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Proportions

A proportion states that two ratios are equal:

\[\frac{a}{b} = \frac{c}{d}\]

In nursing, proportions appear any time you apply a stock ratio to a specific order. The stock ratio and the ordered dose are two equal expressions of the same relationship — one known, one to be found.

Proportions and Stock Ratios

Every dosage calculation is a proportion. You have a stock ratio from the label, and you need to find the quantity that matches the ordered dose.

Stock: 250 mg per tablet Order: 500 mg

These form a proportion:

\[\frac{250 \text{ mg}}{1 \text{ tablet}} = \frac{500 \text{ mg}}{x \text{ tablets}}\]

The same ratio holds — you just need to find x.

Solving with Dimensional Analysis

Rather than solving for x algebraically, dimensional analysis sets up the proportion as a cancellation chain:

\[500 \cancel{\text{ mg}} \times \frac{1 \text{ tablet}}{250 \cancel{\text{ mg}}} = 2 \text{ tablets}\]

The stock ratio is written as a factor, oriented so mg cancels. The result is x directly — no algebra needed.

This is why DA is the preferred method. The proportion structure is still there; the cancellation handles the solving.

Alternative methods

If you have learned cross-multiplication or ratio-proportion algebraic solving, those methods work for the same problems. They are covered in Additional Methods.

Reasonableness Check

Before accepting any answer, ask:

  • Would a nurse realistically give this many tablets?
  • Is this volume reasonable to administer?
  • Does the direction make sense — more drug, more volume?

General guidelines:

  • Oral tablets: rarely more than 3 tablets per dose
  • Oral liquid: typically 5–30 mL per dose

If your answer falls outside these ranges, recheck the setup.

Clinical Application

Example 1 — oral suspension: Stock: 125 mg/5 mL Order: 250 mg How many mL?

\[250 \cancel{\text{ mg}} \times \frac{5 \text{ mL}}{125 \cancel{\text{ mg}}} = \frac{1250}{125} = 10 \text{ mL}\]

Example 2 — injectable: Stock: 40 mg/mL Order: 100 mg How many mL?

\[100 \cancel{\text{ mg}} \times \frac{1 \text{ mL}}{40 \cancel{\text{ mg}}} = \frac{100}{40} = 2.5 \text{ mL}\]

Practice Problems

Problem 1

Stock: 500 mg per tablet Order: 1000 mg How many tablets?

Answer
\[1000 \cancel{\text{ mg}} \times \frac{1 \text{ tablet}}{500 \cancel{\text{ mg}}} = 2 \text{ tablets}\]

Problem 2

Stock: 250 mg/5 mL Order: 375 mg How many mL?

Answer
\[375 \cancel{\text{ mg}} \times \frac{5 \text{ mL}}{250 \cancel{\text{ mg}}} = \frac{1875}{250} = 7.5 \text{ mL}\]

Problem 3

Stock: 0.25 mg per tablet Order: 0.5 mg How many tablets?

Answer
\[0.5 \cancel{\text{ mg}} \times \frac{1 \text{ tablet}}{0.25 \cancel{\text{ mg}}} = 2 \text{ tablets}\]

Problem 4

Stock: 10 mg/mL Order: 25 mg How many mL?

Answer
\[25 \cancel{\text{ mg}} \times \frac{1 \text{ mL}}{10 \cancel{\text{ mg}}} = 2.5 \text{ mL}\]

Problem 5

Stock: 80 mg/2 mL Order: 60 mg How many mL?

Answer
\[60 \cancel{\text{ mg}} \times \frac{2 \text{ mL}}{80 \cancel{\text{ mg}}} = \frac{120}{80} = 1.5 \text{ mL}\]

Self-Check