Adding and Subtracting Rational Expressions Interactive Math Notebook Activities and Scaffolded Notes

Similar documents
7.3 Adding and Subtracting Rational Expressions

Day 3: Section P-6 Rational Expressions; Section P-7 Equations. Rational Expressions

Define a rational expression: a quotient of two polynomials. ..( 3 10) (3 2) Rational expressions have the same properties as rational numbers:

Parts of a Plant Interactive Notebook

Lesson #9 Simplifying Rational Expressions

WORKING WITH EXPRESSIONS

Interactive Science Journal, 6 Experiment Stations & more! By: Jessica Sibucao

SOLUTIONS. Math 130 Midterm Spring True-False: Circle T if the statement is always true. Otherwise circle F.

Problem 1 Oh Snap... Look at the Denominator on that Rational

Complex fraction: - a fraction which has rational expressions in the numerator and/or denominator

Math-1010 Lesson 4-2. Add and Subtract Rational Expressions

4th Grade COMMON CORE MATH. Interactive Notebook 4.NBT.1 BY BLAIR TURNER

4.3 Division of Polynomials

Algebra Final Exam Review Packet

Math 1320, Section 10 Quiz IV Solutions 20 Points

Algebra III and Trigonometry Summer Assignment

1. Write three things you already know about expressions. Share your work with a classmate. Did your classmate understand what you wrote?

Eleven reference pages that conveniently fit a standard composition book!

4.2 Reducing Rational Functions

A2T. Rational Expressions/Equations. Name: Teacher: Pd:

Daily Skill Builders:

ALGEBRA. COPYRIGHT 1996 Mark Twain Media, Inc. ISBN Printing No EB


TECHNIQUES IN FACTORISATION

Handwriting. Practice Makes Perfect. ~ Lowercase Letters ~ Lavinia Pop

Adding and Subtracting Rational Expressions

Math 154 :: Elementary Algebra

Algebra Review C H A P T E R. To solve an algebraic equation with one variable, find the value of the unknown variable.

Fractions. Review R.7. Dr. Doug Ensley. January 7, Dr. Doug Ensley Review R.7

Factor each expression. Remember, always find the GCF first. Then if applicable use the x-box method and also look for difference of squares.

The Rock Cycle. Interactive Science Notebook

Unit 9 Study Sheet Rational Expressions and Types of Equations

ACCUPLACER MATH 0311 OR MATH 0120

EARTH S REVOLUTION -and- EARTH S ROTATION

Math Review Packet. for Pre-Algebra to Algebra 1

2014 Caryn White: Caryn Loves Math 1

CAHSEE on Target UC Davis, School and University Partnerships

6.6 General Form of the Equation for a Linear Relation

Section 6.2 Long Division of Polynomials

Table of Contents. Amy Harrison,

SUMMER REVIEW PACKET. Name:

Chapter 7 Class Notes. Intermediate Algebra, MAT1033C. SI Leader Joe Brownlee. Palm Beach State College

Review of Rational Expressions and Equations

A. Incorrect! Perform inverse operations to find the solution. B. Correct! Add 1 to both sides of the equation then divide by 2 to get x = 5.

TABLE OF CONTENTS. Introduction to Finish Line Indiana Math 10. UNIT 1: Number Sense, Expressions, and Computation. Real Numbers

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

Grades 2-7. Exploring Creation with Astronomy 2 nd Edition Lapbook. Sample Page. A Journey Through Learning

Section 2.4: Add and Subtract Rational Expressions

Table of Contents. Unit 3: Rational and Radical Relationships. Answer Key...AK-1. Introduction... v

Bishop Kelley High School Summer Math Program Course: Algebra 2 A

MATH 1111 Section P.1 Bland. Algebraic Expressions - An algebraic expression is a combination of variables and numbers using operations.

Algebra Concepts Equation Solving Flow Chart Page 1 of 6. How Do I Solve This Equation?

