition to solving for theunknown quantity, it is essential to also be competent in setting up the proportion correctly.

SAFETY ALERT!

If you set up the proportion incorrectly, you could calculate the dose incorrectly and administer thewrong dose, which could have serious consequences for the client.

For example, suppose you had a medication with a dosage strength of 50 mg per 1 mL,and the prescriber orders a dosage of 25 mg. A ratio and proportion may be used to deter-mine how many milliliters to administer. Remember to include units when writing a ratioand proportion to avoid errors.

When setting up the ratio and proportion using the fraction format to calculate dosages,the known ratio is what you have available, or the information on the medication label, andis stated first (placed on the left side of the proportion). The desired, or what is ordered tobe administered, is the unknown (placed on the right side). Therefore, using the examplethe ratio and proportion would be stated as follows:

Example 1: !

(known) (unknown)

25 mg"x mL

50 mg"1 mL

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218 UNIT THREE Methods of Administration and Calculation

Copyright © 2014 by Mosby, an imprint of Elsevier Inc. All rights reserved.

When writing the ratio and proportion using the colons (ratio format), the known ratio,what you have available or the information on the medication label, is stated first, and theunknown ratio is stated second.

Example 1: 50 mg!1 mL ! 25 mg!x mL(known) (unknown)

Solution: To solve for x, use the principles presented in Chapter 4 on ratio and pro-portion.

!

(known) (unknown)

!

x ! 0.5 mL

Remember that, as shown, the known is stated as the first fraction, and the unknown as thesecond. When stated in fraction format, solve by cross multiplication.

or

50 mg!1 mL ! 25 mg!x mL(known) (unknown)

50x ! product of extremes

25 ! product of means

50x ! 25 is the equation

!

x ! 0.5 mL

SAFETY ALERT!

It is important to remember when stating ratios that the units of measure should be stated in the same

sequence (in the examples, ! or mg!mL ! mg : mL). Labeling the terms in the ratios, including

x, is also essential. These pointers are crucial to preventing calculation errors.

Example 2: Order: 40 mg p.o. of a medication.

Available: 20 mg tablets. How many tablets will you administer?

Solution: !

(known) (unknown)

!

x ! 2 tabs

or

20 mg!1 tab ! 40 mg!x tab(known) (unknown)

!

x ! 2 tabs

40"20

20x"20

40"20

20x"20

40 mg"x tab

20 mg"1 tab

mg"mL

mg"mL

(Divide both sides by 50,the number in front of x.)

25"50

50x"50

25"50

50x"50

25 mg"x mL

50 mg"1 mL

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CHAPTER 14 Dosage Calculation Using the Ratio and Proportion Method 219

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Example 3: Order: 1 g p.o. of an antibiotic

Available: 500 mg capsules. How many capsules will you administer?

Solution: Notice that the dosage ordered is in a different unit from what is available.Proceed first by changing the units of measure so they are the same. Asshown in Chapter 8, ratio and proportion can be used for conversion.

After making the conversion, set up the problem and calculate the dosageto be given. In this example, the conversion required is within the samesystem (metric).

In this example, grams are converted to milligrams by using the equivalent1,000 mg ! 1 g. After making the conversion of 1 g to 1,000 mg, the ratiois stated as follows:

! or 500 mg!1 cap ! 1,000 mg!x caps

(known) (unknown) (known) (unknown)

x ! 2 caps x ! 2 caps

An alternate method of solving might be to convert milligrams to grams. In doing this,500 mg would be converted to grams by using the same equivalent: 1,000 mg ! 1 g. How-ever, decimals are common when measures are changed from smaller to larger in the met-ric system: 500 mg ! 0.5 g. Even though converting the milligrams to grams would net thesame final answer, conversions that net decimals are often the source of calculation errors.Therefore, if possible, avoid conversions that require their use. As a rule, it is best to con-vert to the measure stated on the medication label. Doing this consistently can prevent con-fusion. As with the other examples, this proportion could be stated as a fraction as well.

For the purpose of learning to calculate dosages by using ratio and proportion, thischapter emphasizes the mathematics used to calculate the answer. Determining whether ananswer is logical is essential and necessary in the calculation of medication. An answermust make sense. Determining whether an answer is logical will be discussed further inlater chapters covering the calculation of dosages by various routes.

POINTS TO REMEMBER

Important Points When Calculating Dosages Using Ratio and Proportion• Make sure all terms are in the same unit and system of measure before calculating. If they are not, a

conversion will be necessary before calculating the dosage.• When conversion of units is required, conversions can be made by converting what is ordered to the

units in which the medication is available or by changing what is available to the units in which the med-ication is ordered. Be consistent as to how you make conversions. It is usual to convert what is orderedto the same unit and system of measure you have the medication available in.

• When stating ratios, the known is stated first. The known ratio is what is available or on hand or the in-formation obtained from the medication label.

• The unknown ratio is stated second. The unknown ratio is the dosage desired, or what the prescriberhas ordered.

• The terms of the ratios in a proportion must be written in the same sequence.

Example: mg : mL ! mg : mL or ! .

• Label all terms of the ratios in the proportion, including x.• Before calculating the dosage, make a mental estimate of the approximate and reasonable answer.• Label the value you obtain for x (e.g., mL, tabs). Double-check the label for x by referring back to the la-

bel of x in the original ratio and proportion; it should be the same.• A proportion can be stated in a horizontal fashion using colons (ratio format) or as a fraction.

mg"mL

mg"mL

1,000 mg""

x caps500 mg"

1 cap

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