Ratio and Proportion in Nursing Math

Why Nurses Need Ratios and Proportions

Almost every medication calculation in nursing comes down to a ratio or proportion. Whether you're figuring out how many tablets, how many mL, or how fast an IV drips — you're using the same math.

This lesson ties together everything you've learned into the nursing context.

The Four Core Calculations

1. Oral/Injectable Dosage

Formula: D/H × Q (Desired ÷ Have × Quantity)

Order: 500 mg. Available: 250 mg/5 mL

500/250 × 5 = 10 mL

2. Weight-Based Dosage

Dose = Weight (kg) × mg/kg

Order: 15 mg/kg. Patient: 70 kg

70 × 15 = 1,050 mg

3. IV Flow Rate

gtt/min = (Volume × Drop factor) ÷ Time in minutes

1,000 mL over 8 hrs, 15 gtt/mL set

(1,000 × 15) ÷ 480 = 31 gtt/min

4. Dilution/Concentration

C₁V₁ = C₂V₂

Dilute 50 mL of 10% to 2%

10 × 50 = 2 × V₂ → V₂ = 250 mL total

The Universal Strategy

Every nursing math problem follows the same pattern:
1. Identify what you know and what you need
2. Set up a proportion with matching units
3. Cross multiply and solve
4. Check: does the answer make sense?

💡 TEAS exam tip: Practice setting up the proportion before solving. Most errors come from incorrect setup, not arithmetic. Write out the units on both sides to make sure they match.

🎯 Practice Problems

1. Order: 750 mg. Available: 500 mg per 10 mL. How many mL to give?

A) 7.5 mL

B) 10 mL

C) 15 mL

D) 20 mL

2. Patient weighs 154 lbs. Order: 10 mg/kg. What is the dose? (1 kg = 2.2 lbs)

A) 350 mg

B) 500 mg

C) 700 mg

D) 1,540 mg

3. Infuse 500 mL over 4 hours with a 20 gtt/mL set. What drip rate?

A) 25 gtt/min

B) 42 gtt/min

C) 63 gtt/min

D) 100 gtt/min

Want more practice?

5 more problems are ready for you. Enter your email to unlock extra practice on all lessons.

No spam, ever. Unsubscribe anytime.

🎯 Bonus Practice

1. How much NaCl in 1 liter of 0.9% saline?

A) 0.9 g

B) 9 g

C) 90 g

D) 0.09 g

2. Order: 1,200 mg/day in 3 divided doses. Available: 200 mg tablets. How many tablets per dose?

A) 1

B) 2

C) 3

D) 6

3. A child weighs 44 lbs. Safe dose range: 20–40 mg/kg/day. What is the safe daily range?

A) 200–400 mg

B) 400–800 mg

C) 440–880 mg

D) 880–1,760 mg

4. An IV bag has 250 mL left running at 50 mL/hr. How long until it's empty?

A) 2.5 hours

B) 3 hours

C) 5 hours

D) 12,500 hours

5. Dilute 20 mL of 25% solution to 5%. What final volume? How much water to add?

A) 80 mL total, add 60 mL

B) 100 mL total, add 80 mL

C) 50 mL total, add 30 mL

D) 125 mL total, add 105 mL