Study guide
3.4 Ratios and Proportions
ATI TEAS 7 Nursing Admission
Track your progress as you read
Finished sections get a check mark.
1 Introduction to the ATI TEAS 7
1.1 About the ATI TEAS 7 Exam 1.2 Content Area Breakdown 1.3 Scoring and Program Requirements 1.4 Building Your TEAS Study Plan
2 Reading
2.1 Identifying the Main Idea 2.2 Making Inferences and Drawing Conclusions 2.3 Summarizing and Paraphrasing 2.4 Understanding Text Structure 2.5 Author's Purpose, Tone, and Point of View 2.6 Evaluating Arguments, Evidence, and Credibility 2.7 Integrating Information and Interpreting Graphics 2.8 TEAS Reading Strategies, Pacing, and Practice
3 Mathematics
3.1 Whole Numbers and Basic Operations 3.2 Fractions 3.3 Decimals and Percentages 3.4 Ratios and Proportions 3.5 Algebra and Equations 3.6 Measurement and Unit Conversions 3.7 Statistics and Data Interpretation 3.8 Geometry Basics
4 Science
4.1 The Cardiovascular System 4.2 The Respiratory System 4.3 The Digestive System 4.4 The Nervous System 4.5 The Musculoskeletal System 4.6 The Urinary and Reproductive Systems 4.7 Cell Biology and Genetics 4.8 Chemistry Basics 4.9 Scientific Reasoning and the Scientific Method
5 English & Language Usage
5.1 Grammar and the Parts of Speech 5.2 Sentence Structure 5.3 Punctuation 5.4 Spelling and Word Usage 5.5 Vocabulary in Context and Word Parts 5.6 Paragraph Organization and the Writing Process 5.7 Formal vs. Informal Language, Audience, and Tone 5.8 TEAS English Section Strategies and Pacing
3.4 Ratios and Proportions
Key Takeaways Explain This Topic AI
A ratio compares two quantities and can be written 3:4, 3/4, or "3 to 4"
A proportion states two ratios are equal (a/b = c/d) and is solved by cross-multiplication: ad = bc
A unit rate has a denominator of 1, such as miles per hour or mL per hour
In dosage math, keep like units aligned: Have/Quantity = Desired/x
- Always label units and check that the answer is reasonable before selecting it
- Last updated: October 2026
Ratios and Proportions on the TEAS
Ratios and proportions are a practical math skill for nursing, and the ATI TEAS 7 tests them within Numbers and Algebra . Medication calculations — how many tablets, how many milliliters, how many drops per minute — are proportions in disguise. Mastering the setup once lets you answer a whole family of questions with the same four steps.
Ratios
A ratio compares two quantities and can be written three equivalent ways.
- Format Example
- With a colon 3:4
- As a fraction 3/4
- With the word "to" 3 to 4
Ratios should be reduced just like fractions: 6:8 simplifies to 3:4. They come in three flavors.
- Type Description Example
- Part-to-part Compares parts of a whole 3 nurses to 4 doctors
- Part-to-whole Compares a part to the total 3 nurses out of 7 staff
- Rate Compares different units 60 miles per hour
- Unit Rates
- A unit rate has a denominator of 1, which makes comparison easy. Divide to get "per one."
Worked Example: A nurse walks 12 miles in 3 hours. The unit rate is 12 ÷ 3 = 4 miles per hour . Unit rates also tell you the better buy or the faster infusion when two options are stated over different amounts.
Proportions and Cross-Multiplication
A proportion is an equation stating two ratios are equal, such as 1/2 = 2/4. The defining property is cross-multiplication : if a/b = c/d, then ad = bc . This turns a fraction equation into a simple linear equation you can solve for the unknown.
Worked Example: Solve 3/4 = x/12.
Cross-multiply: 3 × 12 = 4 × x.
Simplify: 36 = 4x.
Divide both sides by 4: x = 9 .
Follow four steps every time: (1) identify the knowns and the unknown, (2) set up the proportion with units labeled, (3) cross-multiply and solve, and (4) check that the answer is reasonable.
Setting Up Proportions Correctly
The golden rule is keep like units on the same side (or in the same position top-and-bottom) of the proportion. Mixing milligrams with milliliters across the equals sign is a common error.
Worked Example: If 500 mg is contained in 10 mL, how many mL contain 250 mg? Set up mg over mL on both sides: 500 mg / 10 mL = 250 mg / x mL. Cross-multiply: 500x = 250 × 10 = 2,500, so x = 5 mL .
Dosage Calculations Using Proportions
A reliable nursing formula is Have / Quantity = Desired / x , where "Have" is the strength on hand, "Quantity" is the form it comes in (one tablet or some mL), and "Desired" is the ordered dose.
Worked Example (tablets): Order: 750 mg. Available: 250 mg tablets. 250 mg / 1 tablet = 750 mg / x → 250x = 750 → x = 3 tablets .
Worked Example (liquid with unit conversion): Order: 0.5 g. Available: 250 mg per 5 mL. First convert grams to milligrams: 0.5 g = 500 mg. Then 250 mg / 5 mL = 500 mg / x mL → 250x = 2,500 → x = 10 mL . Converting units before you set up the proportion is essential — a 0.5 versus 500 mismatch is a tenfold error.
Scale, Maps, and Similar Figures
Proportions also handle scale drawings and similar figures, where corresponding sides keep the same ratio.
Worked Example: A map scale reads 1 inch = 50 miles. Two cities are 3.5 inches apart. Set up 1 inch / 50 miles = 3.5 inches / x miles → x = 50 × 3.5 = 175 miles .
Direct vs. Inverse Proportion
- Type Relationship Model Everyday example
- Direct Both rise or both fall together y = kx More hours worked → more pay
- Inverse One rises as the other falls xy = k More workers → less time to finish
For a direct proportion you set the ratios equal and cross-multiply. For an inverse proportion you set the products equal.
Worked Example (inverse): If 3 nurses finish a task in 8 hours, how long would 6 nurses take? Inverse means workers × time is constant: 3 × 8 = 6 × x → 24 = 6x → x = 4 hours . Doubling the workers halves the time, which passes the reasonableness check.
Common Healthcare Proportion Setups
- Scenario Proportion setup
- Medication dosing Dose ordered / Dose available = x / Volume
- IV flow rate Volume / Time = mL per hour
- Concentration Drug / Solution = percent or ratio
- Staffing ratio Nurses / Patients = required staff
Whenever a TEAS question gives you a known relationship and asks for a fourth value, reach for a proportion, label the units, cross-multiply, and confirm the magnitude makes sense before answering.