Worksheet: Properties of Addition and Multiplication in Algebraic Expressions

In this worksheet, we will practice identifying the properties of addition and multiplication that are used to evaluate an algebraic expression.

Q1:

In the solution of 4 ( 𝑥 3 ) = 2 4 , consider the steps

In going from the second equation to the third equation, the fact that 1 4 × 4 = 1 is used. What other property of numbers is used in this step?

  • Athe commutative property
  • Bthe distributive property
  • Cthe zero property of addition
  • Dthe associative property
  • Ethe property of opposites

Q2:

Sameh has used properties of addition and multiplication to write equivalent expressions.

Name property A.

  • AAssociative property
  • BCommutative property of addition
  • CMultiplicative property
  • DDistributive property

Name property B.

  • AMultiplicative property
  • BAssociative property
  • CDistributive property
  • DCommutative property of addition

Q3:

Samar has used properties of addition and multiplication to write equivalent expressions.

Name property A.

  • ACommutative property of addition
  • BDistributive property
  • CAssociative property
  • DInverse property of multiplication
  • EIdentity property of multiplication

Name property B.

  • ACommutative property of multiplication
  • BDistributive property
  • CInverse property of multiplication
  • DCommutative property of addition
  • EAssociative property

Name property C.

  • ACommutative property of multiplication
  • BAssociative property
  • CDistributive property
  • DCommutative property of addition
  • EInverse property of multiplication

Q4:

Which equation shows the associative property of addition?

  • A 2 + 𝑥 = 𝑥 + 2
  • B 2 ( 𝑥 + 3 ) = 2 𝑥 + 6
  • C 2 ( 𝑥 3 ) = ( 2 𝑥 ) 3
  • D 2 + ( 𝑥 + 3 ) = ( 2 + 𝑥 ) + 3
  • E ( 𝑥 ) + 𝑥 = 0

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