Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting

$Page 1: Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting$
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Fractions

02/12/112

Table of Contents

Learning Objectives/Previous Knowledge

Basic rules of fractions

Adding fractions

Adding and subtracting more than two fractions

Ipsative Choice

Multiplying fractions

Cross Cancellation

Dividing fractions

Simplify polynomials with fractions

1

2

3

4

5

6

7

8

9

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Learning Objectives

LO 1

LO 2

Understand what a fraction represents

Perform basic operations with fractions

LO 3 Simplify expressions and solve equations with fractions

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Definitions

Definition 1 A fraction is a way of expressing part of a whole number

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Definition 2 A fraction is also called a ratio and is part of the rational number set

Definition 3 A fraction consists of a numerator (the top)which represents the pieces

Definition 4 A fraction consists of a denominator (the bottom)which represents how many pieces in the whole number

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Previous knowledge

PK 1

PK 2

Basic Operations and Properties

Combine Like Terms

PK 3 Exponent Rules

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Rule 1

Rule 2

Adding and subtracting fractions requires cross multiplication

Multiplying fractions requires straight across multiplication

Rule 3 Dividing requires flipping a fraction and multiplying straight across

Rule 4 Learn to “get rid” of fractions by turning expressions into equations

Basic Rules of Fractions

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Adding Fractions

2 + 3 5 7

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Step 1

Step 2

Construct matrix with numerators on top and denominators on side

Blank out boxes diagonally

Step 3 Multiply matrix

Step 4 Add the results; this becomes the numerator

2 + 35 7

+ 15

+ 14

= 29

5 x 7 = 35

2 35 7

Step 5 Multiply left side numbers (denominators); this becomes the denominator

35

Step 6 Reduce fraction if possible

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Now you try

3 + 54 7

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Step 1

Step 2





3 + 54 7

+ 20

+ 21

= 41

4 x 7 = 28

3 54 7


28


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Now you try

3 ─ 54 7

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Step 1

Step 2





3 ─ 54 7

- 20

+ 21

= 1

4 x 7 = 28

3 - 54 7


28


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Adding/Subtracting more than 2 fractions

3 + 5 - 2 4 7 3

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Step 1

Step 2

Construct cascading matrix


Step 3 Multiply matrix; you can only multiply by the box above!


3 + 54 73 54 7



─ 23

- 23

+ 20 - 8

+ 21 - 56

+ 63 + 60

= 67

4 x 7 x 3 = 8484

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Now you try

3 + 5 - 1 4 7 6

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Step 1

Step 2

Construct cascading matrix


Step 3 Multiply matrix; you can only multiply by the box above!


3 + 54 73 54 7



─ 16

- 16

+ 20 - 4

+ 21 - 28

+ 126 + 120

= 218

4 x 7 x 6 = 168168

= 109 84

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Is there another method?

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Rooftop Method

3 + 5 - 1 4 7 6

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Step 1

Step 2

Build a rooftop

Add the results; this is your numerator

Step 3 Multiply the denominators; this is your denominator

Step 4

3 + 54 7

Reduce fraction if possible

─ 16

3 x 7 x 6 = 126

+ 126

4 x 5 x 6 = 120

+ 120

4 x 7 (-1) = - 28

- 28218

4 x 7 x 6 = 168 168

= 109 84

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Now you try!

3 + 5 + 1 5 7 3

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Step 1

Step 2

Build a rooftop

Add the results; this is your numerator

Step 3 Multiply the denominators; this is your denominator

Step 4

3 + 55 7

Reduce fraction if possible

+ 13

3 x 7 x 3 = 63

+ 63

5 x 5 x 3 = 75

+ 75

5 x 7 x 1 = 35

35173

5 x 7 x 3 = 105 105

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Ipsative Choice

Decide which method you will master

Matrix or Rooftop?

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Define

Decide

Ipsative choice means “forced choices”

Either choice works – matrix or rooftop method

Master Do all problems the same way until you have mastered the method

Ipsative Choice

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Multiplying Fractions

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Rule 1

Rule 2






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Rule 1

Rule 2

Multiply numerators; this becomes the new numerator

Multiply denominators; this becomes the new denominator

Rule 3 Reduce fraction if possible

23

57

2 (5) = 103 7 21

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Now you try!

34 43

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Rule 1

Rule 2

Multiply numerators; this becomes the new numerator

Multiply denominators; this becomes the new denominator


34

34

3 (3) = 94 4 16

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Cross Cancellation

74 63

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Rule 1

Rule 2

Numerators can be moved anytime YOU want

Reduce fraction

Rule 3 Multiply straight across

34

76

3 (7)(4) 6

12

1 x 7 = 72 x 4 = 8


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Now you try!

54 93

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Rule 1

Rule 2

Numerators can be moved anytime YOU want

Reduce fraction


34

59

3 (5)(4) 9

13

1 x 5 = 53 x 4 = 12


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Dividing Fractions

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Rule 1

Rule 2






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Divide

54 93 /

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Rule 1

Rule 2

Write top fraction

Flip bottom fraction

Rule 3 Check for cross cancellation; you can here but we will skip it

34

95


─

34

95

3 x 5 = 154 x 9 = 36


512

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Now you try!

45 73 /

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Rule 1

Rule 2

Write top fraction

Flip bottom fraction

Rule 3 Check for cross cancellation; none here

35

47


─

35

47

3 x 7 = 215 x 4 = 40


2140

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Simplify Expressions with Fractions

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Simplify

2x2 + 4x – 10x 3 5

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Step 4

Step 5

Combine like terms if necessary

Divide by the y coefficient

Step 6 Simplify if possible

Step 7 You can erase the “= y ” if you want

Step 2

Step 1 Turn the expression into an equation by introducing “ = y”

Every term gets a denominator

Step 3 Multiply every term’s numerator with every other denominator(Roof top method)

2x²3

+ 4x – 10x15

= y(5) (1)

2x² + 4x(3) (1)

– 10x(3) (5) (1)(3) (5)

=

y

10x² + 12x – 150x = 15y

10x² – 138x = 15y

10x² – 138x = y 15

x (10x – 138) 15

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Now you try!

2x2 + 3x – 10x 7 5

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Step 4

Step 5

Combine like terms if necessary

Divide by the y coefficient

Step 6 Simplify if possible

Step 7 You can erase the “= y ” if you want

Step 2

Step 1 Turn the expression into an equation by introducing “ = y”

Every term gets a denominator

Step 3 Multiply every term’s numerator with every other denominator(Roof top method)

2x²7

+ 3x – 10x15

= y(5) (1)

2x² + 3x(7) (1)

– 10x(7) (5) (1)(7) (5)

=

y

10x² + 21x – 350x = 35y

10x² – 329x = 35y

10x² – 329x = y 35

x (10x – 329) 35

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End Fractions

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Documents

Fractions 02/12/112lntaylor ©. Table of Contents Learning Objectives/Previous Knowledge Basic rules of fractions Adding fractions Adding and subtracting