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S4 credit
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Equivalent and Simplifying Fractions
Adding Fractions
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Multiplying Fractions
Algebraic Fractions
Dividing Fractions
Subtracting Fractions
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S4 credit
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
S3 Starter QuestionsS3 Starter Questions
www.
mat
hsre
visio
n.co
m
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
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S4 credit
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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.
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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
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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
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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
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Examples
2
26bb
26
bb b
13b
3
2
aa
a a aa a 1
aa
3
1
1
1
1
1
1
1
412pqq
412
pqq 3
p
2 2
3
122e fef
2 2
3
122
e fef
6 ef
3
1
1
1
1
6
1
1
1
1
Algebraic Fractions
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Examples
2
3
( 1)( 1)yy
( 1)( 1)( 1)( 1)( 1)
y yy y y
1( 1)y
1
1
1
1
6 310 5
yy
3(2 1)5(2 1)
yy
35
1
1
Algebraic Fractions
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What Goes In The Box ?
262ww
3
432yy
3
6
( 2)2( 2)ff
3w2
18y 3
12( 2)f
2
( 1)( 1)
w xx
3
ay aay
2 1( 1)xx
3
1yy
1x 2
( 1)( 1)
w xx
S4 Credit
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Now try MIA
Ex 2.1
Ch6 (page 117)
S4 Credit
Algebraic Fractions
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S4 credit
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Questionsww
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-4
2
1. True or f alse
2. Write in scientifi c notation
45 2.56 10
3. Factorise k
4. Explain why 65% of £ 40=£ 26
3 1 16 = =14 4 16
- 6k + 8
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S4 credit
www.mathsrevision.comwww.mathsrevision.comww
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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
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3 48 5
310
Numerical fraction
2
5 36
a
a
52
a
Algebraic Fraction
Algebraic FractionsMultiplication
1240
2
156aa
S4 Credit
1240
10
3
2
156aa
2
15
1
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3ab b
2
3ab
Example 2
2
2( 1)3( 1)
m mm m
23m
Example 3
Algebraic FractionsMultiplication
2
2 ( 1)3 ( 1)mmm m
1
11
1
S4 Credit
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What Goes In The Box ?
2 13 4
16
6bc 2
12b
2 3b c
3 4b b
S4 Credit
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Now try MIA
Ex 3.1
Ch6 (page 120)
S4 Credit
Algebraic FractionsMultiplication
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Questions
2 2
5
(2 3 4)
8 4 (2
4 45 115 9
4 1)
3 65 25
1. Does
2. Expand
3. Does factorise to
4.
y y x
d d dd
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S4 credit
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ion
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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
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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
S4 Credit
2215xyx
1
1
2445
15
8
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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
S4 Credit
20( 2)15( 3)
xx
4
3
Example 2 Example 3
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( 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 FractionsDivisionS4 Credit
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
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What Goes In The Box ?
25
2abc
14
1 56 12
a cb a
4x x
y y
S4 Credit
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Now try MIA
Ex 4.1
Ch6 (page 122)
S4 Credit Division
Algebraic Fractions
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19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
2 2 where a = 4 and b = (-5) a b
Starter Questions
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.
S4 Credit
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S4 credit
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1. To explain how to add algebraic fractions.
1.1. Know how to add simple Know how to add simple fractionsfractions
Algebraic Fractions
2.2. Apply same knowledge to Apply same knowledge to add algebraic fractions.add algebraic fractions.
Addition
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Example 1a Example 1b
2+
68
84
34
÷2
÷2
4d
d+3dd2
4dd2
÷d
÷d
3 1
d d
1 12 4
S4 Credit Addition
Algebraic Fractions
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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
S4 Credit Addition
Algebraic Fractions
x2 + 2x + 3(x - 1)(x + 1)
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What Goes In The Box ?
2 13 4
1112
2 2x yxy7
b
3 4b b
yx
y x
S4 Credit
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ion
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Now try MIA
Ex 5.1 & Ex 5.2
Ch6 (page 124)
S4 Credit Addition
Algebraic Fractions
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Starter QuestionsStarter Questions
1. Simplify the following fractions : 3
4
3g 5e (a) (b)
9g 2e
2. True or f alse the lowest multiple of 6 and 9 is 3
1 1 3 53. Calculate (a) (b)
2 5 10 6
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S4 credit
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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
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Example 1a Example 1b
8-
2015
720
3m ppm
p-3mpm
3 1p m
3 24 5
S4 Credit Subtraction
Algebraic Fractions
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Example 2 Example 3
fg-
5g15 x-3(x + 5)
x(x + 5)
3 1-
x (x+5)
3 f-
g 5
S4 Credit Subtraction
Algebraic Fractions
x-3x + 15
x(x + 5)
2x + 15
x(x + 5)
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What Goes In The Box ?
142
2 3c bbc ad bc
bd
1 16 7
2 3b c
a cb d
S4 Credit
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Now try MIA
Ex 6.1 & Ex 6.2
Ch6 (page 127)
S4 Credit Subtraction
Algebraic Fractions