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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: 5 1 + = 0 + 5 1 = 5 1 .

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

Q2:

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

  • A π‘₯ + π‘₯ = 0
  • B π‘₯ β‹… 0 = π‘₯
  • C π‘₯ + 1 = 1 + π‘₯
  • D π‘₯ + 0 = π‘₯
  • E π‘₯ β‹… 1 = π‘₯

Q3:

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

Q4:

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

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

Q5:

What is the additive inverse of βˆ’ 2 9 9 ?

Q6:

Given that 4 4 + ( βˆ’ 4 4 ) = 𝑛 , find the value of 𝑛 .

Q7:

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 2 5 0 0 0 0 0 βˆ’ π‘₯ = 0 . What property of addition tells us what the value of π‘₯ must be?

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

Q8:

Given that π‘Ž Γ· 𝑏 = βˆ’ 1 , is 𝑏 the additive, or multiplicative inverse of π‘Ž ?

  • A additive
  • B multiplicative

Q9:

Given that 𝑏 is the additive inverse of π‘Ž , which of the following is true?

  • A π‘Ž + 𝑏 = 1
  • B π‘Ž βˆ’ 𝑏 = 0
  • C π‘Ž βˆ’ 𝑏 = 1
  • D π‘Ž + 𝑏 = 0
  • E π‘Ž Γ— 𝑏 = 1

Q10:

Find the value of 𝑛 in the equation βˆ’ 9 1 0 Γ— 𝑛 = 1 .

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

Q11:

Find the multiplicative inverse of 3 7 .

  • A βˆ’ 7 3
  • B βˆ’ 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 Γ— 1 ?