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Problem-of-the-Week

Baffling Birthdays

The Problem

Suzanne was having a party at her house. The group was discussing birthdays and talking about planning parties. After listening for a while Suzanne said, There is something interesting about my birthday. Two days ago I was 13, but next year Ill be 16. If Suzanne was telling the truth, what kind of party was she having?

s

Expression

Rational

Simplify

Strategies and Hints

1.Read the problem carefully so you understand exactly what Suzanne said.

2.List several kinds of parties Suzanne might be having.

3.Determine the dates of specific types of parties. For example, a Valentines Day party would occur on February 14.

4.What important things would you list if you were making a chart to solve this problem?

RAISING THE BAR

***Guess the the problem of the week ACCURATELY by Friday, October 22nd and your name will be included in the weekly raffle for a candy bar. Each Scholar only gets ONE submission.****

GOOD LUCK! (

Algebra 1 Copyright Glencoe Division, Macmillan/McGraw-Hill

Cornell Notes: Simplifying Rational Expressions

(Add, Subtract, Multiply, Divide)

SPI Focus of the week

SPI 3102.3.4 Operate with, evaluate, and simplify rational expressions including determining restrictions on the domain of the variables.

Check for Understanding: By the end of this week you should be able to simplify expressions using exponent rules including negative exponents and zero exponents; and add, subtract, multiply, and divide rational expressions and simplify those results.

Key Vocabulary

Key Concepts

-Opposites:

***Polynomial, Rational Expression, Domain of a Rational Expression, Reduced Form, Excluded, Value, Domain Restrictions,****

What is a rational expression? A rational expression is an expression that can be written as a _________ of two __________polynomials where the __________________ is not _____. A rational expression is undefined when the denominator is 0. A number that makes a rational number ___________is called an ___________ ___________.

For example, ------------ is undefined when x = 3. So, 3 is an __________ _______________.

To simplify a rational expression you __________ out the numerator and denominator. Then ____________ out the common factors. ***A rational expression is in ________________ _______________ when the numerator and denominator have no factors in common than 1.

When you are simplifying a rational expression look for factors that are opposites of each other. For example, (x 1) and (1 x) are opposites.

Factoring Out a Rational Expression

Factoring a Trinomial Review

Steps to Factoring a Trinomial

1. Form the __________ of _____

2. Factor out the ___________ of ______ so that the sum of the factors equal your ___ _________

3. ______________ _______ _____________________

4. Factor by __________________

5. _________________ out common factors

6. Use the method _______________ to check your answer.

________________ & ___________________ a Rational Expression

Guided Practice

When multiplying a rational expression by a polynomial be sure to write the polynomial as a fraction with a denominator of 1.

Steps to Multiplying & Dividing

1. ________________________________

2. ________________________________

3. ________________________________

*The only difference when dividing is to make sure you use the Reciprocal Property and flip the fraction. Then multiply as needed.

__________________ & _____________________ a Rational Expression

Guided Practice

When adding or subtracting rational expressions utilize the skills of adding or subtracting fractions.

*If your denominators are the same just add/subtract the numerators.

*To add or subtract rational expressions that have different denominators, use the LCD (Least Common Denominator) to write equivalent rational expressions that have the same denominator just like if it was a numerical fraction.

Steps to Adding & Subtracting

1. Rewrite the fractions using _________

2. Subtract/Add the fractions

3. Simplify the __________________

Summarize what you learned:

Questions?

In a small paragraph or bullet points summarize what you learned from the lesson. This is solely for your benefit and you should answer truthfully. Reflect on something you didnt know before. Then at the end write down any questions you may have to ask your teacher.

_____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

_______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________.

ALGEBRA UNIT VOCABULARY SHEET

Vocabulary Word

Formal Definition

In Your Own Words

Synonyms

Clarifying

Illustration

This Vocabulary Sheet should be used as an interactive tool for you to learn and remember words relating to Algebra. Be sure to list all the words on the Class Word Wall as well as add your own words that you have learned as well. Extra points (1pt each) will be given towards a unit test for each additional word a scholar completes in its entirety.

Multiplying Rational Expressions

Dividing Rational Expressions

Adding/ Subtracting Rational Expressions

Solving Rational Equations

s

Expression

Rational

Simplify

EMBED Equation

Simply Rational Expression

Adding/Subtracting with Like Denominators

Multiplying Rational Expressions

Dividing Rational Expressions

Adding/Subtracting with Unlike Denominators

Real Life Application:

(Multiplying/Dividing)

A. Zoo Exhibition The directors of a zoo have drawn up preliminary plans for a rectangular exhibition. They have decided on dimensions that allows one side to be (4x + 3) and the other side (4x - 2)

Write a rational expression for the ratio of the perimeter to the area of the exhibit.

Simplify your expression from part (a).

B. Materials Used The material consumed M (in thousands of pounds) by a plastic injection molding machine per year between 1995 and 2004 can be modeled by

M=____8x2 + 66t + 70____

(3 0.2t + 0.1t2)(t + 7)

where t is the number of years since 1995. Simplify the model and approximate the number of pounds consumed in 2000.