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Properties of Real Numbers - Precalculus

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Termini in questo insieme (22)

  • What is the opposite of a number?
    The opposite of a number is the number with the opposite sign. Positive numbers become negative, and negative numbers become positive.
  • What is the reciprocal of a number?
    The reciprocal of a number is found by flipping the number as a fraction. An integer becomes \(\frac{1}{a}\), and a fraction flips numerator and denominator.
  • State the Commutative Property of Addition.
    The Commutative Property of Addition states that \(a + b = b + a\).
  • State the Commutative Property of Multiplication.
    The Commutative Property of Multiplication states that \(ab = ba\).
  • State the Associative Property of Addition.
    The Associative Property of Addition states that \((a + b) + c = a + (b + c)\).
  • State the Associative Property of Multiplication.
    The Associative Property of Multiplication states that \((ab)c = a(bc)\).
  • What is the Identity Property of Addition?
    The Identity Property of Addition states that adding zero to a number leaves it unchanged: \(a + 0 = a\).
  • What is the Identity Property of Multiplication?
    The Identity Property of Multiplication states that multiplying a number by one leaves it unchanged: \(a \times 1 = a\).
  • Explain the Additive Inverse Property.
    The Additive Inverse Property states that a number plus its opposite equals zero: \(a + (-a) = 0\).
  • Explain the Multiplicative Inverse Property.
    The Multiplicative Inverse Property states that a number times its reciprocal equals one: \(a \times \frac{1}{a} = 1\).
  • State the Distributive Property.
    The Distributive Property states that \(a(b + c) = ab + ac\) and \((b + c)a = ba + ca\).
  • Find the opposite and reciprocal of 7.
    Opposite: \(-7\). Reciprocal: \(\frac{1}{7}\).
  • Find the opposite and reciprocal of -2.
    Opposite: \(2\). Reciprocal: \(-\frac{1}{2}\).
  • Example of Commutative Property of Addition with variables.
    For variables \(x\) and \(y\), \(x + y = y + x\).
  • Example of Commutative Property of Multiplication with variables.
    For variables \(x\) and \(y\), \(xy = yx\).
  • Example of Associative Property of Addition.
    For numbers 3, \(x\), and 2: \((3 + x) + 2 = 3 + (x + 2)\).
  • Example of Associative Property of Multiplication.
    For numbers 4, 5, and \(y\): \((4 \times 5) \times y = 4 \times (5 \times y)\).
  • Identify the property: \(2 + (-2) = 0\).
    This is the Additive Inverse Property.
  • Identify the property: \(1 \times (-3) = -3\).
    This is the Multiplicative Identity Property.
  • Identify the property: \(0 + 8 = 8\).
    This is the Additive Identity Property.
  • Use the distributive property to expand \(3(x + 8)\).
    Expands to \(3x + 24\).
  • Use the distributive property to expand \(x(x - 2)\).
    Expands to \(x^2 - 2x\).