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Ratios

A ratio expresses a relationship between two quantities. In nursing, ratios describe concentrations, doses, and rates.

Writing Ratios

A ratio can be written three ways:

Format Example
Fraction \(\frac{250 \text{ mg}}{1 \text{ tablet}}\)
Colon notation 250 mg : 1 tablet
Word form 250 mg per tablet

In calculations, fraction format is preferred because it integrates directly into a dimensional analysis chain.

Ratios in Medication Labels

Every medication label expresses a ratio:

Label Ratio meaning
500 mg per tablet 500 mg : 1 tablet
250 mg/5 mL 250 mg : 5 mL
10 units/mL 10 units : 1 mL
0.9% NaCl 0.9 g : 100 mL

The stock ratio

A concentration like 250 mg/5 mL tells you exactly how much drug is in how much liquid. This is your stock ratio — write it as a fraction before starting any calculation.

Unit Rates

A unit rate simplifies a ratio so the denominator equals 1. This makes comparisons and calculations easier.

Example: Stock is 250 mg/5 mL. What is the unit rate?

\[\frac{250 \text{ mg}}{5 \text{ mL}} = \frac{50 \text{ mg}}{1 \text{ mL}}\]

There are 50 mg in every 1 mL of this solution.

Equivalent Ratios

Two ratios are equivalent if they simplify to the same unit rate.

\[\frac{250 \text{ mg}}{5 \text{ mL}} = \frac{500 \text{ mg}}{10 \text{ mL}} = \frac{50 \text{ mg}}{1 \text{ mL}}\]

All three express the same concentration. Recognizing equivalent ratios lets you verify that two labels represent the same dose.

Clinical Application

Example 1 — unit rate from an IV label: A stock solution is labeled 1000 mg/250 mL. Express as a unit rate.

\[\frac{1000 \text{ mg}}{250 \text{ mL}} = \frac{4 \text{ mg}}{1 \text{ mL}}\]

Example 2 — comparing concentrations: Two solutions are available:

  • Solution A: 500 mg/10 mL
  • Solution B: 250 mg/4 mL

Which is more concentrated?

\[\text{A: } \frac{500 \text{ mg}}{10 \text{ mL}} = \frac{50 \text{ mg}}{1 \text{ mL}}\]
\[\text{B: } \frac{250 \text{ mg}}{4 \text{ mL}} = \frac{62.5 \text{ mg}}{1 \text{ mL}}\]

Solution B is more concentrated.

Practice Problems

Problem 1

Write the ratio 5 mg per 2 mL in fraction format.

Answer
\[\frac{5 \text{ mg}}{2 \text{ mL}}\]

Problem 2

A stock solution contains 125 mg/5 mL. What is the unit rate?

Answer
\[\frac{125 \text{ mg}}{5 \text{ mL}} = \frac{25 \text{ mg}}{1 \text{ mL}}\]

Problem 3

Are these ratios equivalent? \(\frac{250 \text{ mg}}{5 \text{ mL}}\) and \(\frac{500 \text{ mg}}{10 \text{ mL}}\)

Answer

[\frac{250}{5} = 50 \text{ mg/mL} \qquad \frac{500}{10} = 50 \text{ mg/mL}] Yes — equivalent.

Problem 4

A medication label reads 0.5 mg/2 mL. Express as a unit rate.

Answer
\[\frac{0.5 \text{ mg}}{2 \text{ mL}} = \frac{0.25 \text{ mg}}{1 \text{ mL}}\]

Problem 5

Which solution is more concentrated?

  • Solution A: 200 mg/4 mL
  • Solution B: 150 mg/2 mL
Answer

[\text{A: } \frac{200}{4} = 50 \text{ mg/mL} \qquad \text{B: } \frac{150}{2} = 75 \text{ mg/mL}] Solution B is more concentrated.

Self-Check