Worksheet: The Identity and Inverse Properties of Addition and Multiplication

In this worksheet, we will practice identifying the identity and inverse properties of addition and multiplication and applying these properties in real-life situations.

Q1:

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

  • A ๐‘ฅ + ๐‘ฅ = 0
  • B ๐‘ฅ โ‹… 0 = ๐‘ฅ
  • C ๐‘ฅ + 1 = 1 + ๐‘ฅ
  • D ๐‘ฅ + 0 = ๐‘ฅ
  • E ๐‘ฅ โ‹… 1 = ๐‘ฅ

Q2:

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

Q3:

Complete the expression stating which property is being used: 5 3 ร— 1 = 1 ร— = 5 3 .

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

Q4:

What is the additive inverse of โˆ’ 6 6 ?

Q5:

Given that ๐‘ is the additive inverse of ๐‘Ž , which of the following is true?

  • A ๐‘Ž + ๐‘ = 1
  • B ๐‘Ž โˆ’ ๐‘ = 0
  • C ๐‘Ž โˆ’ ๐‘ = 1
  • D ๐‘Ž + ๐‘ = 0
  • E ๐‘Ž ร— ๐‘ = 1

Q6:

Complete the following and state which property is being used: 5 1 + = 0 + 5 1 = 5 1 .

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

Q7:

Given that 4 4 + ( โˆ’ 4 4 ) = ๐‘› , find the value of ๐‘› .

Q8:

Sherif 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, Sherif 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

Q9:

Given that ๐‘Ž รท ๐‘ = โˆ’ 1 , is ๐‘ the additive or multiplicative inverse of ๐‘Ž ?

  • A Additive
  • B Multiplicative

Q10:

Find the value of ๐‘› in the equation โˆ’ 9 1 0 ร— ๐‘› = 1 .

  • A 1 0 9
  • B 9 1 0
  • C โˆ’ 9 1 0
  • D โˆ’ 1 0 9
  • E 1 9 1 0

Q11:

Find the multiplicative inverse of 3 7 .

  • A โˆ’ 7 3
  • B โˆ’ 3 7
  • C 3 7
  • D 7 3
  • E 1

Q12:

What can be said about two different numbers that add up to zero?

  • AThey are equal to zero.
  • BThey have the same absolute value but different signs.
  • CThey have absolute values of different signs.
  • DThey are additive inverses.

Q13:

What is 1 , 9 3 6 ร— 1 ?

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