Worksheet: Simplifying Expressions: Commutative and Associative Properties

In this worksheet, we will practice simplifying algebraic expressions using the commutative and associative properties for addition and multiplication.

Q1:

If 𝑦5+45=45+35, what is the value of 𝑦?

Q2:

Use the properties of real numbers to simplify the expression 52+(𝑦+95) to one without parentheses.

  • A 5 2 𝑦 + 9 5
  • B 𝑦 + 1 4 7
  • C 𝑦 1 4 7
  • D 9 5 𝑦 + 5 2
  • E 1 4 7 𝑦

Q3:

Which of the following illustrates the associative property of addition?

  • A 𝑧 + 4 1 = 4 1 + 𝑧
  • B ( 4 1 × 𝑧 ) × 4 = 4 1 × ( 𝑧 × 4 )
  • C ( 4 1 + 𝑧 ) + 4 = 4 1 + ( 𝑧 + 4 )
  • D ( 4 1 + 𝑧 ) × 4 = ( 4 1 × 4 ) + ( 𝑧 × 4 )
  • E ( 4 1 + 𝑧 ) + 4 = ( 4 1 + 4 ) + ( 𝑧 + 4 )

Q4:

Rewrite the expression (𝑥+7)+2 using the associative property.

  • A ( 𝑥 + 2 ) + ( 𝑥 + 7 )
  • B ( 𝑥 + 2 ) ( 2 + 7 )
  • C ( 𝑥 + 2 ) + ( 2 + 7 )
  • D 𝑥 + ( 7 + 2 )
  • E 𝑥 ( 7 + 2 )

Q5:

In a class, Victoria calculates (𝑎+𝑏)𝑐 and Liam calculates 𝑎+(𝑏𝑐). Which property of addition tells us that their answers will be the same?

  • Adistributive property
  • Bcommutative property
  • Cidentity property
  • Dassociative property

Q6:

If (45×𝑥)×50=45×(35×50), what is the value of 𝑥?

  • A36
  • B45
  • C50
  • D35

Q7:

If (𝑥+55)+32=24+(55+32), what is the value of 𝑥?

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