Mini Lecture 9.1 Finding Roots

Inverse Variation. y varies inversely as x. REMEMBER: Direct variation y = kx where k is not equal to 0.

A Quick Algebra Review

Eby, MATH 0310 Spring 2017 Page 53. Parentheses are IMPORTANT!! Exponents only change what they! So if a is not inside parentheses, then it

Math Tutor: Algebra Skills

LESSON 9.1 ROOTS AND RADICALS

Math 101 Study Session Spring 2016 Test 4 Chapter 10, Chapter 11 Chapter 12 Section 1, and Chapter 12 Section 2

MATH98 Intermediate Algebra Practice Test Form B

Reciprocal Science Teaching Junkie, Inc. 1

Transition to College Math and Statistics

AP Calculus AB Summer Assignment

(1) Assignment # 1 Absolute Value. (2) Assignment # 2 Compound Absolute Values. (3) Assignment # 3 Exponents. (4) Assignment # 4 Simplifying Radicals

Solving Quadratic Equations

Alg 1B Chapter 7 Final Exam Review

Math Analysis Chapter 2 Notes: Polynomial and Rational Functions

27 Wyner Math 2 Spring 2019

Lecture 5: Finding limits analytically Simple indeterminate forms

Module 2, Section 2 Solving Equations

Chapter 7 Rational Expressions, Equations, and Functions

Rational Expressions

Fortune Teller. Eukaryotic vs. Prokaryotic Cells. Hands on Study Tool

FIVE. The Types of. Folktales

Classifying Polynomials. Classifying Polynomials by Numbers of Terms

Elementary Algebra Study Guide Some Basic Facts This section will cover the following topics

Mathematics 96 (3581) CA (Class Addendum) 4: Identity Properties Mt. San Jacinto College Menifee Valley Campus Spring 2013

Polynomials and Factoring

Algebra 2 Segment 1 Lesson Summary Notes

MATH98 Intermediate Algebra Practice Test Form A

RAMAPO&INDIAN*HILLS*SCHOOL*DISTRICT*

Summer Packet Geometry PAP

Color-by- Number 2015 Science Teaching Junkie, Inc.

Solving Equations. Solving Equations - decimal coefficients and constants. 2) Solve for x: 3(3x 6) = 3(x -2) 1) Solve for x: 5 x 2 28 x

John L. Lehet

5.2 Polynomial Operations

Lesson 9: Radicals and Conjugates

Simplifying Rational Expressions

Eureka Math. Algebra II Module 1 Student File_A. Student Workbook. This file contains Alg II-M1 Classwork Alg II-M1 Problem Sets

Unit 6: 10 3x 2. Semester 2 Final Review Name: Date: Advanced Algebra

Algebra. Table of Contents

April 30, Name: Amy s Solutions. Discussion Section: N/A. Discussion TA: N/A

Lesson 3 Algebraic expression: - the result obtained by applying operations (+, -,, ) to a collection of numbers and/or variables o

8.3 Zero, Negative, and Fractional Exponents

Ch. 12 Rational Functions

6.1. Rational Expressions and Functions; Multiplying and Dividing. Copyright 2016, 2012, 2008 Pearson Education, Inc. 1

Pre-Algebra Notes Unit 12: Polynomials and Sequences

Math 31A Discussion Session Week 1 Notes January 5 and 7, 2016

Math-3. Lesson 3-1 Finding Zeroes of NOT nice 3rd Degree Polynomials

POLYNOMIAL EXPRESSIONS PART 1

Transcription:

Adding and Subtracting Rational Epressions Interactive Math Notebook Activities and Scaffolded Notes Review: Simplifying Fractions What is a common denominator? Steps for Adding Fractions with a Common Denominator Adding Fractions with a Common Denominator Steps for Subtracting Fractions with a Common Denominator Distribute Before Adding Fractions Distribute Before Subtracting Fractions Adding/Subtracting Fractions with Different Denominators Adding/Subtracting an Integer and a Fraction Adding/Subtracting a Polynomial and a Fraction Finding the Least Common Denominator (Denominators are Integers) Finding the Least Common Denominator (Denominators are Terms) Finding the Least Common Denominator (Denominators are Polynomials) Use Common Denominators to Solve Equations What is a proportion?

