# 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
- 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

**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 .

**Q8: **

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