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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: .

  • A0, associative
  • B51, commutative
  • C51, associative
  • D0, additive identity

Q2:

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

  • Aassociative
  • Bcommutative
  • Cclosure
  • Dadditive identity

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?

  • A0
  • B1
  • Cthe same number

Q6:

What is ?

Q7:

Identify the property demonstrated in the following equation: .

  • Aassociative property of multiplication
  • Bcommutative property of multiplication
  • Cdistributive property
  • Didentity property of multiplication

Q8:

Complete the expression stating which property is being used: .

  • A0, multiplicative identity property
  • B1, multiplication by zero
  • C53, multiplication by zero
  • D53, multiplicative identity property

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?

  • Aassociative property of multiplication
  • Bcommutative property of multiplication
  • Cdistributive property
  • Didentity 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:

Ethan 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, Ethan 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?

  • Adistributive property of addition
  • Bassociative properties of addition
  • Cidentity property of addition
  • Dinverse property of addition
  • Ecommutative property of addition

Q15:

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

  • A additive
  • B multiplicative

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 ?

  • A a negative number
  • B a positive number
  • Czero

Q19:

Find the value of in the equation .

  • A
  • B
  • C
  • D
  • E

Q20:

Which property of multiplication is used in ?

  • Acommutative property
  • Bclosure property
  • Cmultiplicative-identity property
  • Dmultiplicative-inverse property
  • Eassociative property

Q21:

Find the multiplicative inverse of .

  • A
  • B
  • C
  • D
  • E 1

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