Scaffolded Notes

Review: Simplifying Fractions First, factor the numerator and denominator. Then, cancel out factors that occur in both the numerator and denominator. 8 1 9y 1 + 8y + 1 + 5 5 + 8 + 8 + 16 What is a common denominator? Eample

Review: Simplifying Fractions First, factor the numerator and denominator. Then, cancel out factors that occur in both the numerator and denominator. 8 1 9y y y 1 + 8y ( + 1) y + 1 y + 1 + ( + 1) ( + 1) 1 5 5 ( 5) ( + 5)( 5) 1 + 5 + 8 + 8 + 16 ( + ) ( + )( + ) + What is a common denominator? Eample When two fractions have the same denominator it is said that they have common denominators. The fractions 1 a and 5 a have a common denominator of a.

Steps for Adding Fractions with a Common Denominator Add the numerators, but keep the denominator the same. Combine like terms and simplify. Add two fractions with a common integer as a denominator. Adding Fractions with a Common Denominator Add two fractions with a common variable term as a denominator. Add two fractions with a common binomial as a denominator. Add two fractions with a common polynomial as a denominator. Steps for Subtracting Fractions with a Common Denominator Replace the subtraction sign with an addition sign and distribute the subtraction sign to the numerator that follows. Add the numerators, but keep the denominator the same. Step : Combine like terms and simplify.

Steps for Adding Fractions with a Common Denominator Add the numerators, but keep the denominator the same. Combine like terms and simplify. 5 + 5 + 5 5 Adding Fractions with a Common Denominator Add two fractions with a common integer as a denominator. Add two fractions with a common variable term as a denominator. Add two fractions with a common binomial as a denominator. Add two fractions with a common polynomial as a denominator. + 5 + 5 = 7 + 8 + 8 = 11 1 + 1 + 5 + 1 1 + 5 + 1 = 6 + 1 9 + + 1 + + + 1 9 + + + 1 = 11 + + 1 Steps for Subtracting Fractions with a Common Denominator Replace the subtraction sign with an addition sign and distribute the subtraction sign to the numerator that follows. Add the numerators, but keep the denominator the same. 9 9 9 + 9 + ( ) 9 Step : Combine like terms and simplify. 9

5( + 1) Distribute Before Adding Fractions First, make sure that the numerators and denominators are in simplest form. Then, add the numerators. Finally, combine like terms. + ( + ) ( + ) + 8( 1) 9( + ) 7 + ( + ) 7 1( + ) 6 ( + 1) + 6 ( + ) ( + ) + ( + 7) ( ) 9 + 9 5( + ) Distribute Before Subtracting Fractions First, make sure that the numerators and denominators are in simplest form. Then, change the subtraction problem to an addition problem and add the numerators. Finally, combine like terms. ( + 1) ( + 1) ( + 5) ( + 1) 9( 1)

5( + 1) 5 + 5 Distribute Before Adding Fractions First, make sure that the numerators and denominators are in simplest form. Then, add the numerators. Finally, combine like terms. + ( + ) + + 6 ( + ) + 8 + 8( 1) + 8 8 9( + ) 7 9 + 7 7 + ( + ) 7 + + 7 5 + 5 + + 6 8 + 11 + 8 + 8 8 10 9 + 7 + + 7 11 + 1 7 1( + ) 6 ( + 1) + 6 ( + ) ( + ) + ( + 7) ( ) 9 + 9 6 + + 6 + 6 + + 6 6 + 1 9 + 9 + + 6 + 6 + 6 + + 6 5 + 1 5 + 1 = 6 + 1 + 9 7 + 1 7 + 1 9 = 9 5( + ) Distribute Before Subtracting Fractions First, make sure that the numerators and denominators are in simplest form. Then, change the subtraction problem to an addition problem and add the numerators. Finally, combine like terms. 5 + 15 ( + 1) + ( + 1) + ( + 5) + 10 ( + 1) 9( 1) ( ) + ( ) 9 9 5 + 15 + + 1 + ( ) + + 6 = + ( 10) + + 9 + 9 + 10 + 9

