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

Q1:

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

  • A51, associative
  • B0, additive identity
  • C0, associative
  • D51, commutative

Q2:

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

  • Aclosure
  • Badditive identity
  • 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: .

  • Adistributive property
  • 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?

  • Adistributive property
  • 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?

  • Acommutative property of addition
  • Bidentity property of addition
  • Cinverse property of addition
  • Ddistributive property of addition
  • Eassociative properties of addition

Q15:

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

  • Aadditive
  • 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