# Worksheet: Identifying the Identity and Inverse Properties of Addition and Multiplication

Q1:

Complete the following and state which property is being used: .

• A51, associative
• C0, associative
• D51, commutative

Q2:

Which addition property of natural numbers is used in the expression ?

• Aclosure
• Cassociative
• Dcommutative

Q3:

Which of the following equations illustrates the zero property of addition?

• A
• B
• C
• D
• E

Q4:

What is the identity element for addition in the set of algebraic fractions?

Q5:

What do you get when you multiply a number by 1?

• Athe same number
• B0
• C1

Q6:

What is ?

Q7:

Identify the property demonstrated in the following equation: .

• Bidentity property of multiplication
• Cassociative property of multiplication
• Dcommutative property of multiplication

Q8:

Complete the expression stating which property is being used: .

• A53, multiplication by zero
• B53, multiplicative identity property
• C0, multiplicative identity property
• D1, multiplication by zero

Q9:

A vehicle traveled at a speed of 86 miles per hour for one hour. The distance it traveled can be represented as . What property of the real numbers was used in solving this expression?

• Bidentity property of multiplication
• Cassociative property of multiplication
• Dcommutative property of multiplication

Q10:

Find the additive inverse of .

• A
• B
• C
• D

Q11:

Find the additive inverse of .

Q12:

What is the additive inverse of ?

Q13:

Given that , find the value of .

Q14:

Ralph runs the marketing department at his company. His department gets a budget every year, and every year, he must spend the entire budget without going over. If he spends less than the budget, then his department gets a smaller budget the following year. At the beginning of this year, Ralph got \$2.50 million for the annual marketing budget. He must spend the budget such that . What property of addition tells us what the value of must be?

Q15:

Given that , is the additive, or multiplicative inverse of ?

• Bmultiplicative

Q16:

What is the additive inverse of 0?

Q17:

Given that is the additive inverse of , which of the following is true?

• A
• B
• C
• D
• E

Q18:

Which of the following is the sum ?

• Azero
• Ba negative number
• Ca positive number

Q19:

Find the value of in the equation .

• A
• B
• C
• D
• E

Q20:

Which property of multiplication is used in ?

• Aassociative property
• Bmultiplicative-identity property
• Cmultiplicative-inverse property
• Dcommutative property
• Eclosure property

Q21:

Find the multiplicative inverse of .

• A1
• B
• C
• D
• E

Q22:

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