Ratios & Proportions

Why This Matters for Nursing: Medication mixing, IV drip rates, and staffing calculations all use ratios. "Mix 1 part medication to 3 parts saline" or "1 nurse for every 4 patients" are ratios you'll use daily.

What You Need to Know

A ratio compares two quantities. It can be written three ways: - 1 to 3 - 1:3 - 1/3

A proportion states that two ratios are EQUAL: - 1:3 = 2:6 (both simplify to the same ratio)

🧠 Memory Trick

Cross multiply to solve proportions!

If a/b = c/d, then a × d = b × c

Think of it as an "X" — multiply across the diagonal!

"Cross products are equal"

Setting Up Ratios

Order Matters!

"The ratio of nurses to patients is 1:4" means: - Nurses : Patients = 1 : 4 - Nurses comes first because it's mentioned first

If there are 3 nurses, there are 12 patients (3:12 = 1:4)

Solving Proportions

Method: Cross-Multiplication

Problem: If 2 tablets contain 500 mg, how many mg are in 5 tablets?

Setup:

2 tablets     5 tablets
--------- = -----------
500 mg          x mg

Cross-multiply: - 2 × x = 500 × 5 - 2x = 2500 - x = 1250

Answer: 1,250 mg

✏️ Worked Examples

Example 1: Simple Proportion

Problem: Solve for x: 3/4 = x/20

Step 1 — Set up cross-multiplication. When two fractions are equal (a proportion), you can "cross multiply" — multiply diagonally across the equals sign. Take the top-left times the bottom-right, and set it equal to the bottom-left times the top-right.

3/4 = x/20 → cross multiply → 3 × 20 = 4 × x

Step 2 — Do the multiplication. 3 × 20 = 60. So: 60 = 4x.

Step 3 — Solve for x. Divide both sides by 4: x = 60 ÷ 4 = 15.

Step 4 — Check. Does 3/4 = 15/20? Simplify 15/20 by dividing by 5: 3/4. ✓

Answer: x = 15