Clinical Applications of Ratio and Proportion¶
Overview¶
This section brings together ratios, proportions, and unit cancellation to solve realistic clinical problems. These are the types of calculations you will encounter in practice.
The Standard Approach¶
For every problem:
- Read the order carefully — note the dose and unit
- Read the stock label — note the concentration as a ratio
- Check units — do they match? If not, convert first
- Set up the unit cancellation chain
- Check which unit remains — is it what you want?
- Calculate and round appropriately
- Ask — is this a reasonable amount to administer?
Oral Tablet Problems¶
Example 1: Order: metformin 1000 mg orally Stock: 500 mg per tablet
Example 2: Order: lisinopril 5 mg orally Stock: 10 mg per tablet
Scored Tablets
Only administer half tablets if the tablet is scored (has a line across the middle designed for splitting). Never split unscored or coated tablets.
Oral Liquid Problems¶
Example 3: Order: amoxicillin 400 mg orally Stock: 250 mg/5 mL suspension
Example 4: Order: ibuprofen 300 mg orally Stock: 100 mg/5 mL suspension
Unit Conversion Required First¶
Example 5: Order: amoxicillin 0.5 g orally Stock: 250 mg per capsule
Example 6: Order: digoxin 0.25 mg orally Stock: 125 mcg per tablet
Weight-Based Problems¶
Example 7: Order: amoxicillin 25 mg/kg orally Patient weight: 44 lb Stock: 250 mg/5 mL
One chain: [\frac{44 \cancel{\text{ lb}}}{1} \times \frac{1 \cancel{\text{ kg}}}{2.2 \cancel{\text{ lb}}} \times \frac{25 \cancel{\text{ mg}}}{1 \cancel{\text{ kg}}} \times \frac{5 \text{ mL}}{250 \cancel{\text{ mg}}} = 10 \text{ mL}]
Reasonableness Check Table¶
| Route | Typical Range | Flag if Outside Range |
|---|---|---|
| Oral tablet | 0.5 - 3 tablets | Recheck order and stock |
| Oral liquid | 5 - 30 mL | Recheck concentration |
| Injectable IM/SC | 0.5 - 3 mL | Recheck order and stock |
| IV push | per protocol | Always verify with second nurse |
Never Administer Without Checking
If your calculation produces an answer outside the typical range, do not administer. Recheck your work, verify the order, check the stock label, and consult a colleague or pharmacist before proceeding.
Practice Problems¶
Problem 1
Order: atenolol 25 mg orally Stock: 50 mg per tablet How many tablets?
Answer
Problem 2
Order: cetirizine 10 mg orally Stock: 5 mg/5 mL syrup How many mL?
Answer
Problem 3
Order: amoxicillin 0.75 g orally Stock: 250 mg per capsule How many capsules?
Answer
Problem 4
Order: ibuprofen 10 mg/kg orally Patient weight: 66 lb Stock: 100 mg/5 mL How many mL?
Answer
Problem 5
Order: digoxin 0.125 mg orally Stock: 62.5 mcg per tablet How many tablets?
Answer
Clinical Tip
Digoxin is a high alert medication — errors can be fatal. Always have a second nurse independently verify your calculation before administering. This applies regardless of how confident you are in your answer.