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# Tutorial: PTCB Pharmacy Calculations.

Feb 20th, 2024

### Pharmacy Calculations Tutorial

Pharmacy calculations are one of the most challenging parts of the PTCB exam. But as with everything, practice makes perfect. It’s very important that technicians learn from mistakes, revising any critical points over time. That way, you can plug any knowledge gaps you may have.

In today’s pharmacy calculations tutorial, we put together five sample PTCB pharmacy calculation questions. Before studying the answer explanations below, take a few minutes to practice each question. Then, compare your answer with the answer explanation. Learn where you went right and / or where you went wrong. It’s essential that you try each question first to identify any potential weak spots.

Make notes accordingly and revise these points over time.

Here are today’s calculation questions:

Question 1

1,500 mL of a solution contains 2,500 mg of amoxicillin. What is the ratio strength of this solution?

Question 2

40 mL of sodium chloride is dissolved to make up a 250 mL solution. What is the v / v concentration of the resulting solution?

Question 3

A pharmacy technician has 250 mL of an 8% w/v solution. What volume should this solution be diluted to produce a 2.5% solution?

Question 4

The current rate of an IV solution is 150 mL / hr. Each mL of this solution is fed through 16 gtts. How many drops per minute is the IV solution running at?

Question 5

A 4-year-old child diagnosed with acute bacterial otitis media has been prescribed Omnicef 14 mg / kg daily every 24-hours for 10-days. If the child weighs 16kg, what is the correct dose of Omnicef to be administered daily?

### Question 1 Analysis

Let’s review the question again:

1,500 mL of a solution contains 2,500 mg of amoxicillin. What is the ratio strength of this solution?

As we are dealing with 2,500 mg of drug and 1,500 mL of solution, we have a w / v ratio (weight per volume). In a w / v ratio, we use grams / mL – not milligrams per mL.

The first step must therefore involve a conversion.

2,500 milligrams / 1,000 = 2.5 grams of amoxicillin.

2.5 grams / 1,500 mL = 1 / x

2.5 x = 1,500

x = 1,500 / 2.5

x = 600

Therefore, the ratio strength of this solution is 1 : 600.

### Question 2 Analysis

Let’s review the question again:

40 mL of sodium chloride is dissolved to make up a 250 mL solution. What is the v / v concentration of the resulting solution?

v / v means volume per volume.

In this case, we have two volumes – 40 mL of active ingredient dissolved in 250 mL of solution.

40 mL / 250 mL x 100 = 16 %

Therefore, the concentration of the solution is 16 % v / v.

### Question 3 Analysis

Let’s review the question again:

A pharmacy technician has 250 mL of an 8% w / v solution. What volume should this solution be diluted to produce a 2.5% w / v solution?

The pharmacy technician has 250 mL of solution.

The concentration of this solution is 8% w / v. In other words, weight per volume – so there are 8 grams of active ingredient in each 100 mL of solution.

We are asked to dilute the 250 mL solution to ensure the concentration is lowered to just 2.5% w / v solution.

We achieve this dilution by using the following formula:

C1 . V1 = C2  .V2

C1 = 8%

V1 = 250 mL

C2 = 2.5%

V2 = (250mL + x)

In other words, we already have C1V1; referring to the solution we are starting with.

And then we have C2V2; referring to the solution we are trying to create. “x” refers to what we need to find out i.e. the solution needed to create the new concentration.

0.08 x 250 = 0.025(250 + x)

20 = 6.25 + 0.025x

13.75 = 0.025x

x = 13.75 / 0.025

x = 550 mL

In other words, when we add 300 mL to the 250 mL solution we started with, it dilutes the concentration of that solution from its initial 8% concentration to the target 2.5% w / v concentration.

### Question 4 Analysis

Let’s review the question again:

The current rate of an IV solution is 150 mL / hr. Each mL of this solution is fed through 16 gtts. How many drops per minute is the IV solution running at?

First note that:

• gtts = drops
• IV = intravenous

PTCB exam questions on drop rates are very common. Calculating drops per minute is one of the most frequent examples of this.

We are told that the IV solution is administered to the patient at 150 mL per hour. In other words, that’s the same as 2.5 mL per minute (just divide 150 mL by 60 minutes).

We’re also told that there are 16 drops per milliliter.

Therefore, we simply need to multiply these figures together to give us drops per minute:

2.5 mL per minute x 16 drops per minute = 40 drops per minute.

### Question 5 Analysis

Let’s review the question again:

A 4-year-old child diagnosed with acute bacterial otitis media has been prescribed Omnicef 14 mg / kg daily every 24-hours for 10-days.

If the child weighs 16 kg, what is the correct dose of Omnicef to be administered daily?

The child has been diagnosed with a bacterial ear infection and requires acute treatment of Omnicef; the active ingredient of which is the cephalosporin antibacterial drug, cefdinir.

The child weighs 16 kg.

Omnicef must be administered at a rate of 14 mg / kg, therefore:

16 kg x 14 mg / kg = 224 mg per 16 kg.

224 mg must be administered to the child each day for the prescribed 10-day treatment period.

### Conclusion

We hope you found this pharmacy calculations tutorial helpful. If you have any questions about these calculations, get in touch and we will do our best to assist you.

You can also become a full member of PTCB Test Prep to continue your study of pharmacy calculations with our standalone module we put together dedicated to helping pharmacy technicians prepare for this part of the PTCB exam.

Also, check back to our blog soon for more exclusive content to help you study and prepare for the pharmacy technician exam!

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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.