Www.mathsrevision.com S4 credit Equivalent and Simplifying Fractions Adding Fractions Multiplying...

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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

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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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S4 credit

www.mathsrevision.comwww.mathsrevision.comww

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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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S4 credit


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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S4 credit


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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S4 credit


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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S4 credit


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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S4 credit


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


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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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


2

2 ( 1)3 ( 1)mmm m

1

11

1

S4 Credit

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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


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S4 credit


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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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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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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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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2 13 4

1112

2 2x yxy7

b

3 4b b

yx

y x

S4 Credit

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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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S4 credit


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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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


Algebraic Fractions

x-3x + 15

x(x + 5)

2x + 15

x(x + 5)

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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)


Algebraic Fractions

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Www.mathsrevision.com S4 credit Equivalent and Simplifying Fractions Adding Fractions Multiplying...

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