Order of Operations Quiz: 24 Multiple-Choice Questions
This quiz assesses middle school and Pre‑Algebra skills for evaluating numerical expressions with grouping symbols, exponents, and implied multiplication. It targets the exact decision points emphasized in standards-based instruction (e.g., CCSS 5.OA and 6.EE): applying operation priorities correctly and working left-to-right when operations share the same level. Use it to tighten accuracy on multi-step expressions you’ll see on classroom tests.
True / False
True / False
True / False
Put in order
Put in order
True / False
Put in order
Put in order
Put in order
Put in order
Put in order
True / False
Frequent Order of Operations Errors in Mixed Expressions (and Quick Fixes)
Most wrong answers come from a small set of habits. Use these fixes to eliminate the most common distractors.
1) Treating PEMDAS as a strict “M before D” and “A before S” rule
Problem: Students do division after multiplication (or subtraction after addition) even when the expression reads left-to-right.
Fix: Multiplication and division share a level—compute left to right. Same for addition and subtraction.
2) Skipping implied multiplication next to parentheses
Problem: In 3(5 − 2), some readers ignore the multiplication or incorrectly “add the 3 into the parentheses.”
Fix: Read adjacency as multiplication: 3 × (5 − 2). Evaluate the parentheses first, then multiply.
3) Misreading negatives with exponents
Problem: Confusing −32 with (−3)2.
Fix: Exponents apply to what’s immediately attached. −32 = −(32), but (−3)2 is positive.
4) “Combining” across multiplication or division
Problem: Doing (2 + 5) × 3 when the expression is 2 + 5 × 3.
Fix: Compute products/quotients before adding/subtracting unless parentheses change the grouping.
5) Collapsing a chain of operations as if it were one chunk
Problem: Turning 18 ÷ 3 × 2 into 18 ÷ (3 × 2).
Fix: Only create a grouped denominator if parentheses (or a fraction bar) actually show that grouping.
6) Rounding or simplifying too early
Problem: Rounding during multi-step division/multiplication leads to “close” answer choices.
Fix: Keep exact fractions until the final step; simplify by canceling factors instead of rounding decimals.
Step-by-Step Order of Operations Walkthrough (Parentheses, Exponents, Implied ×)
Work the expression below exactly the way a strong multiple-choice solution should be shown on paper.
Example: Evaluate
8 − 23 + 3(6 − 4)2 ÷ 3 + 12 ÷ 4 × 5
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Grouping symbols (parentheses) first
(6 − 4) = 2, so the expression becomes:
8 − 23 + 3(2)2 ÷ 3 + 12 ÷ 4 × 5
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Exponents
23 = 8 and (2)2 = 4:
8 − 8 + 3 × 4 ÷ 3 + 12 ÷ 4 × 5
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Multiplication and division left-to-right
For 3 × 4 ÷ 3: 3 × 4 = 12, then 12 ÷ 3 = 4.
For 12 ÷ 4 × 5: 12 ÷ 4 = 3, then 3 × 5 = 15.
Now you have:
8 − 8 + 4 + 15
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Addition and subtraction left-to-right
8 − 8 = 0, then 0 + 4 + 15 = 19.
Why the wrong choices look tempting
- Doing × before ÷ in 12 ÷ 4 × 5 as 12 ÷ (4 × 5) gives 12 ÷ 20 = 0.6, which can still “fit” distractors if earlier steps were also off.
- Forgetting implied multiplication and treating 3(2)2 as 3 + 22 changes the structure of the expression and produces a plausible but incorrect total.
Best self-check: After exponents, rewrite the expression using only × and ÷ with clear left-to-right steps before touching any + or −.
Printable PEMDAS Quick Reference for Order of Operations Problems
Print/save as PDF: Use your browser’s print option to keep this as a one-page reference while practicing.
Core rule (what PEMDAS really means)
- Grouping symbols first: parentheses (), brackets [], braces {}, absolute value bars | |, and fraction bars.
- Exponents next: powers, squares, cubes (and roots if included).
- Multiplication and division share a priority: compute left to right.
- Addition and subtraction share a priority: compute left to right.
Fast decision checks for common quiz traps
- Left-to-right check: In a chain like a ÷ b × c, do the operation that appears first.
- Implied multiplication: 3(…) means 3 × (…). So does (…)(…) and 2x in algebra.
- Exponent scope with negatives:
- −32 = −(32) = −9
- (−3)2 = 9
- Don’t combine across × or ÷: In 2 + 5 × 3, the 5×3 is a product term you must finish before adding.
- Fraction bar acts like parentheses: If the expression is a single fraction, treat the entire numerator as grouped and the entire denominator as grouped.
Reliable step-by-step procedure
- Rewrite adjacency as multiplication (e.g., 4(2 − 1) → 4 × (2 − 1)).
- Simplify inside each set of grouping symbols.
- Compute exponents (be careful with negatives and parentheses).
- Work × and ÷ left-to-right across the whole expression.
- Work + and − left-to-right across the whole expression.
Accuracy tips
- Keep exact values (fractions) until the end; avoid early rounding.
- Mark negatives clearly: write subtraction as “add a negative” if it helps you stay organized.
- One line per step prevents accidentally reordering operations.
Order of Operations (PEMDAS) FAQ for Multiple-Choice Expressions
Does PEMDAS mean multiplication always comes before division?
No. Multiplication and division are the same priority level, so you compute them left to right. For example, 24 ÷ 6 × 2 = 4 × 2 = 8, not 24 ÷ 12.
How should I treat a fraction bar in an order of operations problem?
A fraction bar is a grouping symbol. Treat the entire numerator as one grouped expression and the entire denominator as one grouped expression, then divide. This prevents mistakes like dividing only the last term in the numerator.
What’s the difference between −32 and (−3)2?
−32 means the negative is outside the exponent: −(32) = −9. (−3)2 means the negative is included in what gets squared, so it becomes positive: 9. On multiple-choice items, this is one of the most common sign traps.
Is 3(5 − 2) the same as (3 + 5 − 2)?
No. 3(5 − 2) means 3 × (5 − 2). You simplify the parentheses first (5 − 2 = 3), then multiply: 3 × 3 = 9. Adding the 3 into the parentheses changes the expression and breaks the meaning of implied multiplication.
How can I eliminate answer choices quickly on order of operations multiple-choice questions?
After you handle grouping and exponents, rewrite the expression as a clean left-to-right chain for ×/÷, then a clean left-to-right chain for +/−. If a choice matches a common trap (like treating a ÷ b × c as a ÷ (b × c)), you can often eliminate it immediately.
When does order of operations connect to algebra skills?
Any time you simplify expressions with variables (like 2x + 3(x − 1)), order of operations and implied multiplication still apply. If you want practice that bridges arithmetic-to-algebra reasoning, try 10 Algebra Questions and Answers - Free Practice Quiz or focus on distribution and products with Product Rule Practice Problems - Free Quiz.