Study guide
3.1 Whole Numbers and Basic Operations
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
3.1 Whole Numbers and Basic Operations
Key Takeaways Explain This Topic AI
PEMDAS sets the order of operations: Parentheses, Exponents, Multiplication/Division (left to right), then Addition/Subtraction (left to right)
Same-sign multiplication or division gives a positive result; different signs give a negative result
To round, look at the digit immediately to the right: 5 or greater rounds up, less than 5 rounds down
The distributive property a(b + c) = ab + ac lets you break apart multiplication for faster mental math
- Estimation by rounding gives a quick reasonableness check that catches calculator slips on the TEAS
- Last updated: October 2026
Why Whole-Number Operations Matter on the TEAS
The ATI TEAS 7 Mathematics section contains 34 scored questions (plus unscored pretest items) answered in 57 minutes, and the largest sub-content area is Numbers and Algebra . Whole-number arithmetic is the foundation under every other topic: you cannot solve a dosage proportion or read a chart if you stumble on basic order of operations. A four-function on-screen calculator is provided, but it will faithfully compute whatever you type — so the exam really tests whether you know the correct sequence of steps, not whether you can press buttons.
Whole Numbers, Integers, and Place Value
Whole numbers are the non-negative counting numbers: 0, 1, 2, 3, 4, 5, and so on. Integers extend that set to include negatives, giving …, -3, -2, -1, 0, 1, 2, 3, ….
- Term Definition Example
- Whole number Non-negative integer 0, 1, 42, 1000
- Positive integer Whole number greater than zero 1, 2, 3, 4
- Negative integer Integer less than zero -1, -2, -3
- Integer Any positive or negative whole number, plus zero -3, -2, -1, 0, 1, 2, 3
Place value tells you what each digit is worth based on its position. In 4,738 the 4 means 4,000, the 7 means 700, the 3 means 30, and the 8 means 8.
- Place Value Digit in 4,738
- Ones 1 8
- Tens 10 3 (represents 30)
- Hundreds 100 7 (represents 700)
- Thousands 1,000 4 (represents 4,000)
Expanded form: 4,738 = 4,000 + 700 + 30 + 8. Place value is also why you line up decimal points later when adding money or lab values.
Order of Operations (PEMDAS)
When an expression mixes operations, you must evaluate it in a fixed order or you will get the wrong answer. Remember PEMDAS : P arentheses, E xponents, M ultiplication and D ivision (left to right), A ddition and S ubtraction (left to right).
- Letter Operation Example
- P Parentheses (or brackets) (2 + 3) = 5
- E Exponents (powers, roots) 2³ = 8
- M/D Multiply/Divide, left to right 6 × 2 ÷ 3 = 4
- A/S Add/Subtract, left to right 5 + 3 - 2 = 6
A common trap is the M/D and A/S tiers: multiplication and division share a rank and are done in reading order, not "all multiplication first." The same is true of addition and subtraction.
Worked Example: Evaluate 12 + 3 × 4 - 2.
No parentheses or exponents.
Multiply: 3 × 4 = 12, giving 12 + 12 - 2.
Add/subtract left to right: 12 + 12 = 24, then 24 - 2 = 22 .
A test-taker who adds 12 + 3 first gets the wrong answer of 58.
Worked Example (parentheses + exponent): Evaluate (8 - 3)² ÷ 5 + 1.
Parentheses: 8 - 3 = 5, giving 5² ÷ 5 + 1.
Exponent: 5² = 25, giving 25 ÷ 5 + 1.
Divide: 25 ÷ 5 = 5, giving 5 + 1 = 6 .
Properties That Speed Up Mental Math
- Property What it says Example
- Commutative Order doesn't matter (+ and ×) 3 + 5 = 5 + 3
- Associative Grouping doesn't matter (+ and ×) (2 + 3) + 4 = 2 + (3 + 4)
- Distributive Multiply across a sum 2(3 + 4) = 2·3 + 2·4 = 14
- Identity Add 0 or multiply by 1 5 + 0 = 5; 5 × 1 = 5
- Zero Multiply by 0 5 × 0 = 0
The distributive property is the one most worth practicing because it lets you compute things like 6 × 23 as 6(20 + 3) = 120 + 18 = 138 without a calculator.
Factors and Multiples
A factor of a number divides it evenly (no remainder); a multiple is the result of multiplying that number by an integer.
Factors of 12: 1, 2, 3, 4, 6, 12.
Multiples of 12: 12, 24, 36, 48, ….
A prime number has exactly two factors, 1 and itself (2, 3, 5, 7, 11, 13…).
Finding the greatest common factor (GCF) and least common multiple (LCM) is the engine behind simplifying fractions and finding common denominators in the next section.
Signed Numbers
Addition, same signs: add and keep the sign (-4 + -3 = -7).
Addition, different signs: subtract and take the sign of the larger absolute value (-9 + 4 = -5).
Subtraction: add the opposite — 5 - (-3) = 5 + 3 = 8.
Multiplication/Division: same signs → positive; different signs → negative.
- Operation Example Result
- Positive × Positive 3 × 4 12
- Negative × Negative (-3) × (-4) 12
- Positive × Negative 3 × (-4) -12
- Negative × Positive (-3) × 4 -12
- Rounding and Estimation
To round: identify the target place, look at the digit just to its right, round up on 5 or more, down on less than 5, and zero out everything to the right.
Worked Example: Round 3,847 to the nearest hundred. The hundreds digit is 8; the digit to its right is 4 (< 5), so round down to 3,800 .
Estimation rounds before calculating so you can sanity-check a result. To estimate 487 + 312, round to 500 + 300 = 800; the exact answer 799 is reassuringly close. On the TEAS, a fast estimate is your best defense against a mistyped calculator entry.