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Equivalent and Simplifying Fractions
Adding & Subtracting Fractions
Algebraic Fractions
Multiplication & Division of Fractions
Factorising and Simplifying Fractions
Exam Type Questions
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Nat 5
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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Nat 5
www.mathsrevision.comwww.mathsrevision.comww
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1. We are learning 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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Nat 5
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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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Nat 5
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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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Nat 5
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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 FractionsWe can only
simplify if fraction is a product of
factors.
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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
( 3)( 2)( 2)
m mm
Algebraic FractionsWe can only
simplify if fraction is a product of
factors.
( 3) m1
1
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Examples
3
2 2
(1 5g)(1 5 )(1 5 ) (1 5 )
gg g
(1 5 )(1 5g)
g
Algebraic FractionsWe can only
simplify if fraction is a product of
factors.
1
1
2
2
6(1 )(1 )8(1 ) (1 )
f ff f
3(1 )4(1 )
ff1
13
4
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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
Nat 5
Factorise first
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Now try N5 TJ
Ex 9.1
Ch9 (page 90)
Nat 5
Algebraic Fractions
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Nat 5
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Questions
In pairs,
write down the three types of factorising
and show an example of each.
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Nat 5
www.mathsrevision.comwww.mathsrevision.comww
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1. We are learning how to simplify algebraic fractions by first factorising.
1.1. Know the three types of Know the three types of factorisations.factorisations.
Algebraic Fractions
2.2. Simplify algebraic Simplify algebraic fractions by first fractions by first factorising.factorising.
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Nat 5
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Type 1
3 69x 3( 2)
9 x ( 2)
3 x
3
1
Algebraic Fractions
6 310 5
yy
3(2 1)5(2 1)
yy
35
1
1
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Type 2
2
4 4
x xyx y
( )4( )
x x yx y 4
x
1
1
Algebraic Fractions
2 12 2
yy
( 1)( 1)2( 1)
y yy
( 1)2 y
1
1
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Type 3
2
2
6 51
x xx
( 1)( 5)( 1)( 1)
x xx x
( 5)( 1)
xx
1
1
Algebraic Fractions
2
2
3 24
a aa
( 1)( 2)( 2)( 2)
a aa a
( 1)( 2)
aa
1
1
ww
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Now try N5 TJ
Ex 9.2
Ch9 (page 92)
Nat 5
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.
Nat 5
ww
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Nat 5
www.mathsrevision.comwww.mathsrevision.comww
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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. We are learning how to add & subtract algebraic fractions.
1.1. Know how to add and Know how to add and subtract algebraic subtract algebraic fractions using equivalent fractions using equivalent fractions.fractions.
Algebraic FractionsAddition
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3 1
d d
1 12 4
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Example Example
1+42
34
4d
1+3d
Nat 5 Addition
Algebraic Fractions
LCM = 4
4
LCM = d
d
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3 1
p m
3 24 5
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Example Example
8-2015
720
3
m ppm
p-
3mpm
Nat 5 Subtraction
Algebraic Fractions
LCM = 20
20
LCM = pm
pm
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3 x+
x - 1 x + 1
3 x+
x 4
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Example Example
x2+
4x
12 x(x - 1)+3(x + 1)
(x - 1)(x + 1)
3x + 3 + x2 – x(x - 1)(x + 1)
Nat 5 Addition
Algebraic Fractions
x2 + 2x + 3(x - 1)(x + 1)
4x
12 + x2
4x
(x - 1)(x + 1)
LCM = 4x
LCM = (x-1)(x+1)
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3 1 -
x (x + 5)
3 f -
g 5
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Example Example
fg-
5g
15 x-
3(x + 5)
x(x + 5)
Nat 5 Subtraction
Algebraic Fractions
x-3x + 15
x(x + 5)
2x + 15
x(x + 5)
LCM = 5g
LCM = x(x+5)
5g
15 - fg
5g
x(x + 5)
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What Goes In The Box ?
2 13 4
1112
2 2x yxy7
b
3 4b b
yx
y x
Nat 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
Nat 5
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Now try N5 TJ
Ex 9.3 Q1 ...Q9
Ch6 (page 93)
Nat 5 Addition & Subtraction
Algebraic Fractions
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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Fraction EquationsNat 5
+ 5 = 8x + 24
(x 4)
x + 2 + 20 = 32
x + 22 = 32- 22 - 22
x = 10
Multiply EVERY term to get rid of fractional term.
and then apply ‘Balancing Method’
Example
Tidy Up !
19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww
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MTH 3-15aMTH 4-15a
(x 6)
18x
22x - 36 = 96
(÷ 22)x = 6
(2x – 4) + x = 1632
23
(2x – 4) + x = 969 4
22x = 132
- 36 + 4x = 96
Example
Tidy Up !
+ 36 + 36
Fraction Equations
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Now try N5 TJ
Ex 9.3 Q10
Ch6 (page 94)
Nat 5 Addition & Subtraction
Algebraic Fractions
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Nat 5
19 Apr 202319 Apr 2023 Compiled by Mr. Lafferty Maths Dept.Compiled by Mr. Lafferty Maths Dept.
Starter Questions
-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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Nat 5
www.mathsrevision.comwww.mathsrevision.comww
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srevis
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.com Learning IntentionLearning Intention Success CriteriaSuccess Criteria
1. We are learning how to multiply and divide algebraic fractions.
1.1. Know rules for multiplying Know rules for multiplying and dividing fractions.and dividing fractions.
2.2. Apply knowledge to Apply knowledge to algebraic fractions.algebraic fractions.
Algebraic FractionsMultiplication & Division
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3 48 5
310
Numerical fraction
2
5 36
a
a
52
a
Algebraic Fraction
Algebraic Fractions
1240
2
156aa
Nat 5
1240
10
3
2
156aa
2
15
1
Multiplication & Division
Remember you can simplify top and bottom and diagonally first to
make things easier
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4 59 6
815
Numerical Fraction
2 53
xy x
y
2215
y
Algebraic Fraction
Algebraic Fractions
4 69 5
23 5
xy y
x
Nat 5
2215xyx
1
1
2445
15
8
Multiplication & Division
Be careful !!! ONLY at the multiplication stage
can you simplify to make things easier
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3ab b
2
3ab
Example 2
2
2( 1)3( 1)
m mm m
23m
Example 3
Algebraic Fractions
2
2 ( 1)3 ( 1)mmm m
1
11
1
Nat 5 Multiplication & Division
Remember you can simplify top and bottom and diagonally first to
make things easier
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2 33 y
29y
2 4 3 95 10
x x
4( 2)3( 3)xx
Algebraic Fractions
23 3
y
2 4 105 3 9
xx
Nat 5
20( 2)15( 3)
xx
4
3
Example 2 Example 3
Multiplication & Division
Be careful !!! ONLY at the multiplication stage
can you simplify to make things easier
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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 FractionsNat 5
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
Multiplication & Division
Be careful !!! ONLY at the multiplication stage
can you simplify to make things easier
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What Goes In The Box ?
2 13 4
16
6bc 2
12b
2 3b c
3 4b b
Nat 5 Multiplication & Division
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What Goes In The Box ?
25
2abc
14
1 56 12
a cb a
4x x
y y
Nat 5 Multiplication & Division
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Now try N5 TJ
Ex 9.4
Ch9 (page 95)
Nat 5 Multiplication & Division
Algebraic Fractions
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