Adding/Subtracting Fractions with Different Denominators Find a common denominator between your two fractions. Substitute your equivalent fractions into your problem. Step : If it is not already an addition problem, change it to addition. Step : Add the numerators, but keep the denominator the same. Step 5: Combine like terms and simplify. Rewrite your integer as a fraction. Find a common denominator between your two fractions. Step : Substitute your equivalent fractions into your problem. Step : If it is not already an addition problem, change it to addition. Step 5: Add the numerators, but keep the denominator the same. Step 6: Combine like terms and simplify. Adding/Subtracting an Integer and a Fraction

Adding/Subtracting Fractions with Different Denominators Find a common denominator between your two fractions. Substitute your equivalent fractions into your problem. + 6 6 + 6 = 6 If I multiply by it will also be 6. Step : If it is not already an addition problem, change it to addition. Step : Add the numerators, but keep the denominator the same. Step 5: Combine like terms and simplify. 6 + 6 + 6 5 6 Adding/Subtracting an Integer and a Fraction Rewrite your integer as a fraction. Find a common denominator between your two fractions. Step : Substitute your equivalent fractions into your problem. 8 8 1 8 1 8 1 = If I multiply 1 by it will also be. Step : If it is not already an addition problem, change it to addition. Step 5: Add the numerators, but keep the denominator the same. Step 6: Combine like terms and simplify. + ( ) + ( ) 9

Adding/Subtracting a Polynomial and a Fraction Rewrite your integer as a fraction. Find a common denominator between your two fractions. Step : Substitute your equivalent fractions into your problem. Step : If it is not already an addition problem, change it to addition. Step 5: Add the numerators, but keep the denominator the same. Step 6: Combine like terms and simplify. Finding the Least Common Denominator (Denominators are Integers) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify.

Adding/Subtracting a Polynomial and a Fraction Rewrite your polynomial as a fraction. Find a common denominator between your two fractions. Step : Substitute your equivalent fractions into your problem. + 1 + 1 1 + 1 1 + + 1 1 = + If I multiply 1 by it will also be. Step : If it is not already an addition problem, change it to addition. Step 5: Add the numerators, but keep the denominator the same. Step 6: Combine like terms and simplify. + + ( ) + + ( ) + + ( ) Finding the Least Common Denominator (Denominators are Integers) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify. 1 6 5 1 + 7 8 8 5 = 1 7 = 8 5 = 10 1 7 = 1 8 10 + 1 1 1 = 8 =

Finding the Least Common Denominator (Denominators are Terms) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify. Finding the Least Common Denominator (Denominators are Polynomials) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify.

Finding the Least Common Denominator (Denominators are Terms) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify. + y y = y y y y y = y y y y + y y = y y = yy y = y y = y y + y Finding the Least Common Denominator (Denominators are Polynomials) Factor the denominators. Multiply each denominator by the factors of the other denominator that are missing. Step : Multiply each numerator by the factors of the other denominator that are missing. Step : Simplify. 5 + 5 + 10 5 = ( + 5)( 5) 5 = ( + 5)( 5) 6 ( + 5)( 5) + 5 5 ( + 5)( 5) 5 = ( + 5)( 5) 5 + 10 = ( + 5)( 5) 5 + 10 = 5( 5) ( + 5)( 5) 6 + 5 5 ( + 5)( 5) 5 19 ( + 5)( 5) + 10 = ( + 5)

