Lesson Worksheet: Algebraic Properties Mathematics

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?

  • A2+𝑥=𝑥+2
  • B2+(𝑥+3)=(2+𝑥)+3
  • C(𝑥)+𝑥=0
  • D2(𝑥+3)=2𝑥+6
  • E2(3𝑥)=3(2𝑥)

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
  • B4161
  • C161
  • D32
  • E2161

Q8:

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

This lesson includes 11 additional questions and 27 additional question variations for subscribers.

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.