Study guide
3.2 Fractions
ATI TEAS 7 Nursing Admission
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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
3.2 Fractions
Key Takeaways Explain This Topic AI
Add or subtract fractions only after rewriting them over a common denominator, usually the least common denominator (LCD)
Multiply fractions straight across (numerators × numerators, denominators × denominators), then simplify
Divide fractions by multiplying by the reciprocal of the second fraction (keep–change–flip)
Simplify any fraction by dividing numerator and denominator by their greatest common factor (GCF)
Convert a mixed number to an improper fraction with (whole × denominator) + numerator over the same denominator
Last updated: October 2026
Fractions on the TEAS
Fractions appear throughout the Numbers and Algebra portion of the ATI TEAS 7, and they reappear inside dosage, measurement, and data questions. A fraction represents part of a whole and is written as a numerator over a denominator . The denominator names how many equal parts make a whole; the numerator counts how many of those parts you have. Because the provided calculator handles decimals more easily than fractions, knowing the hand methods below keeps you accurate when answer choices are written in fraction form.
Types of Fractions
- Term Definition Example
- Numerator Top number (parts you have) In ¾, the numerator is 3
- Denominator Bottom number (total equal parts) In ¾, the denominator is 4
- Proper fraction Numerator < denominator (value < 1) ¾, ½, ⅔
- Improper fraction Numerator ≥ denominator (value ≥ 1) 5/4, 7/3, 8/8
- Mixed number Whole number plus a fraction 1½, 2¾, 3⅔
- Converting Between Improper Fractions and Mixed Numbers
Improper → Mixed: divide the numerator by the denominator. The quotient is the whole number, the remainder is the new numerator, and the denominator stays the same.
Worked Example: Convert 11/4. 11 ÷ 4 = 2 remainder 3, so 11/4 = 2¾ .
Mixed → Improper: multiply the whole number by the denominator, add the numerator, and keep the denominator.
Worked Example: Convert 3¾. (3 × 4) + 3 = 15, so 3¾ = 15/4 .
You will almost always convert mixed numbers to improper fractions before multiplying or dividing — skipping this step is a common setup error on fraction questions.
Equivalent Fractions and Simplifying
Two fractions are equivalent if they name the same value. Multiply or divide the top and bottom by the same nonzero number to generate equivalents: 1/2 = 2/4 = 3/6 = 4/8 = 50/100.
To simplify (reduce) a fraction, divide the numerator and denominator by their greatest common factor (GCF) .
Worked Example: Simplify 12/16. The GCF of 12 and 16 is 4: 12 ÷ 4 = 3 and 16 ÷ 4 = 4, so 12/16 = ¾ . Reduce fully before you match your answer to the choices.
Adding and Subtracting Fractions
Same denominator: add or subtract the numerators and keep the denominator. 3/8 + 2/8 = 5/8.
Different denominators: find the least common denominator (LCD) — the smallest common multiple of the denominators — rewrite each fraction, then combine.
Find the LCD.
Rewrite each fraction with that denominator.
Add or subtract the numerators.
Simplify if possible.
Worked Example: Compute 1/3 + 1/4. The LCD of 3 and 4 is 12. Rewrite: 1/3 = 4/12 and 1/4 = 3/12. Add: 4/12 + 3/12 = 7/12 (already in lowest terms).
Worked Example (mixed numbers): Compute 2½ + 1¾. Convert to improper: 5/2 + 7/4. LCD is 4: 5/2 = 10/4. Add: 10/4 + 7/4 = 17/4 = 4¼ .
Multiplying Fractions
Multiply numerators together and denominators together, then simplify. You do not need a common denominator.
Worked Example: 2/3 × 3/4 = (2 × 3)/(3 × 4) = 6/12 = ½ .
Cross-cancel before multiplying to keep numbers small: in 2/3 × 3/4 the 3s cancel, leaving 2/1 × 1/4 = 2/4 = ½. A whole number multiplies as if it sits over 1: 5 × 2/3 = 5/1 × 2/3 = 10/3 = 3⅓.
Dividing Fractions
Use keep–change–flip : keep the first fraction, change ÷ to ×, and flip the second fraction to its reciprocal .
Worked Example: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3 = 2⅔ .
Worked Example (mixed): 2½ ÷ ¾. Convert: 5/2 ÷ 3/4 = 5/2 × 4/3 = 20/6 = 3⅓ .
Comparing Fractions
Common-denominator method: rewrite both with the same denominator and compare numerators. To compare 3/4 and 5/6, use 12ths: 3/4 = 9/12 and 5/6 = 10/12, so 3/4 < 5/6.
Cross-multiply method: multiply each numerator by the other denominator. For 3/4 and 5/6: 3 × 6 = 18 versus 4 × 5 = 20; since 18 < 20, 3/4 < 5/6.
Fractions in Healthcare
- Application Example
- Medication dosage Give ½ tablet of a 250 mg pill
- IV progress ¾ of the bag has infused
- Intake/output Patient drank 2⅓ cups of water
- Scheduling Medication every 4½ hours
These contexts are why the TEAS emphasizes fractions: a nurse who reduces 12/16 to ¾ or correctly halves a dose protects patient safety, and the exam mirrors that reasoning.