# Math help from the Learning Centre

This guide provides useful resources for a wide variety of math topics. It is targeted at students enrolled in a math course or any other Centennial course that requires math knowledge and skills.

## Calculating Dosages

 Single Dosage Amount $X=D\times \frac{Q}{H}$ where, $$X$$ is the single individual dose amount of medication given (usually in tablets or mL); $$D$$, Dosage Ordered, is the amount of drug prescribed or ordered by the physician to be administered to the patient; $$H$$, Strength on Hand, is the available strength of one dose of the drug to be administered to the patient; and $$Q$$, Quantity, is the available form of one dose of the drug.

Examples:

1. Physician orders 500 mg of ibuprofen p.o. q.8.h. x 14 days for a patient. Quantity of Ibuprofen is 250 mg.

a. What single dose should you administer?

$X=D\times \frac{Q}{H}$

$$D=500$$ mg of ibuprofen

$$H=250$$ mg

$$Q=1$$ tablet of ibuprofen

$X=500mg\times \frac{1\,tablet}{250mg}=2\,tablets$

So, you would administer 2 tablets of ibuprofen in a single dose orally.

b. What is the daily dose?

The order is q.8.h. represents every 8 hours. Since there are 24 hours each day. Every 8 hours represents three times a day.

So the patient will receive $$3\times 2=6$$ tablets each day.

c. What is the total dose for 14 days

In 14 days, the patient will receive $$14\times 6=84$$ tablets.

2. The prescriber orders Zoloft (sertraline hydrochloride) oral solution 25 mg b.i.d. for 7 days. The drug label can be seen below. a. What single dose should you administer?

$X=D\times \frac{Q}{H}$

$$D=25$$ mg of sertraline oral solution

$$H=20$$ mg

$$Q=1$$ mL

$X=25\,mg\times \frac{1\,mL}{20\,mg}=1.25\,mL$

So, you would administer 1.25 mL of Zoloft oral solution in a single dose orally.

b. What is the daily dose?

The order is b.i.d. or twice a day.

So the patient will receive $$2\times 1.25=2.5$$ mL each day.

c. What is the total dose for 7 days

In 7 days, the patient will receive $$7\times 2.5=17.5$$ mL.

3. How many 300-mg Ziagen (abacavir sulfate) tablets contain 0.9g of Ziagen?

Notice that there are mg and g listed as the unit of the tablets. Thus, you need to convert into the same unit of measurement before finding the number of tablets.

We can start by converting 0.9g into mg, knowing that $$1g=1000mg$$

$0.9\,g\times\frac{1000\,mg}{1\,g}=900\,g$

Now we convert 900mg into tablets.

$900\,mg\times\frac{1\,tablet}{300\,mg}=3\,tablets$

So, three 300 mg tablets contain 0.9 g of Ziagen.

4. An order of Aldactazide (spinolactone and hydrochlorothiazide) 100 mg/100 mg p.o. b.i.d. Read the label below and determine how many tablets of this diuretic you will administer each day? The order is for 100 mg/100 mg and the label reads 25 mg/25 mg per tablet.

$100 mg/100 mg \times\frac{1\,tablet}{25\,mg/25\,mg}=4\,tablets$

Each dose will contain 4 tablets of Aldactazide. B.i.d. represents twice a day, so in one day, the patient will receive 8 tablets of Aldactazide.