Www.mathsrevision.com Nat 5 Equivalent and Simplifying Fractions Adding & Subtracting Fractions Algebraic Fractions Multiplication

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Nat 5

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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

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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


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


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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Nat 5


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


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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Nat 5


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



factors.

( 3) m1

1

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Nat 5


Examples

3

2 2

(1 5g)(1 5 )(1 5 ) (1 5 )

gg g

(1 5 )(1 5g)

g



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


Starter Questions

In pairs,

write down the three types of factorising

and show an example of each.

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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


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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Nat 5


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

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Now try N5 TJ

Ex 9.2

Ch9 (page 92)

Nat 5

Algebraic Fractions

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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

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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


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


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


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


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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2 13 4

1112

2 2x yxy7

b

3 4b b

yx

y x

Nat 5

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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


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


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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


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




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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




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2 13 4

16

6bc 2

12b

2 3b c

3 4b b


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25

2abc

14

1 56 12

a cb a

4x x

y y


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Now try N5 TJ

Ex 9.4

Ch9 (page 95)


Algebraic Fractions

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