Rates & Unit Rates

Why This Matters for Nursing: IV drip rates (mL per hour), medication dosing (mg per kg), and vital signs (beats per minute) are all rates. Understanding unit rates helps you calculate exactly what each patient needs.

What You Need to Know

A rate is a ratio that compares two quantities with DIFFERENT units:

• 60 miles per 2 hours
• $15 for 3 items
• 120 mL in 4 hours

A unit rate expresses how much of one thing per ONE unit of another:

• 30 miles per 1 hour (30 mph)
• $5 per 1 item
• 30 mL per 1 hour

🧠 Memory Trick

"Per" means DIVIDE

"Miles per hour" = miles ÷ hours "Price per item" = price ÷ items

To find a unit rate, divide to get "per 1"

Finding Unit Rates

Method:

Divide the first quantity by the second quantity

Example: 240 miles in 4 hours

Unit rate = 240 miles ÷ 4 hours = 60 miles per hour

Using Unit Rates

Once you have a unit rate, multiply to find any amount:

If a car travels 60 mph, how far in 7 hours?

• 60 miles/hour × 7 hours = 420 miles

✏️ Worked Examples

Example 1: Finding Unit Rate

Problem: A 500 mL IV bag runs over 4 hours. What's the rate in mL per hour?

Step 1 — Identify what "per hour" means. A unit rate always tells you the amount "per 1" of something. Here we want mL per 1 hour.

Step 2 — Divide the total by the number of units. 500 mL ÷ 4 hours = 125 mL/hour.

Answer: 125 mL per hour

💡 "Per" always tells you to divide. mL per hour = mL ÷ hours. If you get confused, just remember: the word "per" means ÷.

Example 2: Using Unit Rate

Problem: A medication dosage is 5 mg per kg of body weight. How much for a 70 kg patient?

Step 1 — Identify the unit rate. 5 mg for every 1 kg.

Step 2 — Multiply by the number of units. If 1 kg needs 5 mg, then 70 kg needs 70 × 5 mg.

70 × 5 = 350 mg.

Answer: 350 mg

Example 3: Comparing Unit Rates

Problem: Store A sells 6 bandages for $4.50. Store B sells 10 bandages for $7.00. Which is the better deal?

Step 1 — Find the unit rate (cost per 1 bandage) for each store.

• Store A: $4.50 ÷ 6 bandages = $0.75 per bandage
• Store B: $7.00 ÷ 10 bandages = $0.70 per bandage

Step 2 — Compare. $0.70 < $0.75, so Store B is cheaper per bandage.

Answer: Store B is the better deal

Example 4: Heart Rate — Nursing Context

Problem: A patient's heart beats 18 times in 15 seconds. What's the heart rate in beats per minute?

What we're solving: We have beats per 15 seconds. We need beats per 60 seconds (since 1 minute = 60 seconds).

Step 1 — Set up a proportion. Keep beats on top and seconds on bottom.

18 beats / 15 seconds = x beats / 60 seconds

Step 2 — Cross-multiply. 15 × x = 18 × 60 → 15x = 1,080.

Step 3 — Solve. x = 1,080 ÷ 15 = 72.

Answer: 72 beats per minute

💡 Shortcut: Notice 60 ÷ 15 = 4. So just multiply 18 × 4 = 72. When the second number is a multiple of the first, this shortcut is fast.

Example 5: IV Drip Calculation — Nursing Context

Problem: An IV runs at 50 mL/hour. How long will it take to deliver 400 mL?

Step 1 — Identify what we know and what we need.

• Rate: 50 mL per hour
• Total to deliver: 400 mL
• Find: time (hours)

Step 2 — Use the formula: Time = Total ÷ Rate. Time = 400 mL ÷ 50 mL/hour = 8 hours.

Answer: 8 hours

💡 Pro Tips

• Always check your units: mL/hour is different from hours/mL—make sure you set it up correctly
• To find time: Time = Amount ÷ Rate
• To find amount: Amount = Rate × Time
• When comparing prices: Lower unit price = better deal
• On the TEAS: Watch for different time units (seconds, minutes, hours)—convert as needed

⚠️ Common Mistakes to Avoid

• Dividing in the wrong order: "Miles per hour" means miles ÷ hours, not hours ÷ miles
• Unit confusion: 60 mL/hr ≠ 60 hr/mL — keep track of what goes on top
• Not converting time units: If rate is per minute but you need per hour, multiply by 60
• Forgetting to answer the actual question: Find the unit rate, then use it to calculate what's asked

Quick Reference

Common Healthcare Rates:

• IV rate: mL/hour or drops/minute (gtt/min)
• Dosing: mg/kg (milligrams per kilogram)
• Heart rate: beats/minute (bpm)
• Respiratory rate: breaths/minute

Time Conversions:

• 1 hour = 60 minutes
• 1 minute = 60 seconds
• 1 day = 24 hours

Rates down! 💪 Next up: Order of Operations (PEMDAS)