#### Math - 2017-18

# 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.1The student willa)

add,subtract,multiply,divide, andsimplifyrational algebraic expressions;

**Bloom's Level:** Apply

*Adopted: 2009*

### 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.
- Only radicals with a common radicand and index
can be added or subtracted.
- 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.1a_{2} Simplify a rational algebraic
expression w/ common monomial or binomial factors.

·
AII.1a_{2} Simplify
a rational algebraic expression with monomial or binomial factors. Algebraic
expressions should be limited to linear and quadratic expressions.

__Operations__

All.1a_{1} Add,
subtract, multiply, divide
rational algebraic expressions.

·
AII.1a_{1} Add,
subtract, multiply, and divide rational
algebraic expressions.

__Complex Rationals__

All.1a_{3} Recognize
a complex algebraic fraction, and simplify
it as a quotient or product of simple algebraic fractions.

·
AII.1a_{3} 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*