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Prealgebra

Key Concepts

PrealgebraKey Concepts

Key Concepts

7.1 Rational and Irrational Numbers

  • Real numbers

7.2 Commutative and Associative Properties

  • Commutative Properties
    • Commutative Property of Addition:
      • If a,ba,b are real numbers, then a+b=b+aa+b=b+a
    • Commutative Property of Multiplication:
      • If a,ba,b are real numbers, then a⋅b=b⋅aa⋅b=b⋅a
  • Associative Properties
    • Associative Property of Addition:
      • If a,b,ca,b,c are real numbers then (a+b)+c=a+(b+c)(a+b)+c=a+(b+c)
    • Associative Property of Multiplication:
      • If a,b,ca,b,c are real numbers then (a⋅b)⋅c=a⋅(b⋅c)(a⋅b)⋅c=a⋅(b⋅c)

7.3 Distributive Property

  • Distributive Property:
    • If a,b,ca,b,c are real numbers then
      • a(b+c)=ab+aca(b+c)=ab+ac
      • (b+c)a=ba+ca(b+c)a=ba+ca
      • a(b⋅c)=ab⋅aca(b⋅c)=ab⋅ac

7.4 Properties of Identity, Inverses, and Zero

  • Identity Properties
    • Identity Property of Addition: For any real number a: a+0=a0+a=aa+0=a0+a=a 0 is the additive identity
    • Identity Property of Multiplication: For any real number a: a⋅1=a1⋅a=aa⋅1=a1⋅a=a 1 is the multiplicative identity
  • Inverse Properties
    • Inverse Property of Addition: For any real number a: a+(-a)=0-aa+(-a)=0-a is the additive inverse of a
    • Inverse Property of Multiplication: For any real number a: (a≠0)a⋅1a=11a(a≠0)a⋅1a=11a is the multiplicative inverse of a
  • Properties of Zero
    • Multiplication by Zero: For any real number a, a⋅0=00⋅a=0The product of any number and 0 is 0. a⋅0=00⋅a=0The product of any number and 0 is 0.
    • Division of Zero: For any real number a, 0a=00+a=0Zero divided by any real number, except itself, is zero. 0a=00+a=0Zero divided by any real number, except itself, is zero.
    • Division by Zero: For any real number a, 0a0a is undefined and a÷0a÷0 is undefined. Division by zero is undefined.
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