Percent Problems (Percent Of, Percent Change)

Why This Matters for Nursing: Calculating percent change in vital signs, determining what percent of patients responded to treatment, or figuring out percent concentration of medications—percent problems are everywhere in healthcare.

What You Need to Know

There are three main types of percent problems:

1. Finding a percent of a number: "What is 15% of 80?"
2. Finding what percent one number is of another: "12 is what percent of 48?"
3. Percent change: "Price went from $50 to $65. What's the percent increase?"

🧠 Memory Trick

The word "OF" means MULTIPLY

"What is 25% OF 80?" → 0.25 × 80

"IS over OF equals PERCENT over 100"

Set up a proportion: Part/Whole = Percent/100

Type 1: Finding a Percent of a Number

"What is 20% of 150?"

Method:

1. Convert percent to decimal: 20% = 0.20
2. Multiply: 0.20 × 150 = 30

Formula:

Part = Percent × Whole

Type 2: Finding the Percent

"15 is what percent of 60?"

Method:

1. Divide the part by the whole: 15 ÷ 60 = 0.25
2. Convert to percent: 0.25 = 25%

Formula:

Percent = Part ÷ Whole × 100

Type 3: Percent Change (Increase or Decrease)

"A patient's heart rate went from 80 to 92. What's the percent increase?"

Formula:

Percent Change = (New - Original) ÷ Original × 100

Method:

1. Find the change: 92 - 80 = 12
2. Divide by the original: 12 ÷ 80 = 0.15
3. Convert to percent: 15% increase

✏️ Worked Examples

Example 1: Percent Of

Problem: A hospital has 250 beds. If 78% are occupied, how many beds are filled?

Step 1 — Translate the question into math. "78% OF 250" — the word "of" means multiply. So we need 78% × 250.

Step 2 — Convert the percent to a decimal. 78% → move decimal 2 left → 0.78.

Step 3 — Multiply. 0.78 × 250 = 195.

Answer: 195 beds

💡 Quick check: 78% is close to 80%, and 80% of 250 = 200. Our answer of 195 is close to 200 — makes sense!