Lesson Worksheet: Simplifying Expressions: Commutative and Associative Properties Mathematics • 6th Grade

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.

  • A52𝑦+95
  • B𝑦+147
  • C𝑦−147
  • D95𝑦+52
  • E147−𝑦

Q3:

Which of the following illustrates the associative property of addition?

  • A𝑧+41=41+𝑧
  • B(41×𝑧)×4=41×(𝑧×4)
  • C(41+𝑧)+4=41+(𝑧+4)
  • D(41+𝑧)×4=(41×4)+(𝑧×4)
  • E(41+𝑧)+4=(41+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)
  • D𝑥+(7+2)
  • E𝑥⋅(7+2)

Q5:

In a class, Victoria calculates (𝑎+𝑏)−𝑐 and Liam calculates 𝑎+(𝑏−𝑐). 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?

Q7:

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

Q8:

Given that 𝑏=−4, evaluate 𝑏(𝑥+6)+𝑏(𝑐−6𝑥)−𝑏(𝑐−5𝑥).

Q9:

Which of the following illustrates the associative property of multiplication?

  • A𝑎×(48×10)=(𝑎×48)+10
  • B(𝑎+48)×10=𝑎×(48+10)
  • C(𝑎×48)×10=𝑎×(48×10)
  • D(𝑎+48)×10=𝑎+(48+10)
  • E(𝑎×48)+10=𝑎+(48×10)

Q10:

Given that 𝑥×(8×17)=(9×(−8))×17, find the value of 𝑥.

Q11:

Knowing that 𝑎=𝑏, which of the following equations is not true?

  • A𝑎−2=𝑏−2
  • B15−𝑎=𝑏−15
  • C7−𝑏=7−𝑎
  • D𝑎+3=3+𝑏
  • E5+𝑏=5+𝑎

Q12:

Use the properties of real numbers to fill in the blanks: 10×𝑥×14=×𝑥=𝑥.

  • A(10𝑥×14), 140
  • B(10×14), 24
  • C(10×14𝑥), 140
  • D(10+14), 24
  • E(10×14), 140

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