Order of Operations With Parentheses and Brackets
Skill: Evaluating expressions with parentheses, brackets and the four operations
Download PDF worksheetAnswer key (PDF)
Free for personal and classroom use. Print at 100% / "Actual size" on US Letter paper.
About this worksheet
When an expression has more than one operation, everyone needs to agree on which step comes first. Otherwise, the same expression could give different answers. This fifth-grade worksheet has sixteen expressions using addition, subtraction, multiplication, division, parentheses, and brackets. Students evaluate each expression and write the answer. There are no exponents, matching the fifth-grade standard, and every answer is a whole number.
The expressions are written to catch common errors. For example, in 28 − 24 ÷ 4, students who simply work from left to right get 1, but dividing first gives the correct answer, 22. Expressions with grouping symbols, such as 3 × [6 + (5 − 1)], show how parentheses and brackets change the order.
How to use it: review the order before starting. First, do the work inside grouping symbols, starting with the innermost parentheses and then the brackets. Next, multiply and divide from left to right. Finally, add and subtract from left to right. Students sometimes think multiplication always comes before division, or addition before subtraction, so stress that each of those pairs is done left to right. Encourage students to rewrite the expression after each step, underlining the part they are working on.
The answer key gives the value of every expression. If an answer is wrong, have students compare each rewritten step with the order of operations. This worksheet supports Common Core standard 5.OA.A.1 (use parentheses, brackets, or braces in numerical expressions, and evaluate expressions with these symbols).
Count and Trace Numbers 1-10
Addition Within 10
Subtraction Within 10