Ratios¶
What Is a Ratio?¶
A ratio expresses a relationship between two quantities. In nursing, ratios describe concentrations, doses, and rates — how much of something exists relative to something else.
Writing Ratios¶
A ratio can be written three ways — all equivalent:
| Format | Example |
|---|---|
| Fraction | \(\frac{250 \text{ mg}}{1 \text{ tablet}}\) |
| Colon notation | 250 mg : 1 tablet |
| Word form | 250 mg per tablet |
In calculations, the fraction format is preferred because it integrates cleanly with dimensional analysis.
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 |
Reading Concentration Ratios
A concentration like 250 mg/5 mL tells you exactly how much drug is in how much liquid. This is your stock ratio — the foundation of every liquid medication 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 (mg per mL)?
There are 50 mg in every 1 mL of this solution.
Equivalent Ratios¶
Two ratios are equivalent if they simplify to the same value. This is the foundation of proportion — covered in the next section.
All three express the same concentration.
Clinical Application¶
Example 1: A stock solution is labeled 1000 mg/250 mL. Express as a unit rate.
There are 4 mg of drug in every 1 mL.
Example 2: Two solutions are available: - Solution A: 500 mg/10 mL - Solution B: 250 mg/4 mL
Which is more concentrated?
Solution A unit rate: [\frac{500 \text{ mg}}{10 \text{ mL}} = \frac{50 \text{ mg}}{1 \text{ mL}}]
Solution B unit rate: [\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
Problem 2
A stock solution contains 125 mg/5 mL. What is the unit rate in mg/mL?
Answer
Problem 3
Are these ratios equivalent? \(\frac{250 \text{ mg}}{5 \text{ mL}}\) and \(\frac{500 \text{ mg}}{10 \text{ mL}}\)
Answer
Simplify both to unit rates: [\frac{250}{5} = 50 \text{ mg/mL}] [\frac{500}{10} = 50 \text{ mg/mL}]
Yes — they are equivalent.
Problem 4
A medication label reads 0.5 mg/2 mL. Express as a unit rate.
Answer
Problem 5
Which solution is more concentrated? - Solution A: 200 mg/4 mL - Solution B: 150 mg/2 mL
Answer
Solution A: [\frac{200 \text{ mg}}{4 \text{ mL}} = 50 \text{ mg/mL}]
Solution B: [\frac{150 \text{ mg}}{2 \text{ mL}} = 75 \text{ mg/mL}]
Solution B is more concentrated.
Clinical Tip
Always identify the stock ratio from the medication label before starting any calculation. Writing it down explicitly as a fraction prevents confusion and sets up your dimensional analysis chain correctly.