The Laws Of Surds.

1
Algebraic Fractions
Equivalent and Simplifying Fractions
Multiplying Fractions
Dividing Fractions
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Adding Fractions
Subtracting Fractions
2
S3 Starter Questions
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3
Algebraic Fractions
Learning Intention
Success Criteria

1. To explain how to simplify algebraic fractions.

• Understand term
• Highest Common Factor.

2. Simplify algebraic fractions by identifying
HCF.
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4
Equivalent Fractions
Multiply top and bottom by any number or letter
Multiply top and bottom by any number
We already know how to create an equivalent
fraction for numerical fractions. The exact same
process is used for algebraic fractions.
Numerical Fraction
Algebraic Fraction
5
Equivalent Fractions
Common Denominator for 2 fractions
Numerical Fraction
Algebraic Fraction
6
Algebraic Fractions
We can sometimes reduce fractions to a simpler
form if the numerator and denominator have a
number or letter in common.
Examples
HCF Y
HCF 3
7
Algebraic Fractions
Examples
1
1
1
1
3
1
3
1
6
1
1
1
1
1
1
1
1
1
8
Algebraic Fractions
Examples
1
1
1
1
1
1
9
What Goes In The Box ?
S4 Credit
10
Algebraic Fractions
S4 Credit
Now try MIA Ex 2.1 Ch6 (page 117)
11
Starter Questions
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12
Algebraic Fractions
Multiplication
Learning Intention
Success Criteria

1. To explain how to multiply algebraic fractions.

1. Know rules for multiplication simple fractions.

2. Apply knowledge to algebraic fractions.
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13
Algebraic Fractions
Multiplication
S4 Credit
Algebraic Fraction
Numerical fraction
3
1
5
10
1
2
14
Algebraic Fractions
Multiplication
S4 Credit
Example 3
Example 2
1
1
1
1
15
What Goes In The Box ?
S4 Credit
16
Algebraic Fractions
Multiplication
S4 Credit
Now try MIA Ex 3.1 Ch6 (page 120)
17
Starter Questions
18
Algebraic Fractions
Division
Learning Intention
Success Criteria

1. To explain how to divide algebraic fractions.

1. Know rules for division of simple fractions.

2. Apply knowledge to algebraic fractions.
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19
Algebraic Fractions
Division
S4 Credit
Algebraic Fraction
Numerical Fraction
8
1
15
1
20
Algebraic Fractions
Division
S4 Credit
Example 3
Example 2
4
3
21
Algebraic Fractions
Division
S4 Credit
Example 4
1
1
1
1
1
1
22
What Goes In The Box ?
S4 Credit
23
Algebraic Fractions
Division
S4 Credit
Now try MIA Ex 4.1 Ch6 (page 122)
24
Starter Questions
S4 Credit
Q1. Explain why 4 6 x 5 34 and not 50
Q2. Calculate
Q3. Does x2 121 factorise to (x 11) (x - 11)
Q4. The cost of an iPod is 80 including VAT.
How much is the iPod BEFORE VAT.
25
Algebraic Fractions
Addition
Learning Intention
Success Criteria

1. To explain how to add algebraic fractions.

1. Know how to add simple fractions

2. Apply same knowledge to add algebraic
fractions.
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26
Algebraic Fractions
Addition
S4 Credit
Example 1a
Example 1b
d
3d

2
4

d2
d
2
4d
d
2
d2
27
Algebraic Fractions
Addition
S4 Credit
Example 2
Example 3
x(x - 1)
3(x 1)

x2
12

(x - 1)(x 1)
3x 3 x2 x
(x - 1)(x 1)
x2 2x 3
(x - 1)(x 1)
28
What Goes In The Box ?
S4 Credit
29
Algebraic Fractions
Addition
S4 Credit
Now try MIA Ex 5.1 Ex 5.2 Ch6 (page 124)
30
Starter Questions
1. Simplify the following fractions
31
Algebraic Fractions
Subtraction
Learning Intention
Success Criteria

1. To explain how to subtract algebraic fractions.

1. Know how to subtract simple fractions

2. Apply same knowledge to subtract algebraic
fractions.
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32
Algebraic Fractions
Subtraction
S4 Credit
Example 1a
Example 1b
-
8
15
p
3m
-
pm
33
Algebraic Fractions
Subtraction
S4 Credit
Example 2
Example 3
-
fg
15
x
-
3(x 5)
x(x 5)
x
-
3x 15
x(x 5)
2x 15
x(x 5)
34
What Goes In The Box ?
S4 Credit
35
Algebraic Fractions
Subtraction
S4 Credit
Now try MIA Ex 6.1 Ex 6.2 Ch6 (page 127)