Arithmetic properties: Identity property

Arithmetic properties: Identity property

Lessons

In this lesson, we will learn:

  • What is the additive identity property of zero
  • What is the multiplicative identity property of one
  • How to write the general formulas/equations for the identity properties
  • What are the three properties of zero?
  • How the identity properties are different from the properties of zero
  • How to write the general formulas/equations for properties of zero

Notes:

  • The identity property is observed when the identity of the original number does NOT change after the equal sign. The answer will be the same number that you started with.
    • The numbers can be any real number (whole numbers, fractions, decimals, integers, etc.)
    • The word “identity” can mean who you are or what you are


  • The identity property only happens for TWO cases in math:
    • For addition: adding zero to any number will NOT change that number
      • Ex. 8 + 0 = 8
      • Ex. 0.5 + 0 = 0.5
      • Ex. 12\large \frac{1}{2} + 0 = 12\large \frac{1}{2}
    • For multiplication: multiplying any number by one will NOT change that number
      • Ex. 8 × 1 = 8
      • Ex. 1.47 × 1 = 1.47
      • Ex. 34\large \frac{3}{4} × 1 = 34\large \frac{3}{4}

  • The general formulas for the identity property (where a is aa variable that represent a real number) are:

  • Arithmetic Property

    Of Addition

    Of Multiplication

    (Additive)

    Identity property of 0

    a+0=aa + 0 = a

    0+a=a0 + a = a

    *

    (Multiplicative)

    Identity property of 1

    a×1=aa × 1 = a

    1×a=a1 × a = a


  • It is important to know the properties of zero – *what happens when you multiply and divide by zero so that you don't get them confused with the identity property of zero
    • There are three properties of zero:
      • (1) when you multiply by zero, the answer will always be zero
      • (2) when zero is divided by any number, the answer will always be zero
      • (3) when you attempt to divide any number by zero, the answer will always be undefined

  • The general formulas for the properties of zero are:

  • Arithmetic Property

    Of Multiplication

    Of Division

    Properties of Zero

    a×0=0a × 0 = 0

    0×a=00 × a = 0

    0÷a=00 ÷ a = 0

    - - - - - - - - - - - - - - - - -

    a÷0=undefined a ÷ 0 = undefined

  • Introduction
    Introduction to the identity property of addition and multiplication (and properties of zero):
    a)
    Showing that a+0=aa + 0 = a

    b)
    Why is it called the "identity" property?

    c)
    Showing that a × 1 = a

    d)
    The general formulas for the identity property

    e)
    The three properties of zero involving multiplication and division (a × 0 = 0; 0 ÷ a = 0; and a ÷ 0 = undefined)

    f)
    The general formulas for the properties of zero


  • 1.
    Additive identity property of 0
    Use the additive identity of 0 to fill in the blanks.
    a)
    287 + __ = 287

    b)
    __ + 0 = 0.39

    c)
    0 + __ = 5171000 \large \frac{517}{1000}


  • 2.
    Multiplicative identity property of 1
    Use the multiplicative identity of 1 to fill in the blanks.
    a)
    657 × __ = 657

    b)
    1 × __ = 8.914

    c)
    __ × 832900\large \frac{832}{900} = 832900\large \frac{832}{900}


  • 3.
    Multiplying and dividing using properties of 0
    Use the properties of 0 to fill in the blanks.
    a)
    1325\large \frac{13}{25} × 0 = __

    b)
    __ × 1 = 0

    c)
    0 ÷ 25 = __

    d)
    35 ÷ __ = undefined

    e)
    7.6 × 0 = __

    f)
    439 ÷ 0 = __


  • 4.
    Identity properties and all four operations
    What happens to the identity of number 46 when:
    a)
    46 + 0 =

    b)
    46 - 0 =

    c)
    46 × 0 =

    d)
    46 × 1 =

    e)
    46 ÷ 1 =

    f)
    46 ÷ 0 =

    g)
    0 ÷ 46 =


  • 5.
    Identity properties word problem
    If aa, bb and cc are real numbers with secret identities:
    a)
    What happens to a when it is added to 0

    b)
    What happens to b when it is multiplied with 1

    c)
    What happens to c when it is multiplied with 0

    d)
    What happens to a when it is divided by 0