# AII.1a and *AII.1a - Simplify Rational Expressions

AII.1    The student, given rational, radical, or polynomial expressions, will

a)  add, subtract, multiply, divide, and simplify rational algebraic expressions;

AII.1  The student will

a)  add, subtract, multiply, divide, and simplify rational algebraic expressions;

Bloom's Level:  Apply

### BIG IDEAS

• I can design the track of a roller coaster, determine the sloped curve of an exit ramp, trace the free falling path of a skydiver, and understand the mechanics of controllers like autopilot, cruise control, and a living room thermostat.
• I will apply mathematical processes for basic operations to algebraic expressions and divide algebraic terms out of algebraic expressions.

### UNDERSTANDING THE STANDARD

• Computational skills applicable to numerical fractions also apply to rational expressions involving variables.
• Radical expressions can be written and simplified using rational exponents.
• A relationship exists among arithmetic complex fractions, algebraic complex fractions, and rational numbers.
• The complete factorization of polynomials has occurred when each factor is a prime polynomial.
• Pattern recognition can be used to determine complete factorization of a polynomial.

·  Computational skills applicable to numerical fractions also apply to rational expressions involving variables.

·  Radical expressions can be written and simplified using rational exponents.

·  Only radicals with a common radicand and index can be added or subtracted, which may require rewriting a radical with a lower base and different index.

·  A relationship exists among arithmetic complex fractions, algebraic complex fractions, and rational numbers.

·  The complete factorization of polynomials has occurred when each factor is a prime polynomial.

·  Pattern recognition can be used to determine complete factorization of a polynomial.

·  Polynomials may be factored in various ways, including, but not limited to grouping or applying general patterns such as difference of squares, sum and difference of cubes, and perfect square trinomials.

### ESSENTIALS

Simplifying

All.1a2  Simplify a rational algebraic expression w/ common monomial or binomial factors.

·  AII.1a2  Simplify a rational algebraic expression with monomial or binomial factors. Algebraic expressions should be limited to linear and quadratic expressions.

Operations

All.1a1  Add, subtract, multiply, divide rational algebraic expressions.

·  AII.1a1  Add, subtract, multiply, and divide rational algebraic expressions.

Complex Rationals

All.1a3  Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions.

·  AII.1a3  Recognize a complex algebraic fraction, and simplify it as a quotient or product of simple algebraic fractions.

### KEY VOCABULARY

rational, radical, polynomial expression, simplify, variables, equation vs. expression, factor completely, rational exponents,  sum, difference,product, quotient,monomial, binomial, complex algebraic fraction, simple algebraic fraction, radical expression, radical notation, exponential notation, rationalizing, numerator, denominator, difference of squares, difference of cubes, sum of cubes, perfect square trinomial, integer, verify

Updated: Oct 27, 2017