Alg. 2: Chapter 5 Review—Rational Expressions10/31/14

(b) 5.1-5.2 Laws of Exponents with rational expressions Objectives: Simplifying quotients

(fractions) using laws of exponents

Vocabulary:

Rational expression = An expression with a numerator and a denominator, or, the ratio of two polynomials.

Tools and Rules: Exponents

Examples:

(In-class)

Homework:

Pg. 213 (Written) #1-20 all

(b) 5.3 Scientific Notation Objectives: Use Sci. Notation to

deal with very large or very small numbers.

Vocabulary:

Notation- A way of writing something that usually involves symbols, characters, or abbreviations.

Tools and Rules:

Scientific Notation- A number in the form m x where 1 < m < 10, and n is an integer.

Examples:

In-Class, Homework:

Pg. 223 (ORAL): #1-8 All; (WRITTEN) #1-20 evens

10n

(b) 5.3 Significant Digits Objectives: Understand how to

identify which digits are significant in a solution.

Vocabulary:

Significant Digit (aka Significant Figure): Any non-zero digit or any zero that has a purpose other than placing the decimal point. (See pg. 221)

Tools and Rules:

Rules for Sig Digs (Sig Figs):

See Hand-Out

Examples:

In-Class

(b) 5.4 Rational Expressions Objectives: Learn how to simplify

rational expressions. Vocabulary:

Rational Expression- See 5.1-5.2 notes.

Numerator: Top part of a fraction/rational expression.

Denominator: Bottom part of a fraction/rational expression.

Tools and Rules:

To simplify a rational expression, factor the numerator and the denominator, then cross out common factors.

Examples:

In-Class

Homework:

Pg. 228

#1-14 all (Written)

(b) 5.5 Multiplication and Division of rational expressions Objectives: To multiply and

divide rational expressions. Vocabulary: None.

Tools and Rules:

When you divide, flip (one after the division sign) and multiply.

Examples:

In class.

Homework:

Do Pg. 229 #22-26 evens

Do pg. 234 #2-14 evens

(b) 5.6 Sums and Differences of Rational Expressions Objectives: Add and Subtract

rational expressions. Vocabulary:

none

Tools and Rules: Examples:

In-Class.

Homework:Pg. 237 #1- 14 all

(b) 5.7 Complex Fractions Objectives: Simplifying complex

fractions. Vocabulary:

Complex fraction- if numerator, denominator, or both has one or more fractions, or powers with negative exponents.

Ex:

Tools and Rules:

Method 1)Simplify numerator and denominator separately; then divide.

Method 2) Multiply numerator and denominator by LCM of all the fractions appearing in the numerator and denominator.

For powers with negative exponents, first rewrite powers using positive exponents. Then simplify.

Examples:

In-Class.

Homework: Pg. 239 #1-10 all

(b) 5.8 Fraction Coefficients Objectives: Solve equations and

inequalities with fractional coefficients.

Vocabulary:

Coefficient: The number that is being multiplied by a variable.

Ex: 3x….3 is the coefficient

2x/3…..2/3 is the coefficient

-x……-1 is the coefficient

x/5……1/5 is the coefficient

Tools and Rules:

To get rid of all denominators in an equation or inequality, multiply both sides of an equation by the LCM.

Examples:

In-Class.

Homework: p. 245 #1-12 all

Word Problems Involving Fractional Coefficients Two types:

Work Problems Two people (or things) with different rates that work together. Formula:

Example:

% Mixture Problems Two things with different amounts and different concentrations that are mixed together to form a new

amount with a new concentration. Formula: (%A)(Amount of A) + (%B)(Amount of B) = (%Mix)(Amt. A + Amt. B) Example: Arnold Palmer mixes 5 quarts of iced tea that is 30% lemonade with 7 quarts of iced tea that is

50% lemonade. What percent of lemonade will he have when he mixes it together?

Homework: p. 245 #1-8all

11 1X Y

(b) 5.9 Fractional Equations Objectives: Solving and using

fractional equations. Vocabulary:

Fractional equation: an equation where a variable occurs in the denominator.

Extraneous root: an “extra” root that occurs when transforming a fractional equation that is NOT part of the original equation.

Tools and Rules:

If you transform an equation by multiplying by a polynomial, always check each root of the new equation in the original one.

Examples:

Homework: Pg. 249 #2-16 evens