equivalent and simplifying fractions adding fractions multiplying fractions fractions dividing...
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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
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.
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
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
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
What Goes In The Box ?
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
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
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
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
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
( 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
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
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)
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
Example 1a Example 1b
8-20
15
720
3m ppm
p-3m
pm
3 1p m
3 24 5
Subtraction
Algebraic 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)