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Mathematics > Course Model Mathematics II (Integrated Pathway) > The Real Number System
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Mathematics | Course : Model Mathematics II (Integrated Pathway)

Domain - The Real Number System

Cluster - Use properties of rational and irrational numbers.

[MII.N-RN.B.3] - Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Resources:


  • Irrational number
    A number that cannot be expressed as a quotient of two integers, e.g.,√2 . It can be shown that a number is irrational if and only if it cannot be written as a repeating or terminating decimal.
  • Rational number
    A number expressible in the form a∕b or – a∕b for some fraction a∕b. The rational numbers include the integers.

Predecessor Standards:

  • 8.NS.A.1
    Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.
  • 8.EE.A.2
    Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.N-CN.A.1
    Know there is a complex number i such that i2 = −1, and every complex number has the form a + bi with a and b real.
  • MIII.A-APR.D.6
    Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x), where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using inspection, long division, or, for the more complicated examples, a computer algebra system.