# PROPORTIONS MATH

Proportions math is very commonly used by pharmacy technicians. It is mandatory to learn this process to prepare for the PTCB or ExCPT. A majority of the calculations you'll do use proportions math.

You must know 3 factors
and be looking for the fourth (unknown or X)
.

Let's jump right into a practice question and see how this works.

Practice Question #1 :
If Fifty tabs of Clarithromycin 500mg costs \$25.00, how much would ten tabs of Clarithromycin 500mg cost ?

1) In this case, we know that 50 tabs cost \$25.00, those are the first two factors. We also know we want to figure out how much only 10 tabs would cost, 10 is the third factor and its cost is the unknown.

This is how you want to write your two fractions:

 \$25.00 ? 50 tabs 10 tabs

2) Next, we want to multiply the denominator from the unknown side with the numerator on known side and write the product to the left:

 250.00 = \$25.00 ← ? X 50 tabs ← 10 tabs

3) Next, we want to take this product and divide it by the known sides denominator:

 250.00 \$25.00 → = 5 ÷ ↑ →   → 50 tabs → 10 tabs

4) The calculation you get goes into the numerator on the unknown side and that's

 \$25.00 \$5.00 50 tabs 10 tabs

### The next one is slightly harder.

Practice Question #2 :
You are compounding a batch that requires 227g of drug F, which costs your pharmacy \$94.00 per pound. How much does this ingredient cost the pharmacy for this batch.

1) In this case, we know that 1 Lb. cost \$94.00, those are the first two factors. We also know we want to figure out how much only 227g would cost, which is the third factor and it's cost is the unknown.

This is how you want to write your two fractions:

 \$94.00 ? 1 Lb. 227 g

2) In this case, The first thing you want to do is make all of your terms the same. You'll do this by converting 1 pound to 454 grams:

 \$94.00 → \$94.00 ? 1 Lb. → 454g 227g

3) Next, we want to multiply the denominator from the unknown side with the numerator on known side and write the product to the left:

 21,338 = \$94.00 ← ? X 454 g ← 227g

4) Next, we want to take this product and divide it by the known sides denominator:

 21,338 \$94.00 → = 47 ÷ ↑ →   → 454g → 227g

5) The calculation you get goes into the numerator on the unknown side and that's YOUR ANSWER!

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