Free order of operations worksheets generator: PEMDAS and BODMAS practice with parentheses, brackets, exponents, negative numbers and word problems, with answer keys.
Free order of operations worksheets for grades 5 to 7. Choose a level, print, and get a new set of problems every time: basic PEMDAS practice with + − × ÷, problems with parentheses, or harder ones with exponents. Every answer is a whole number and every sheet comes with an answer key. Use them as PEMDAS worksheets or BODMAS practice, and finish with order of operations word problems.
A level 2: parentheses page, printed straight from the PEMDAS generator.
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Ready-to-print order of operations worksheets (PDF)
Each of these order of operations worksheets has an answer key. Press Customize to change the level, the number of problems or the paper size.
Level 1: no parenthesesLevel 1 + answer key.PDFCustomizeLevel 2: parenthesesLevel 2 + answer key.PDFCustomizeLevel 3: exponentsLevel 3 + answer key.PDFCustomizeTwo operations (4th grade)Multiply or divide first, then add or subtract.PDFCustomizeBrackets inside parenthesesNested grouping, solved inside out.PDFCustomizeWith negative numbersIntegers in parentheses + answer key.PDFCustomizeWord problemsWrite an expression, then solve it.PDFCustomize
The order of operations in four steps
Step
What to do
Example
1. Parentheses
Work inside parentheses and brackets first.
(3 + 5) × 2 = 8 × 2
2. Exponents
Work out powers and squares.
4² + 1 = 16 + 1
3. Multiply and divide
From left to right, whichever comes first.
12 ÷ 3 × 2 = 4 × 2
4. Add and subtract
From left to right, whichever comes first.
10 − 4 + 3 = 6 + 3
The most common mistake is doing multiplication before division (or addition before subtraction) just because M comes before D in the word. Those pairs are equal partners: work left to right. Every problem on our order of operations worksheets is checked so each step gives a whole number, which keeps the focus on the order itself.
PEMDAS worksheets, BODMAS and GEMDAS explained
These are memory aids for the same rule. In the US, students learn PEMDAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction, often remembered as “Please Excuse My Dear Aunt Sally”. In the UK, India and Australia it is BODMAS or BIDMAS: Brackets, Orders (or Indices), Division and Multiplication, Addition and Subtraction. Some teachers use GEMDAS, where G stands for any grouping symbol: parentheses, brackets, braces or a fraction bar. They all describe the same order, so these PEMDAS worksheets work just as well as BODMAS worksheets. The order of operations article on Wikipedia explains where the conventions come from.
Order of operations with parentheses and brackets
Parentheses tell you to do that part first, even if it is an addition: in (7 + 3) × 4, add first to get 10, then multiply to get 40. When there are grouping symbols inside other grouping symbols, work from the inside out. For 2 × [9 − (3 + 4)], solve (3 + 4) = 7, then the brackets [9 − 7] = 2, then 2 × 2 = 4. The brackets inside parentheses level gives students lots of practice with these nested problems.
Order of operations with exponents
Exponents come straight after grouping symbols. In 3 + 2³ × 4, find 2³ = 8 first, then 8 × 4 = 32, then 3 + 32 = 35. Watch for an exponent outside parentheses: (2 + 4)² means work out 2 + 4 = 6 first, then square it to get 36, which is very different from 2 + 4² = 18. Level 3 of these order of operations worksheets mixes squares and cubes with all four operations.
Order of operations with negative numbers
Negative numbers follow exactly the same order, but students also need the integer sign rules. In (−3) × 4 + 10, multiply first: (−3) × 4 = −12, then −12 + 10 = −2. In 8 − (−2) × 5, the multiplication comes first: (−2) × 5 = −10, so 8 − (−10) = 18. Our negative numbers level shows every negative number in parentheses, the way textbooks do, and pairs well with the integer worksheets.
Order of operations word problems
Word problems ask students to write an expression first, which is where the order of operations really matters. “Mia buys 5 packs of 4 stickers and gets 2 more” becomes 5 × 4 + 2 = 22, not 5 × (4 + 2). “A shop has 3 boxes of 12 apples and 3 loose apples, and sells 9” becomes 3 × 12 + 3 − 9 = 30. The order of operations word problems level has ten real-life problems on each page with room to write the expression.
Order of operations worksheets by grade
4th grade: easy PEMDAS worksheets with two operations and no parentheses, such as 7 × 8 + 8. Use the two operations level.
Most students meet it in 5th grade and use it all through 6th and 7th grade, when it becomes part of evaluating expressions and solving equations. Our order of operations worksheets cover 4th to 7th grade.
Do the problems ever have negative or fraction answers?
No. Every problem is checked so that each step and the final answer are whole numbers, which keeps the focus on the order of the steps.
What does PEMDAS stand for?
Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). BODMAS and BIDMAS describe the same order with different words.
Do you always multiply before you divide?
No. Multiplication and division have the same rank, so you do whichever comes first from left to right. In 12 ÷ 3 × 2, divide first to get 4, then multiply to get 8.
How do you solve problems with brackets inside parentheses?
Work from the innermost grouping symbol outward. Solve the parentheses inside first, then the brackets around them, then the rest of the expression.
Do these order of operations worksheets have answers?
Yes. Every PDF and every sheet you make in the generator has an answer key on the last page, and the online practice checks each answer straight away.
Can I print more than one sheet at a time?
Yes. Set Pages to print up to 10 different sheets in one PDF, with all the answers together on the last page.
More middle school math
Integer worksheets: adding, subtracting, multiplying and dividing negative numbers.
