Worksheet: Algebraic Properties

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(𝑥3)=24, consider the steps 4(𝑥3)=2414(4(𝑥3))=14(24)𝑥3=6.

In going from the second equation to the third equation, the fact that 14×4=1 is used. What other property of numbers is used in this step?

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

Q2:

Matthew 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.

  • AAssociative property
  • BMultiplicative property
  • CDistributive property
  • DCommutative property of addition

Q3:

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

Name property A.

  • ACommutative property of addition
  • BIdentity property of multiplication
  • CAssociative property
  • DDistributive property
  • EInverse property of multiplication

Name property B.

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

Name property C.

  • ACommutative property of addition
  • BDistributive property
  • CInverse property of multiplication
  • DAssociative property
  • ECommutative property of multiplication

Q4:

Which equation shows the associative property of addition?

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

Q5:

A possible beginning to the solution of the equation 7𝑥1=83𝑥 is 7𝑥1=8𝑥3𝑥3𝑥37𝑥1=𝑥1𝑥18𝑥3,

which creates fractions with a common denominator. What algebraic property have we used for this step?

  • AThe associative property of multiplication
  • BThe distributive property of multiplication
  • CThe identity property of multiplication
  • DThe commutative property of multiplication
  • EThe inverse property of multiplication

Q6:

Given that 𝑥=2950 and 𝑦 is the multiplicative inverse of 𝑥, determine the value of (𝑥𝑦).

Q7:

Given that 𝑥=23+7 and 𝑥𝑦=1, find the value of 𝑥256𝑦.

  • A60
  • B 4 1 6 1
  • C 1 6 1
  • D32
  • E 2 1 6 1

Q8:

Given that 𝑥=171+70 and 𝑦 is the multiplicative inverse of 𝑥, determine the value of (𝑥+𝑦).

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