Upload File

4.3$what$does$it$mean$to$be$rational? - weebly

3
Mathematics Vision Project | MV P Licensed under the Creative Commons Attribution4NonCommercial4ShareAlike 3.0 Unported license. 4.3 What Does it Mean to Be Rational? A Solidify Understanding Task Part I: Comparing rational numbers and rational fractions. 1. In your own words, define rational number. Circle the numbers below that are rational and refine your definition, if needed. 3 − 5 ! ! !" ! 14 2.7 5 2 ! 3 !! !"# ! 8 ! ! 2. The definition of a rational function is as follows: A function ! ! is called a rational function if and only if it can be written in the form ! ! = ! ! ! ! where ! !"# ! are polynomials in ! and ! is not the zero polynomial. Interpret this meaning in your own words and then write three examples of rational functions. 3. How are rational numbers and rational functions similar? Different? Part II: Arithmetic of Rational Expressions: making connections between rational numbers and rational expressions. Solve problems in the first column and then use the same process to simplify the rational expressions in the second column. Arithmetic of rational numbers Arithmetic of rational expressions 4a. ! ! + ! ! 4b. ! !!! + ! (!!!) 5a. ! ! + ! ! 5b. !! !!! + !! (!!!)(!!!) 13

Upload: others

Post on 25-Mar-2022

3 views

Category:

Documents


0 download

Report

TRANSCRIPT

Page 1: 4.3$What$Does$it$Mean$to$Be$Rational? - Weebly

!Mathematics!Vision!Project!|!MVP!!

Licensed(under(the(Creative(Commons(Attribution4NonCommercial4ShareAlike(3.0(Unported(license.! (

(

4.3$What$Does$it$Mean$to$Be$Rational?$A"Solidify!Understanding+Task!!

Part!I:!Comparing!rational!numbers!and!rational!fractions.!

1. In!your!own!words,!define!rational(number.!!((Circle!the!numbers!below!that!are!rational!and!refine!your!definition,!if!needed.!

! 3!!!!!! − 5!!!!!!! !! !!!!!!!!!"! !!!!!!!!14!!!!!!!2.7!!!!!!! 5!!!!!!!!2

!!!!!!!!3!!!!!!!!!!"#!8!!!!!!!! !!!!!!!!!

2. The!definition!of!a!rational(function!is!as!follows:!!A!function!! ! !is!called!a!rational!function!if!and!only!if!it!can!be!written!in!the!form!

! ! = ! ! !! ! !!where!!!!"#!!!are!polynomials!in!!!and!!!is!not!the!zero!polynomial.!!

!Interpret!this!meaning!in!your!own!words!and!then!write!three!examples!of!rational!functions.!!!

3. How!are!rational!numbers!and!rational!functions!similar?!Different?!

!

Part!II:!Arithmetic!of!Rational!Expressions:!making!connections!between!rational!numbers!and!rational!expressions.!Solve!problems!in!the!first!column!and!then!use!the!same!process!to!simplify!the!rational!expressions!in!the!second!column.!

Arithmetic!of!rational!numbers! Arithmetic!of!rational!expressions!4a.!!!!!! +

!!!

!!!!

4b.!!!!! !!!! + !

(!!!)!

5a.!!!!! +!!!

!!!!!

5b.!!!! !!!!! + !!

(!!!)(!!!)!

13

Page 2: 4.3$What$Does$it$Mean$to$Be$Rational? - Weebly

!Mathematics!Vision!Project!|!MVP!

!Licensed(under(the(Creative(Commons(Attribution4NonCommercial4ShareAlike(3.0(Unported(license.!

(

(

6a.!!!!!! −

!!!

!!!!

6b.!!!!!!! − !

(!!!)!

7a.!!!!!!×

!!!

!!!!

7b.!!(!!!)(!!!)

(!!!) × (!!!)(!!!)(!!!)!

8a.!!!!! ÷

!!!

!!!!!

8b.!!!(!!!)(!!!)

(!!!) ÷ (!!!)(!!!)(!!!)!

!

!

9.!!To!summarize,!explain!how!you!would!perform!the!following!arithmetic!operations!on!rational!expressions:!!

Adding:!

!

Subtracting:!

!

Multiplying:!

!

Dividing:!

!

!

! !

