# Tutorial: Pharmacy Calculations using Percentages.

Apr 26th, 2024**Percentages in Pharmacy Math.**

**Percentages are widely used in pharmacy math.**

It’s important that pharmacy technicians know how to interpret each percentage – what it means, and how to use these percentages in your methods and calculations.

In this guide, we will go through each of the three main percentage types – explain what each means, and how you should interpret these percentages when practicing pharmacy math.

As with all PTCB pharmacy math, practice makes perfect.

That’s why later in this study guide, we will review some **sample PTCB exam questions** that involve percentages. We would recommend **trying these questions first**, then reviewing and contrasting your answers with the answer explanations at the bottom of this study guide.

This will help you identify and potential or actual weak spots in your understanding of the topic.

**Percentage Type 1**: %W/W

%W/W means Percentage **W**eight per **W**eight.

W/W is used to measure the concentration of a substance where both the active ingredient and non-active base are both measured in grams.

**For example.**

A 5% w/w solution of glycerol means that there is 5 grams of glycerol **in every 100 grams** of solution.

That’s what percent means “**per-cent**” – **per 100**.

**Percentage Type 2: **%V/V

%V/V means Percentage **V**olume per **V**olume.

V/V is used to measure the concentration of a substance where both the active ingredient and non-active base are both measured in the same volume unit, such as milliliters (mL).

**For example.**

A 10% v/v solution of ethanol means that there is 10mL of ethanol **in every 100mL** of solution.

**Percentage Type 3: **%W/V

%W/V means Percentage **W**eight per **V**olume.

W/V is used to measure the concentration of a substance where the active ingredient is measured in grams but where the non-active base is measured in volume units, such as milliliters (mL).

**For example.**

A 25% w/v solution of glucose contains 25 grams of glucose immersed within 100mL of solution.

**Sample PTCB Percentage Questions**.

Pharmacy calculations using percentages are best practiced.

The more practice, the more refined your understanding will become. Here, we have put together three sample PTCB exam-like questions; the style of which get tested on the exam.

Work through each question first, then comparing your answer / answer method with the explained answers below.

**Q1**. A pharmacy technician is presented with 500g of base cream and asked to make a 5% w/w concentration. How much active ingredient must be added to the base cream?

**Q2**. You must prepare 200 mL of a 10% v/v alcohol solution. You have a stock solution that contains 50% v/v alcohol. How much stock solution must be used to prepare the target solution?

**Q3**. A pharmacy technician is tasked to prepare 300mL of a 2% w/v solution. The active ingredient is available in powered form. How many grams of power must be added to prepare the solution?

**Answer Explanations.**

**Answer 1.**

5% w/w means 5 grams of active ingredient per 100 grams of base.

Given that there is 5 grams in 100 grams, then 500 grams must have **25 grams of active ingredient** to achieve the desired concentration.

**Answer 2.**

The best way to answer this question is by using the formula:

**C1.V1 = C2.V2**

C1V1 refer to the concentration and volume of a solution, and C2V2 refers to the second solution. In this case, we are asked to make 200mL of a 10% solution. This is C1.V1. In C2.V2, we have the concentration (i.e. 50%), but we don’t have the volume.

We can now solve the equation to find V2:

C1.V1 = C2.V2

10%.200mL = 50%.x

2,000 = 50x

x = 40mL

40mL of the stock solution is needed to prepare 200mL of a 10% v/v solution.

**Answer 3.**

2% w/v means 2 grams of active ingredient per 100mL of solution.

You are asked to prepare 240mL of solution.

First, find the ratio difference between the two solutions:

240mL / 100mL = 2.4

As each 100mL contains 2 grams, we can multiply this factor by 2:

2.4 x 2 = 4.8 grams

4.8 grams of active ingredient is needed to make 240mL of a 2% w/v solution.

Alternatively, we can say that each 100mL of the 240mL final solution must contain 2 grams. So, the first 100mL has 2 grams, the second 100mL also has 2 grams; and 40% of the final 100mL is 0.8 – so the answer is 4.8 grams.

**Tutorial Review.**

Remember, there are often **multiple ways to solve** pharmacy calculations using percentages.

Here, we put together some of the best ways to answer these types of question. But if you managed to find the correct answer using an alternative method or technique, that’s fine too.

Whatever works best for you matters more than the method itself.

Another technique worth considering is re-arranging exam questions. For instance: at some point later in the week, you could change figures and numbers of the questions in this tutorial, then practicing those questions again yourself. As the method to solve the problems remains the same, this is a great way to test your knowledge.

**Hope you found this tutorial helpful on pharmacy calculations using percentages. Check back to our PTCB blog soon for more exclusive content to help you study and prepare for the pharmacy technician exam.**