6.2 Dosage-Style Proportions

Why Proportions Dominate Dosage Math

In clinical practice you rarely receive a medication in the exact dose ordered. The provider orders 500 mg; the pharmacy stocks 250 mg tablets. The order reads 750 mg; the syrup on the shelf is labeled 250 mg per 5 mL. The ratio-proportion method solves these ordered-versus-available problems cleanly: set up two equal ratios, cross-multiply, and solve for the unknown.

The Ratio-Proportion Setup

The standard form is:

Ordered / Available = Dose to give / On-hand quantity

or equivalently:

Dose1 / Volume1 = Dose2 / Volume2

The key rule: the units must match on both sides. If the left side is mg/mg (ordered mg over available mg), the right side is tablets/tablets or mL/mL. Whatever unit sits in the numerator on the left must sit in the numerator on the right.

Worked Example 1: Tablets

Ordered: 500 mg. Tablets on hand: 250 mg each. How many tablets?

Set up:

500 mg / 250 mg = x tablets / 1 tablet

Cross-multiply: 250x = 500 x 1, so 250x = 500, x = 2.

Answer: 2 tablets.

Sanity check: the ordered dose is twice the strength of one tablet, so two tablets makes sense.

Worked Example 2: Liquid Suspension

Ordered: 750 mg. Syrup on hand: 250 mg per 5 mL. How many mL?

Set up:

750 mg / 250 mg = x mL / 5 mL

Cross-multiply: 250x = 750 x 5 = 3,750, so x = 3,750 / 250 = 15.

Answer: 15 mL.

Sanity check: 750 is three times 250, so you need three times 5 mL = 15 mL. Matches.

Worked Example 3: Weight-Based Dosing

Ordered: 6 mg/kg for a patient weighing 75 kg. What total dose, and how many mL if the stock concentration is 50 mg/mL?

First compute the total dose: 6 mg/kg x 75 kg = 450 mg.

Then set up the proportion for the volume:

450 mg / 50 mg = x mL / 1 mL

Cross-multiply: 50x = 450, x = 9.

Answer: 9 mL.

Dimensional Analysis as an Alternative

The same problems can be solved with dimensional analysis, and many nurses prefer it because it forces units to cancel. Example 2 becomes:

750 mg x (5 mL / 250 mg) = (750 x 5 / 250) mL = 15 mL

The mg cancels, mL survives. Both methods give the same answer; use whichever you find faster and less error-prone under exam conditions. The NEX does not require a particular method — it requires a correct answer.

Worked Example 4: Convert First, Then Proportion

Ordered: 0.3 g. Tablets on hand: 150 mg each. How many tablets?

The order and the stock are in different units (g vs mg), so convert first. Using 1 g = 1,000 mg:

0.3 g x (1,000 mg / 1 g) = 300 mg

Now both sides are in mg. Set up the proportion:

300 mg / 150 mg = x tablets / 1 tablet

Cross-multiply: 150x = 300, x = 2.

Answer: 2 tablets.

Sanity check: the trap here is skipping the g-to-mg conversion. If you had set up 0.3 / 150 directly, you would get 0.002 tablets — an impossible dose (you cannot give a two-thousandth of a tablet). Any answer less than one tablet for an order that is clearly larger than the stock unit is a red flag that a unit conversion was missed. The 0.3 g order is 300 mg, which is twice the 150 mg tablet, so two tablets is the sensible answer.

Choosing a Method

Both ratio-proportion and dimensional analysis solve the same problems. Which should you reach for first?

The NEX grades the answer, not the method, so pick the path that minimizes your chance of a unit or setup error.

Common Traps

• Mismatched units. If ordered is in mcg and available is in mg, convert one before setting up the proportion. 500 mcg is not 500 mg; it is 0.5 mg.
• Dividing instead of multiplying. If the available dose is larger than the ordered dose, your answer should be less than one tablet (or less than the on-hand volume). If you get 3 tablets for an order of 75 mg from 250 mg tablets, you inverted the ratio.
• Forgetting the per unit. "250 mg per 5 mL" means the ratio is 250 mg / 5 mL. Writing 250/5 without units lets you lose track of which side is dose and which is volume.
• Ignoring the sanity check. Always ask: does this answer make sense? If the ordered dose is larger than one unit of stock, the answer should be greater than 1. If smaller, less than 1.

Rounding in Dosage Answers

Nursing-entrance exams usually expect answers rounded to a practical precision — typically one decimal place for mL and tablets, sometimes to the nearest tenth. If a calculation gives 2.33 tablets, the real-world answer is to ask the provider because you cannot accurately split a tablet into thirds, but on the exam, round per the question's stated instructions. Always note the rounding rule stated in the problem.