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# Pharmacy Technician Math Study Guide | Calculation of Doses

Sep 21st, 2019

### Pharmacy Technician Math Practice

For the PTCB exam, candidates must have a thorough and detailed knowledge of how to calculate doses. Here, we review 5 examples of the type, style, and difficulty of math question you can expect on the day of your test.

Knowing math is important.

For example, pharmacy technicians may be given a prescription where the dose recommended by the prescriber is not available by a given brand. Instead, the technician needs to calculate the number of tablets that must be given to match the prescriber’s prescription. In this pharmacy technician math study guide, we examine many of these questions.

Of course, when it comes to dose calculation questions, there are numerous ways you can approach each question. Here, we try to avoid using proportional sets as a mechanism. The reason is two-fold. First, that using proportional sets tends to add more steps to solve the question, thereby increasing the risk of error. Second, using a more logical approach with limited steps decreases the risk of error. Below, we review the logical approach that we recommend.

That said, we would always recommend that you adopt the approach that works best for you. You may find more than one method should be used to ‘confirm’ whether you have arrived at the correct answer. No matter what method you choose, it’s vital that you practice PTCB exam questions. The more questions you practice, the better and more refined your knowledge and understanding of math questions.

Without further ado, then, let’s review 5 sample PTCB math questions – this time, focusing exclusively on dosage calculations.

### Sample PTCB Math Question 1

A physician prescribes ‘ampicillin 0.5g po qid’. The dose available to the pharmacy technician is 250mg per capsule.

How many capsules should be prescribed to the patient?

First, always ask yourself whether units are consistent.

In this case, the physician prescribed 0.5 grams, whereas the medicine is available in the pharmacy as 250mg per capsule. These are inconsistent unit and must therefore be corrected before we can continue.

0.5 grams is the same as 500 milligrams.

Next step – we must know the total dose of drug prescribed to the patient. This means having a detailed knowledge of prescription abbreviations. As you are aware, ‘po qid’ refers to ‘orally 4 times daily’.

This means the patient needs to take 500 milligrams four times during the day – or 2,000 milligrams per day.

The dose available in the pharmacy is 250mg per capsule – meaning that the patient needs to take 2 of these capsules 4 times per day.

8 capsules of the available medicine must therefore be prescribed to the patient to meet the physician’s prescription.

Let’s summarize the steps as follows:

1. Ensure that units are consistent – milligrams, grams etc.
2. Find the total dose prescribed to the patient.
3. Use the dose available in the pharmacy to determine how many tablets should be given to meet that total dose.

Let’s advance onto our second example.

### Sample PTCB Math Question 2

The physician prescribed Cleocin 150mg IM q12h x 4d. The medicine is available as clindamycin phosphate 100mg/2mL.

How many mL of Cleocin should be prescribed to the patient?

Like before, let’s review the question from a methodical, reasoned approach.

First, are units the same? Yes – Cleocin is available as 150mg and the pharmacy has a generic form the medicine available at 100mg.

Next, what is the total dose of Cleocin prescribed to the patient?

Again, we must understand pharmacy abbreviations:

• 150mg IM q12h x 4d

150mg to be administered via the intramuscular route, every 12 hours, for 4 days.

150mg every 12 hours is the same as 300mg per day. 300mg per day must be given for 4 days, so 1,200mg of Cleocin is required.

However, the pharmacy has a generic form, clindamycin phosphate (the active ingredient of Cleocin) available at a dose of 100mg/2mL.

If there is 100mg in 2mL, then 1,200mg must have 24mL – by simple matter of multiplication.

Therefore, 24mL of clindamycin phosphate must be prescribed to the patient to meet the needs of the physician’s prescription.

### Sample PTCB Math Question 3

What dose, in milligrams (to the nearest whole number), should be given to a patient who weighs 196lbs when the drug literature states that the dose should be 0.4mg/4kg?

Again, we must always begin with asking about units – are they the same?

In this case, the answer is no. We have 196lbs and we also have 4kg. Because the question asks to answer in milligrams, we must convert 4 kilograms to lbs – that way all units are the same.

To convert kilos to lbs, we must multiply by 2.2 (remember this conversion!).

• 4 kilograms x 2.2 = 8.8 pounds (lbs)

Now, we know that the patient weighs 196lbs and that, for each 8.8lbs of the patient’s weight, they must take 0.4mg of the drug.

