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Order of operations practice

Algebraic order of operations worksheets

Simplify twelve expressions containing x, with configurable signs, grouping and powers. Practice combining like terms and simplifying products and quotients without substituting a number for x.

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Simplify each expression algebraically. Keep x as a variable, combine like terms and preserve any nonzero restrictions from the original expression.

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US Letter

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A4

Student worksheetWorksheet with answers
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Paper sizes and printing help · More order of operations activities

Choose the expression, then explain the order

Choose easy or hard practice, then select the grouping and exponent form. Advanced and algebraic worksheets also let you choose positive, negative or mixed inputs. These settings describe the operands; a positive-input expression can still have a negative answer.

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Learning objective

What this activity builds

Preserve arithmetic precedence while simplifying variable terms, powers and exact coefficients.

Worked example

Simplify 3 × 4x − 2x + 5x.

12x − 2x + 5x = 15x.

Calculate the product first. Then combine the coefficients of the like x terms in order. No value of x is needed.

Teaching notes

Make the practice count

  • Use only after signed arithmetic and basic algebraic notation are secure.
  • Compare the variable parts before combining terms.
  • A cancelled x in a denominator still requires x to be nonzero in the original expression.
  • For power forms, simplify the complete grouped base before applying the exponent.

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Math SheetNameScore/ 12TeacherDateAlgebraic Order of OperationsSimplify each expression algebraically. Show the order of your work.1.30 · x · (6 · x) ÷ (12 · x) - 5 · x2.3 · x - 30 ÷ 6 · x + 9 · x3.9 · x + 3 · x · 11 - 5 · x4.8 · x · (4 · x) ÷ (8 · x) - 12 · x5.2 · x - 10 ÷ 2 · x + 11 · x6.4 · x + 3 · x · 11 - 11 · x7.30 · x · (10 · x) ÷ (12 · x) - 4 · x8.11 · x - 16 ÷ 4 · x + 8 · x9.3 · x + 9 · x · 4 - 12 · x10.6 · x · (2 · x) ÷ (2 · x) - 12 · x11.11 · x - 54 ÷ 9 · x + 6 · x12.6 · x + 4 · x · 8 - 12 · xmath-sheet.comPage 1 / 1

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