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Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions
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Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Dec 26, 2015

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Dale Hall
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Page 1: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Equivalent and Simplifying Fractions

Adding Fractions

Multiplying Fractions

Fractions

Dividing Fractions

Subtracting Fractions

Page 2: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Starter Questions

2 2

2

4 , 3 2

24 16

3 1 15 2 74 8 8

2z q and r

q

y y

z r

1. True or false

2. I f .

Find

3. Factorise

Page 3: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. To explain how to simplify algebraic fractions.

1.1. Understand term Understand term Highest Common Factor.Highest Common Factor.

Algebraic Fractions

2.2. Simplify algebraic Simplify algebraic fractions by identifying fractions by identifying HCF.HCF.

Page 4: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Equivalent Fractions

We already know how to create an equivalent fraction for numerical fractions. The exact same process is used for algebraic fractions.Numerical Fraction

12

24

36

Algebraic Fraction

Multiply top and bottom by any number

57

1014

5070

Multiply top and bottom by any number or letter

1x

22

x yxy

3( 1)x

62( 1)

x

3( 1)

f

f x

Page 5: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Equivalent Fractions

Numerical Fraction

12

13 6

Algebraic Fraction

57

12 14

1x

1y xy

3( 1)x

62y 2 ( 1)y x

Common Denominator for 2 fractions

Page 6: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

We can sometimes reduce fractions to a simpler form if the numerator and denominator have a number or letter in common.Examples

1215

3 43 5

45

HCF = 3

2yy

y yy

1y

y

HCF = Y

Algebraic Fractions

Page 7: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

What Goes In The Box ?

Page 8: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. To explain how to multiply algebraic fractions.

1.1. Know rules for Know rules for multiplication simple multiplication simple fractions.fractions.

2.2. Apply knowledge to Apply knowledge to algebraic fractions.algebraic fractions.

Multiplication

Algebraic Fractions

Page 9: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

3 48 5

310

Numerical fraction

2

5 36

a

a

52

a

Algebraic Fraction

Algebraic FractionsMultiplication

1240

2

156aa

1240

10

3

2

156aa

2

15

1

Page 10: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. To explain how to divide algebraic fractions.

1.1. Know rules for division of Know rules for division of simple fractions.simple fractions.

2.2. Apply knowledge to Apply knowledge to algebraic fractions.algebraic fractions.

Division

Algebraic Fractions

Page 11: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

4 59 6

815

Numerical Fraction

2 53

xy x

y

2215

y

Algebraic Fraction

Algebraic FractionsDivision

4 69 5

23 5

xy y

x

2215xyx

1

1

2445

15

8

Page 12: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

2 33 y

29y

2 4 3 95 10

x x

4( 2)3( 3)xx

Algebraic FractionsDivision

23 3

y

2 4 105 3 9

xx

20( 2)15( 3)

xx

4

3

Example 2 Example 3

Page 13: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

( 1)( 2)( 3)( 4)( 1)( 2)( 3)( 4)x x x xx x x x

( 2)( 1) ( 4)( 3)( 3)( 1) ( 4)( 2)x x x xx x x x

2 2

2 2

2 6 84 3 7 12

x x x xx x x x

Algebraic FractionsDivision

1

1

Example 4

2 2

2 2

2 7 124 3 6 8

x x x xx x x x

1

1

1

1

( 1)( 1)xx

Page 14: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Example 1a Example 1b

2+

68

8

4

34

÷2

÷2

4d

d+3d

d2

4d

d2

÷d

÷d

3 1

d d

1 12 4

Addition

Algebraic Fractions

Page 15: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Example 2 Example 3

x2+

4x

12x(x - 1)+3(x + 1)

(x - 1)(x + 1)

3x + 3 + x2 – x

(x - 1)(x + 1)

3 x+

x - 1 x + 1

3 x+

x 4

Addition

Algebraic Fractions

x2 + 2x + 3

(x - 1)(x + 1)

Page 16: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1. To explain how to subtract algebraic fractions.

1.1. Know how to subtract Know how to subtract simple fractionssimple fractions

2.2. Apply same knowledge to Apply same knowledge to subtract algebraic subtract algebraic fractions.fractions.

Subtraction

Algebraic Fractions

Page 17: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Example 1a Example 1b

8-20

15

720

3m ppm

p-3m

pm

3 1p m

3 24 5

Subtraction

Algebraic Fractions

Page 18: Equivalent and Simplifying Fractions Adding Fractions Multiplying Fractions Fractions Dividing Fractions Subtracting Fractions.

Example 2 Example 3

fg-5g

15 x-3(x + 5)

x(x + 5)

3 1-

x (x+5)

3 f-

g 5

Subtraction

Algebraic Fractions

x-3x + 15

x(x + 5)

2x + 15

x(x + 5)