Therefore, if we divide 196lbs by 8.8lbs, we will learn the total number of milligrams of drug the patient needs to take.

• 196lbs / 8.8lbs = 22.27 doses of 0.4mg/4kg are needed.
• 22.27 x 0.4mg = 8.9mg of drug

The question asks us “to the nearest whole number”, meaning…

• 8.9mg to the nearest whole number = 9mg

A 196lb patient must take 9mg of the drug.

### Sample PTCB Math Question 4

How many millilitres of ampicillin 250mg/5mL should be dispensed if the patient is prescribed iii tsp po tid x 7d?

To answer this question, we simply need to know the volume of medicine to be dispensed. We can ignore the 250mg/5mL – it is simply the dose available in the pharmacy, but that does not concern us here. Sometimes when answering PTCB sample questions, you need to know when to ignore details in the question. Often, not all details need to be used. Bear this tip in mind as you continue through this math study guide.

Instead, you must identify what information to use and why it needs to be used!

First, we must correctly interpret the prescription abbreviations:

• iii tsp po tid x 7d

3 teaspoons, to be taken orally, 3 times a day, for 7 days

Remember – there is 5mL in 1 teaspoon!

Three teaspoons (15mL) taken 3 times daily = 45mL needed per day.

The prescription requires 7-day’s supply – (45mL x 7) = 315mL

Therefore, 315mL of ampicillin 250mg/5mL should be dispensed to the patient.

So, for added detail – every 5mL of that 315mL of medicine contains 250mg of ampicillin!

Let’s now move onto the last and trickiest of our math study guide!

### Sample PTCB Math Question 5

A pharmacy technician is asked to prepare 360mL of a 250mg/5mL drug solution. The drug is only available in 200mg tablets.

How many tablets are needed to prepare 360mL of a 250mg/5mL solution?

At first, this question might seem difficult. However, if you follow our method below, you’d be surprised how manageable it becomes!

First, we must understand what the question is asking us to do.

You, the pharmacy technician, are asked to prepare a 360mL solution for a patient. In every 5mL of that solution, there must be 250mg of drug.

This means when the patient takes 5mL, they are guaranteed to have 250mg of drug to treat their condition (250mg/5mL is the dose).

The drug is available, but only as tablets – each of which has 200mg.

So, now that we know the groundwork, let’s develop a method solution to work this problem out, and all related PTCB math problems.

First, when you are asked to make a 360mL of a 250mg/5mL solution, you need to work out the total number of milligrams of drug in that solution. In other words, if every 5mL of the 360mL solution has 250mg, then there must be 18,000mg of drug in a 360mL solution:

• 360mL divided by 5mL is 72
• 72 x 250mg = 18,000mg

Imagine the question asked you to prepare 20mL of a 5mg/5mL solution. If there is 5mg in 5mL, then there must be 20mg in 20mL! It’s the same thing here, just the numbers are bigger and far more awkward to deal with!

Now, we know that we need 18,000mg. The question asks us how many 200mg tablets are needed. By simple division then…

• 18,000mg divided by 200mg = 90 tablets

Ninety 200mg tablets are needed to produce a 360mL solution, with each 5mL of that solution containing 250mg!

### Final Thoughts

Math is an important part of the PTCB test. In this pharmacy technician math study guide, we have focused on the calculation of doses. We have offered 5 core examples, all of which can appear on the day of your PTCB exam. We strongly recommend knowing how to calculate doses – questions are almost guaranteed to appear.

The more math PTCB practice tests you practice the better. If you are already a registered member of PTCB Test Prep, we encourage you to enter your online portal and take the practice math questions for this part of the exam. Study each of the explained answers to maximize your understanding of the topic and where you might be going wrong.

PTCB Test Prep is the leading online platform that trains pharmacy technicians throughout the United States. Check back to our blog soon for more great questions and answers on our pharmacy technician math study guide!

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### Elaine Walker

Elaine joined PTCB Test Prep in 2017, currently serving as the lead product development manager overseeing both course development and quality improvement. Mrs. Walker is a graduate of California State University and has worked as a pharmacy technician for over twenty years – with particular interests in pediatric pharmacy, extemporaneous compounding, and hospital pharmacy. Over the past 8-years, she has helped prepare thousands of students for the PTCB examination.