+ 5 = 1 Use Common Denominators to Solve Equations 5 + 5 = + 1 9 = 1 + = 11 1 = 1 6 1 5 10 = Cross multiply. What is a proportion? Simplify Step : Solve

Use Common Denominators to Solve Equations + 5 = 1 5 + 5 = + 1 = 9 1 ( + 5 = 1 ) + 5 = + 5 = 1 = 5 1 1 + = 11 ( + = 11) + + 7 = = 7 1 = 11 5( 5 + 5 = ) 5 5 + 5 = 5 5 + = 0 = 0 1 = 1 6 1 ( 1) ( 1 = 1 6 1 ) ( 1) 1 = ( 1) 1 ( 1) 6 1 6 = 1 1 = 19 9( + 1 9 9( + 1) 9 = 1 ) = 9 9 1 + 1 = = 5 10 = 10( 5 10 = ) 10 5 10 10 = 10 = 0 = 0 Cross multiply. 10 8 = 1 What is a proportion? A simple rational equation stating that one fraction is equal to the other. Simplify Step : Solve 10 1 = 8 10 = 8 10 8 = 8 8 = 15

Interactive Math Notebook Review Activities

Common Denominator 1. Cut along the bold lines and fold along the dotted lines.. Write your eamples inside of the folds.. Insert your finished matchbook into your math notebook. Define and give an eample. Steps for Subtracting Fractions with a Common Denominator Replace the subtraction sign with an addition sign and distribute the subtraction sign to the numerator that follows. Add the numerators, but keep the denominator the same. Step : Combine like terms and simplify. Glue this flap into your math journal. Steps for Adding Fractions with a Common Denominator Add the numerators, but keep the denominator the same. Combine like terms and simplify. Glue this flap into your math journal.

Directions: 1. Cut along the bold lines and fold along the dotted lines.. When you fold along the dotted line you will have a mini-book.. Flip up each flap and write your eamples in the inside pages.. Insert your finished book into your math notebook. Distribute before Adding Fractions Give an eample. Distribute before Subtracting Fractions Give an eample. Directions: 1. Cut along the bold lines and fold along the dotted lines.. When you fold along the dotted line you will have a mini-book.. Flip up each flap and write your definitions and eamples in the inside pages.. Insert your finished book into your math notebook. Add two fractions with different denominators. Add an integer and a fraction. Add a polynomial and a fraction.

Directions: 1. Cut along the bold lines and fold along the dotted lines.. When you fold along the dotted line you will have a mini-book.. Flip up each flap and write your definitions and eamples in the inside pages.. Insert your finished book into your math notebook. Subtract two fractions with different denominators. Subtract an integer and a fraction. Subtract a polynomial and a fraction. Finding the Least Common Denominator Step : Simplify. Step : Multiply each numerator by the factors of the other denominator that are missing. Multiply each denominator by the factors of the other denominator that are missing. Factor the denominators. Directions: 1. Cut along the bold lines and fold along the dotted lines.. Use a little bit of glue underneath the top flap to insert the flap book into your math notebook.. Flip up each flap and write your eamples directly onto your math notebook page.

Definition Proportions Directions: 1. Cut along the bold lines and fold along the dotted lines.. When you fold along the dotted line you will have a triangle flap book.. Flip up each flap and write your eamples in the inside pages.. Insert your finished book into your math notebook.

INB SAMPLES

Thank you for your purchase! Please be sure to visit our store for more high-quality teaching products (click on the star to follow us). If you would please take a moment to rate your purchase, we would greatly appreciate it, and you will receive TpT credits towards future purchases! A special thank you to the following for providing quality borders, fonts, clip art, etc. e COPYRIGHT INFORMATION April Hovjacky 015 Apples and Bananas All content included in this product is the property of Apples and Bananas or its content suppliers and is protected by international copyright laws and the Digital Millennium Copyright Act (DMCA). Permission is granted for personal or classroom use only. Additional licenses may be purchased. Material may not be reproduced or published on the Internet in any form.