Arithmetic Fundamentals
Key Takeaways
- 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.
Arithmetic Fundamentals
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 | ||
| 0 | ||
| - | 5 | |
| -3 + 1 |
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 |
What is the value of 6 + 3 × 4 - 2?
What is (-8) × (-3) + (-2)?
Which mental math technique would be fastest for computing 47 × 8?
What is 3.6 ÷ 0.12?