# 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 , consider the steps

In going from the second equation to the third equation, the fact that 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
• CMultiplicative property
• DDistributive property

Name property B.

• AAssociative property
• BMultiplicative property
• CDistributive property

Q3:

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

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

Name property B.

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

Name property C.

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

Q4:

Which equation shows the associative property of addition?

• A
• B
• C
• D
• E

Q5:

A possible beginning to the solution of the equation is

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 and is the multiplicative inverse of , determine the value of .

Q7:

Given that and , find the value of .

• A60
• B
• C
• D32
• E

Q8:

Given that and is the multiplicative inverse of , determine the value of .