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Arithmetic Fundamentals

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1 Introduction to the OAR

About the OAR Who Takes the OAR and Why Study Plan and Test-Day Strategy

2 Math Skills Test (MST)

Arithmetic Fundamentals Fractions, Ratios, and Proportions Percentages and Real-World Applications Algebra Essentials Geometry Foundations Word Problems, Statistics, and Data Interpretation

3 Reading Comprehension Test (RCT)

RCT Overview and Core Strategies Main Idea and Purpose Questions Detail, Fact, and Inference Questions Vocabulary in Context and Author Tone Advanced Reading Strategies and Passage Types RCT Practice Passages and Questions

4 Mechanical Comprehension Test (MCT)

Forces and Newton's Laws of Motion Energy, Work, and Power Simple Machines and Mechanical Advantage Gears, Belts, and Rotational Motion Fluids, Pressure, and Hydraulics Electricity, Circuits, and Magnetism Motion, Heat, and Thermodynamics MCT Practice Problems and Review

5 Full Practice Tests and Final Review

Practice Test: Math Skills Practice Test: Reading Comprehension Practice Test: Mechanical Comprehension Final Review and Test-Day Preparation

Arithmetic Fundamentals

Key Takeaways Explain This Topic AI

The OAR Math Skills Test covers 30 questions in 40 minutes with no calculator allowed.

Arithmetic is the foundation — master order of operations, integers, decimals, and mental math before moving to algebra.

Estimation is a powerful tool: when answer choices are spread apart, a quick estimate can save 30+ seconds per question.

Negative number rules and absolute value come up frequently in OAR math questions.

Practice mental multiplication and division daily until basic operations feel effortless.

Last updated: March 2026

The OAR Math Skills Test (MST) has 30 questions in 40 minutes , giving you about 80 seconds per question . That sounds generous until you hit multi-step problems without a calculator. Arithmetic fluency — doing basic operations quickly and accurately in your head — is the single most important skill for this subtest.

Order of Operations (PEMDAS)

Every math section on every standardized test depends on this. If you get the order wrong, you get the answer wrong, even if every individual calculation is correct.

  • Step Operation Example
  • P Parentheses Solve (3 + 2) first → 5
  • E Exponents Then 5² → 25
  • M/D Multiplication / Division (left to right) 25 × 2 ÷ 5 → 50 ÷ 5 → 10
  • A/S Addition / Subtraction (left to right) 10 + 3 - 1 → 12
  • Common PEMDAS Traps
  • Multiplication and Division are equal priority — process left to right, not multiplication first
  • Addition and Subtraction are equal priority — process left to right
  • Nested parentheses — work from the innermost set outward
  • Negative signs before parentheses — distribute the negative to every term inside

Example: What is 8 - 2(3 + 1)²?

  • Parentheses: 3 + 1 = 4
  • Exponents: 4² = 16
  • Multiplication: 2 × 16 = 32
  • Subtraction: 8 - 32 = -24
  • Integer Operations
  • Rules for Signed Numbers
  • Operation Rule Example
  • Positive + Positive Add, result is positive 7 + 3 = 10
  • Negative + Negative Add magnitudes, result is negative (-7) + (-3) = -10
  • Different signs (add) Subtract smaller from larger, keep sign of larger (-7) + 3 = -4
  • Positive × Positive Result is positive 5 × 3 = 15
  • Negative × Negative Result is positive (-5) × (-3) = 15
  • Different signs (multiply) Result is negative (-5) × 3 = -15
  • Division Same sign rules as multiplication (-12) ÷ (-3) = 4
  • Absolute Value

The absolute value of a number is its distance from zero on the number line, always non-negative.

  • Expression Value Reasoning
  • |7| 7 Distance from 0 is 7
  • |-7| 7 Distance from 0 is 7
  • |0| 0 Already at 0
  • |5| -5 Negative sign is outside the absolute value
  • |-3 + 1| 2 Evaluate inside first: -3 + 1 = -2, then |-2| = 2
  • Decimal Operations
  • Addition and Subtraction

Line up the decimal points and fill in zeros as needed:

  • 12.45
  • 3.7 → becomes + 3.70 16.15
  • Multiplication

Multiply as if there were no decimals, then count total decimal places in both factors:

  • 2.5 × 1.3: Multiply 25 × 13 = 325, then place decimal (1 + 1 = 2 places) → 3.25
  • Division

Move the decimal in the divisor to make it a whole number, then move the decimal in the dividend the same number of places:

  • 7.2 ÷ 0.3: Move both one place → 72 ÷ 3 = 24
  • Mental Math Techniques
  • Break-Apart Method

Split one number to make the multiplication easier:

  • 23 × 7 = (20 × 7) + (3 × 7) = 140 + 21 = 161
  • 45 × 12 = (45 × 10) + (45 × 2) = 450 + 90 = 540
  • Compensation Method

Round to a convenient number, then adjust:

  • 99 × 6 = (100 × 6) - 6 = 600 - 6 = 594
  • 48 × 5 = (50 × 5) - (2 × 5) = 250 - 10 = 240
  • Doubling and Halving

When one factor is even, halve it and double the other:

  • 16 × 35 = 8 × 70 = 560
  • 14 × 25 = 7 × 50 = 350
  • Division Shortcuts
  • Divisor Shortcut
  • ÷ 2 Halve the number
  • ÷ 4 Halve twice
  • ÷ 5 Multiply by 2 then divide by 10
  • ÷ 8 Halve three times
  • ÷ 9 The digits of the result sum to 9 for multiples
  • ÷ 10 Move decimal one place left
  • ÷ 25 Multiply by 4 then divide by 100