14

Page 3: 4.3$What$Does$it$Mean$to$Be$Rational? - Weebly

RATIONAL MINIMAX APPROXIMATION VIA ADAPTIVE · 2018-09-19 · RATIONAL MINIMAX APPROXIMATION A2429 points (see section 4.3), and our analysis justi es its choice: we prove its optimality

Weebly · 2020-05-08 · Weebly

Rational Ignorance versus Rational Irrationality

Rational Numbers ~ Multiplying Rational Numbers Rational Numbers ~ Multiplying Rational Numbers

Unit 8 Advanced Math 6 Unit 8 Calendar - Weebly · Pg.1a pg. 1b Unit 8 Operations with Rational Numbers Operations with Rational Numbers Converting Fractions, Decimals & Percents

4.3 Powerpoint Using Studies Wisely - Weebly

Rational expressions and rational equations

Algebra 1 Notes 4.3.notebook - Weebly

Ch. 7 Jeopardy - Weebly · 2019-05-16 · Ch. 7 Jeopardy Rational, Root, and Step Functions Power Functions Piecewise and Greatest Integer Functions Solving Rational and Step Functions

Rational Monism and Rational Pluralism

Home - Delran High Schooldhs.delranschools.org/UserFiles/Servers/Server_3013045... · 4.3 Rational Equations, Inequalities, Applications, and Models Solving Rational Equations and

Solving Harder Rational Equations - Weebly

RATIONAL NUMBERS Rational Numbers1

Unit 4 - Rational Expressions Notesvalentinesclass.weebly.com/.../unit_4_-_rational_expressions_notes.pdf · 4.3 Add & Subtract Rational Expressions • Using Rational Expressions

IBM Poutanen 3 - Jyväskylän yliopisto · Rational Software Architect Rational Application Developer Rational Functional & Manual Tester Rational Performance Tester Rational Team

RATIONAL CLEARC - IBM · Apex, Rational CRC, Rational PerformanceArchitect, Rational Rose, Rational Suite, Rational Summit, Rational ... Rational ClearCase is a comprehensive configuration

Copyright © 2011 Pearson Education, Inc. Slide 4.3-1 4.3 Rational Equations, Inequalities, Applications, and Models Solving Rational Equations and Inequalities

Weebly · Dividing Rational Functions When dividing rational functions, you multiply the first fraction by the reciprocal of the second fraction, simplifying where you can. SAME-CHANGE-FLIP!

Chapter 4 4.1 Division of Polynomials 4.2 Rational Equations 4.3 Rational …fd.valenciacollege.edu/file/jrhodes/college alg chap 4.pdf · 2016. 6. 13. · 4.2 Rational Equations

Using Rational DOORS for Rational Rose Interface€¦ · Rational DOORS for Rational Rose Interface creates a Rational DOORS formal surrogate module to store the Rational Rose data

chp 4.1 and 4.3 atomic theory - Weebly

Hodge-Witt Cohomology and Witt-Rational …Witt-rational singularities 742 4.1. The Witt canonical system 743 4.2. Topological finite quotients 747 4.3. Quasi-resolutions and relative

Polynomial and Rational Functions 2 - Weebly

Introduction - University of Hawaiimyounsi/JuliaApprox.pdf · 2017. 10. 16. · 4.3], which deals with rational maps instead of polynomials. The proof of Theorem 1.2 generalizes the

RATIONAL EXPRESSIONS. Rational Expressions and Functions: Multiplying and Dividing Objectives –Simplifying Rational Expressions and Functions –Rational

Rational ALM, Rational Team Concert and Rational Quality Manager

Two-Color Counters - Mello mathematicsmellomathematics.weebly.com/uploads/6/0/5/7/60571637/4.3...sums of rational numbers by describing real-world contexts. c. Understand subtraction

4.3 FURTHER PROGRAMMING - Weebly · PROGRAMMING PARADIGMS 1 4.3 FURTHER PROGRAMMING 4.3.1 PROGRAMMING PARADIGMS PROGRAMMING PARADIGMS Programming paradigms are simply methods of programming

Weebly · Weebly

Section 4.3 The Derivative in Graphing and Applications- “Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents”

Section 4.3 the graph of a rational function

Dividing Rational Numbers - Weebly

4.3 Adding & Subtracting Rational Expressions

11.3 – Rational Functions. Rational functions – Rational functions – algebraic fraction

Rational Ignorance vs. Rational Irrationality