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

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Blaise McGee
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Adding and Subtracting Rational Epressions Interactive Math Notebook Activities and Scaffolded Notes Review: Simplifying Fractions What is a common denominator?

1 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?

2 Scaffolded Notes

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

4 Review: Simplifying Fractions First, factor the numerator and denominator. Then, cancel out factors that occur in both the numerator and denominator y y y 1 + 8y ( + 1) y + 1 y ( + 1) ( + 1) ( 5) ( + 5)( 5) ( + ) ( + )( + ) + 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.

5 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.

6 Steps for Adding Fractions with a Common Denominator Add the numerators, but keep the denominator the same. Combine like terms and simplify 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 = = = = 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 Step : Combine like terms and simplify. 9

7 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) ( ) ( + ) 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)

8 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. + ( + ) ( + ) ( 1) ( + ) ( + ) ( + ) 6 ( + 1) + 6 ( + ) ( + ) + ( + 7) ( ) = = 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) + 10 ( + 1) 9( 1) ( ) + ( ) ( ) = + ( 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

10 Adding/Subtracting Fractions with Different Denominators Find a common denominator between your two fractions. Substitute your equivalent fractions into your problem = 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 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 = 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

11 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.

12 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 = + 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 7 = 8 5 = = = 8 =

13 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.

14 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) 5 = ( + 5)( 5) 6 ( + 5)( 5) ( + 5)( 5) 5 = ( + 5)( 5) = ( + 5)( 5) = 5( 5) ( + 5)( 5) ( + 5)( 5) 5 19 ( + 5)( 5) + 10 = ( + 5)

15 + 5 = 1 Use Common Denominators to Solve Equations = = 1 + = 11 1 = = Cross multiply. What is a proportion? Simplify Step : Solve

16 Use Common Denominators to Solve Equations + 5 = = + 1 = 9 1 ( + 5 = 1 ) + 5 = + 5 = 1 = = 11 ( + = 11) = = 7 1 = 11 5( = ) = = 0 = 0 1 = ( 1) ( 1 = ) ( 1) 1 = ( 1) 1 ( 1) = 1 1 = 19 9( ( + 1) 9 = 1 ) = = = 5 10 = 10( 5 10 = ) = 10 = 0 = 0 Cross multiply = 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 8 = 15

17 Interactive Math Notebook Review Activities

18 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.

19 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.

20 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.

21 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.

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7.3 Adding and Subtracting Rational Expressions

7.3 Adding and Subtracting Rational Epressions LEARNING OBJECTIVES. Add and subtract rational epressions with common denominators. 2. Add and subtract rational epressions with unlike denominators. 3. Add