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Mathematics > Course Model Mathematics III (Integrated Pathway) > Arithmetic with Polynomials and Rational Expressions
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Mathematics | Course : Model Mathematics III (Integrated Pathway)

Domain - Arithmetic with Polynomials and Rational Expressions

Cluster - Rewrite rational expressions.

[MIII.A-APR.D.7] - (+) Understand that rational expressions form a system analogous to the rational numbers, closed under addition, subtraction, multiplication, and division by a nonzero rational expression; add, subtract, multiply, and divide rational expressions.

Resources:


  • Expression
    A mathematical phrase that combines operations, numbers, and/or variables (e.g., 32 ÷ a).
  • 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:

  • 7.NS.A.2
    Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide integers and other rational numbers.
  • 7.NS.A.2.a
    Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
  • 7.NS.A.2.b
    Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.
  • 7.NS.A.2.c
    Apply properties of operations as strategies to multiply and divide rational numbers.
  • 7.NS.A.2.d
    Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Successor Standards:

No Successor Standards found.

Same Level Standards:

  • MII.A-SSE.A.2
    Use the structure of an expression to identify ways to rewrite it. For example, see (x + 2)2 – 9 as a difference of squares that can be factored as ((x + 2) + 3)((x + 2) – 3).
  • MII.A-APR.A.1
    Understand that polynomials form a system analogous to the integers, namely, they are closed under certain operations.
  • 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.