Ratios, Proportions, and Percentages

Proportional reasoning is one of the most heavily tested ideas on the TEAS Math section — and the same skill underlies dosage calculations in nursing practice.

Ratios

A ratio compares two quantities. It can be written as 3:4, "3 to 4", or 3/4. Order matters — a 3:4 ratio of nurses to patients is not the same as 4:3.

Proportions

A proportion states that two ratios are equal. Solve one with cross-multiplication: if 3/4 = x/20, then 4x = 60, so x = 15.

Percentages

"Percent" means "per hundred." Convert a percent to a decimal by moving the decimal point two places left: 25% = 0.25. To find a percentage of a number, multiply: 25% of 80 = 0.25 × 80 = 20.

Percent change

Percent change = (new value − original value) ÷ original value × 100. A drop from 50 to 40 is (40 − 50) ÷ 50 = −20%.

Key takeaways

• Cross-multiply to solve a proportion.
• Convert a percent to a decimal before multiplying.
• Percent change is always measured against the original amount.