Order of Operations Worksheets

Printable order of operations worksheets that build from two-step expressions to parentheses, then exponents — each with 20 problems and an answer key — plus a PEMDAS/BODMAS reference card and a common-mistakes sheet.

What the order of operations is

When an expression has more than one operation, mathematicians agree on an order so everyone gets the same answer. Without it, 3 + 4 × 2 could be 14 or 11. The agreed order is: work inside grouping symbols first (parentheses or brackets), then exponents (powers and roots), then multiplication and division from left to right, then addition and subtraction from left to right. So 3 + 4 × 2 = 3 + 8 = 11.

PEMDAS, BODMAS and BIDMAS

They all describe the same rules. The most important detail is that multiplication and division have equal priority and are done left to right, and so are addition and subtraction — which the acronyms can hide. In 12 ÷ 3 × 2, divide first because it comes first: 4 × 2 = 8, not 12 ÷ 6 = 2.

What is in the pack

• Level 1: two operations — no parentheses, e.g. 7 + 3 × 4.
• Level 2: parentheses — e.g. (6 + 2) × 5 − 3.
• Level 3: exponents — squares and cubes with parentheses, e.g. 4² + 3 × 2.
• Answer keys for every level, on separate pages.
• Rules reference card — PEMDAS and BODMAS side by side with examples.
• Common mistakes sheet — find and fix the error in worked solutions.
• Editable Word versions for creating your own problems.

Worked examples

Common mistakes

• Always doing multiplication before division, or addition before subtraction, instead of working left to right.
• Forgetting to finish everything inside the parentheses first.
• Treating an exponent as multiplication by the exponent (3² as 6).
• Applying an exponent to the wrong number: in 2 × 3², only the 3 is squared.
• Calculators: basic calculators may evaluate left to right as you type; scientific calculators follow the order of operations.

How to use the worksheets

Introduce the rules with the reference card, then have students complete Level 1, showing one step per line. Move to Level 2 once they can explain why multiplication comes first. Level 3 suits grades 6 and up, after exponents are introduced. The common-mistakes sheet works well as a partner discussion: students explain what went wrong and fix it. All answers are whole numbers so students can focus on the order rather than arithmetic with fractions.

Who it is for

Students in grades 5–7 learning the order of operations, older students reviewing before algebra, homeschooling families, and tutors. Every problem was generated by a script and its answer computed automatically, so the keys are consistent.

Formats

Worksheets and keys are print-ready PDFs (US Letter; they also print on A4) and editable DOCX files.

Why the rules matter beyond school

Spreadsheets, programming languages and scientific calculators all follow the order of operations, so the same rules decide whether a budget formula or a line of code gives the right answer. In a spreadsheet, =A1+B1*C1 multiplies before adding, which is often not what the writer intended; parentheses make the intention explicit. Encouraging students to add parentheses whenever an expression might be misread is good practice for later work with formulas and code.