Free Order of Operations Worksheets With Answers
These free order of operations worksheets build from two-operation expressions up to nested brackets with exponents and negative numbers, and every answer is worked through one operation at a time. Order of operations is a small topic that quietly causes errors in algebra for years afterwards, so it is worth getting exactly right. The same questions can be generated as a printable order of operations test with an answer key.
Grades 4–7 · 9 free questions with worked answers · No sign-up to practise
Skills covered in these order of operations worksheets
- Applying PEMDAS or BODMAS correctly
- Working left to right within the same precedence level
- Expressions with brackets and nested brackets
- Expressions containing exponents
- Order of operations with negative numbers
- Using the fraction bar as a grouping symbol
Free order of operations practice questions with answers
Every question below includes the final answer and the steps behind it, so the sheet doubles as its own answer key. Filter by grade or difficulty to build the set you need.
- Question 1easyGrade 4
3 + 2 × 4 = ?
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Answer: 11
Multiplication comes before addition, so 2 × 4 = 8 first, then 3 + 8 = 11.
- Question 2easyGrade 4
(5 + 3) × 2 = ?
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Answer: 16
Brackets first: 5 + 3 = 8. Then 8 × 2 = 16.
- Question 3easyGrade 5
20 − 6 ÷ 3 = ?
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Answer: 18
Division comes before subtraction, so 6 ÷ 3 = 2 first, then 20 − 2 = 18.
- Question 4mediumGrade 5
8 ÷ 2 × 4 = ?
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Answer: 16
Division and multiplication share a level, so work left to right: 8 ÷ 2 = 4, then 4 × 4 = 16.
- Question 5mediumGrade 6
4 + 3 × 2² = ?
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Answer: 16
Exponents first: 2² = 4. Then multiply: 3 × 4 = 12. Then add: 4 + 12 = 16.
- Question 6mediumGrade 6
2 × (7 − 3)² = ?
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Answer: 32
Brackets first: 7 − 3 = 4. Then the exponent: 4² = 16. Then multiply: 2 × 16 = 32.
- Question 7hardGrade 7
12 ÷ (2 + 4) × 3 = ?
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Answer: 6
Brackets first: 2 + 4 = 6. Then left to right: 12 ÷ 6 = 2, then 2 × 3 = 6.
- Question 8hardGrade 7
−3² + (−2)³ = ?
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Answer: −17
In −3² the exponent binds to the 3 only, giving −9. Then (−2)³ = −8. So −9 + (−8) = −17.
- Question 9hardGrade 7
(6 + 2 × 3) ÷ (10 − 2²) = ?
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Answer: 2
Numerator: 2 × 3 = 6, then 6 + 6 = 12. Denominator: 2² = 4, then 10 − 4 = 6. Finally 12 ÷ 6 = 2.
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PEMDAS is four levels, not six
The acronym lists six letters but there are only four levels of precedence: brackets, then exponents, then multiplication and division together, then addition and subtraction together. Multiplication does not outrank division, and addition does not outrank subtraction — within each of those pairs you simply work from left to right. Students who read the acronym as a strict six-step sequence will compute 8 ÷ 2 × 4 as 1 instead of 16.
Where this shows up later
Order of operations errors rarely stay in their own unit. They resurface when students substitute values into a formula, when they evaluate an expression with a squared term, and when they simplify the numerator and denominator of a fraction separately. A student who evaluates 3 + 2 × 4² correctly is far less likely to mis-evaluate the quadratic formula two years later.
Common mistakes to watch for
- Treating multiplication as always coming before division, so 8 ÷ 2 × 4 is computed as 1.
- Adding before multiplying, so 3 + 2 × 4 becomes 20 instead of 11.
- Applying an exponent to the wrong base, evaluating −3² as 9 rather than −9.
- Ignoring the fraction bar as a grouping symbol and dividing before the numerator is simplified.