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Math for Medications

Some terms you’ll see:

Desired Dose

Available Dose

Ratio & Proportion

Cross Product

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Math for Medications

• The purpose of this class is for the learner to be able to calculate drug dosages of tablets and liquids.

• You will calculate the drug dosages using the formula or ratio & proportion method.

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Math for Medications- the Formula Method for Tablets

Desired dose X Vehicle = ATA

Available dose

• dd x v = ATA

ad (amount to administer)

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Problem

• The doctor ordered Benadryl 75 mg. The drug label reads Benadryl 0.025 grams. How many tablets are needed?

• Read the problem and identify what you’ve been given.

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Problem

• dd = 75 mg

• ad = 0.025 grams

• v = 1 tab

• Have both dd & ad in the same unit of measure 0.025 g = 25 mg.

• ad = 25 mg

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Problem

• Put the numbers into the formula:

75 mg x 1 tab = 3 tabs

25 mg

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Math for Medications- The Ratio & Proportion Method for Tablets

• We will use the same problem but will cross multiply.

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Problem

• The doctor ordered Benadryl 75 mg. The drug label reads Benadryl 0.025 grams. How many tablets are needed?

• Read the problem and identify what you’ve been given.

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Problem

• The known ratio: 25 mg

1 tablet

• The unknown ratio: 75 mg

N tablets

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Problem

• Write the proportion :

25 mg x 75 mg

1 tablet N tablets

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Problem

• Cross Multiply:

25 mg x 75 mg

1 tablet N tablets

25mg X N tab = 1 X 75 mg

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Problem

• Solve for N by dividing both sides of the equation by 25:

• 25 N = 75

25 25

or N = 3

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Problem

• Substitute 3 for N in the original proportion and your answer is : You would administer 3 tablets to give a dosage of 75 mg.

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Math for Medications for Liquids

• Calculate drug dosages using the formula method or ratio & proportion method for liquids.

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Problem

• The doctor has ordered Gentamycin Sulphate 25 mg.

• The label reads Gentamycin Sulphate 40 mg/mL. How much Gentamycin will you administer?

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Problem - Using the Formula Method

• Identify:

dd = 25 mg

ad = 40 mg

v = 1 mL

• Put the numbers in the formula:

25 x 1 mL = 0.625 mL

40

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Problem

• Round off to the nearest decimal place:

• 25 x 1 mL= 0.625 mL or 0.6 mL

40

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Problem- Using the Ratio & Proportion method

• Cross product ( Cross Multiply) :

• The know ratio: 40 mg

1 mL

• The unknown ratio: 25 mg

N mL

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Problem

• Proportion: 40 mg = 25mg

1 mL N mL

• Cross Multiply:

40 x N = 1 x 25

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Problem

• Solve for N:

40N = 25

40 40

N = 0.625

N = 0.625

Round off: N = 0.6 mL

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Rules to Remember

• Substitute for N in the original proportion:

• Proportion: 40 mg = 25mg

1 mL 0.6 mL

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Rules to Remember

• Example: 0.66mg = 0.7 mg

1.Put 0 to the left of the decimal if there is no whole number.

2.Adults: round of drug doses to the nearest 1/10 or 0.1.

3.Pediatrics: Round off drug doses to the nearest 1/100 or 0.01

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Rules to Remember

• Do not round off until your final answer:

For example: 100 mg x 15 mL

80 mg

10=1.25 x 15 mL = 18.75 mL

8

Not 1.3 x 15 mL which would =19.5mL

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References

• SIAST. (2006). PHAR 264 – Administration of medications [Coursepack]. Regina : SIAST Wascana Campus.