Algebra

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# Algebra - PowerPoint PPT Presentation

Algebra. Simplifying Algebraic Expressions. Removing Brackets. Removing Brackets &amp; Simplifying. www.mathsrevision.com. Evaluating Expressions. Factorising – The common factor. Starter Questions. www.mathsrevision.com. 2cm. 3cm. 6cm. 2cm. Algebra. Simplifying Algebraic Expressions.

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### Algebra

Simplifying Algebraic Expressions

Removing Brackets

Removing Brackets & Simplifying

www.mathsrevision.com

Evaluating Expressions

Factorising – The common factor

Created by Mr. Lafferty Maths Dept.

### Starter Questions

www.mathsrevision.com

2cm

3cm

6cm

2cm

Created by Mr. Lafferty Maths Dept.

Algebra

Simplifying Algebraic Expressions

Learning Intention

Success Criteria

• To remember the phrase
• ‘ like terms.’
• To review tidying up
• expressions.
• 2. Understand and be able too simplify simple algebraic expressions by collecting ‘ like terms.’

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Reminder !

We can only add and subtract “ like terms “

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Created by Mr. Lafferty Maths Dept.

Rule

Multiply the numbers together

multiply the letters together.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Reminder !

Multiplying terms

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( NOT 2b )

( NOT 8m )

Created by Mr. Lafferty Maths Dept.

1

2

3

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Question : Find the area of each of the 3 sections of this shape.

What is the total area.

y

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2

y

2

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Simplifying Algebraic Expressions

Now try Exercise 1

Ch11 (page 46)

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Created by Mr. Lafferty Maths Dept.

100o

60o

### Starter Questions

2a

6h

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Created by Mr. Lafferty Maths Dept.

Algebra

Removing brackets

Learning Intention

Success Criteria

• Understand the key steps in removing brackets.
• 1. We are learning how to multiply out simply algebraic brackets.
• 2. Apply multiplication rules for positive and negative numbers when removing brackets.

www.mathsrevision.com

Created by Mr. Lafferty Maths Dept.

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 1

+ 15

3(b + 5) =

3b

Example 2

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- 8

4(w - 2) =

4w

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Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 3

- 2

2(y - 1) =

2y

Example 4

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- 42

7(w - 6) =

7w

Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 5

+ 24

8(x + 3) =

8x

Example 6

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- 8m

4(3 -2m) =

12

Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 7 : Write down an expression

for the amount indicate below

in two difference ways.

x+3

x+3

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+ 9

3(x + 3)

=3x

x+3

Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 8 : Write down an expression

for the amount indicate below

in two difference ways.

y-2

y-2

y-2

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- 10

5(y - 2)

= 5y

y-2

y-2

10-Mar-14

Created by Mr. Lafferty@mathsrevision.com

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing brackets

Question : Find the area of the rectangle

(i) With brackets

(ii) Without brackets.

y + 5

(i) A = L x B

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4

= 4(y + 5)

(ii) = 4(y + 5)

= 4y

+ 20

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing brackets

Now try Exercise 2

Ch11 (page 48)

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Created by Mr. Lafferty Maths Dept.

### Starter Questions

www.mathsrevision.com

(x+2)cm

7cm

Created by Mr. Lafferty Maths Dept.

Algebra

Removing Brackets & Simplifying

Learning Intention

Success Criteria

1. Understand how to remove brackets

• 1. We are learning how to remove brackets and simplify.

2. Understand the need to show clear working.

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3. Apply to context questions.

Created by Mr. Lafferty Maths Dept.

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 1

+ 5a

a(b + 5) =

ab

Example 2

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- 2p

p(w - 2) =

pw

Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 3

- y

y(y - 1) =

y2

Example 4

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- 21w

7w(w - 3) =

7w2

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Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 5

+ 3ab

a(a2 + 3b) =

a3

Example 6

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- 2cy2

y2(3y -2c) =

3y3

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Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 7

- y

-(x + y) =

-x

Example 8

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+ 35

-5(a - 7) =

-5a

Created by Mr. Lafferty@mathsrevision.com

Removing a

Single Bracket

Tidy Up

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 9

- 3y

12

7 + 3(4 - y) =

7 +

= 19 - 3y

Tidy Up

Example 10

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- 24

+ 3y

9 - 3(8 - y) =

9

= -15 + 3y

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Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 11

12

10

Find my Area

Find my Area

x

(x - 2)

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A = L x B

A = L x B

A = 10(x – 2)

A = 12x

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Removing a

Single Bracket

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 12 : Find area of the orange border

12

Area =Big Rec – Small Rec

10

x

(x - 2)

= 12x – 10(x - 2)

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= 12x

-10x

+ 20

= 2x + 20

Created by Mr. Lafferty@mathsrevision.com

Removing Two Single Brackets

Tidy Up

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 13

- m - 2

4(m - 3) - (m + 2) =

4m - 12

= 3m - 14

Tidy Up

Example 14

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- 2y - 8

7(y - 1) - 2(y + 4) =

7y - 7

= 5y - 15

Created by Mr. Lafferty@mathsrevision.com

Removing Two Single Brackets

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 15 : Find an expression for the difference in

the areas.

(y - 5)

A = 4(y – 5)

7

4

A = 7(y - 4)

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(y - 4)

Calculate difference if y = 14

Diff = 3 x 14 – 8

= 34

Difference = 7(y - 4) - 4(y – 5)

= 7y - 28

- 4y + 20

= 3y - 8

Created by Mr. Lafferty@mathsrevision.com

Removing Two Single Brackets

MTH 3-14a

MTH 4-14a

MTH 4-14b

Example 16 : Find an expression for the difference in

the areas.

(x + 1)

A = 7(x + 1)

9

7

A = 9(x + 3)

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x + 3

Calculate difference if x = 4

Diff = 2 x 4 + 20

=28

Difference = 9(x + 3) - 7(x + 1)

= 9x + 27

– 7x - 7

= 2x + 20

Created by Mr. Lafferty@mathsrevision.com

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing Brackets & Simplifying

Question : Find the area of the large rectangle, then the small

rectangle and hence find the area of the red section.

x

x-3

4

Ab= 6x

6

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As= 4(x - 3)

= 4x

- 12

As= 6x - 4(x - 3)

= 6x

- 4x

+ 12

= 2x + 12

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Removing Brackets & Simplifying

Now try Exercise 3

Ch11 (page 50)

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Created by Mr. Lafferty Maths Dept.

### Starter Questions

www.mathsrevision.com

(x+2)cm

7cm

Created by Mr. Lafferty Maths Dept.

Algebra

Evaluating Expressions – number for letter

Learning Intention

Success Criteria

1. Be able to substitute numbers for letters in an expression.

• 1. We are learning how to evaluate an expression.

2. Use previous knowledge of Number to evaluate a expression.

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Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

BODMAS

Given the following information find the values of :-

a = 3 ; b = 4 and c = -1

2a + c

b2 – a2

2b2

= 42 – 32

= 2x3 + (-1)

= 2x(4)2

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= 16 – 9

= 2x3 - 1

= 2x16

= 6 - 1

= 7

= 32

= 5

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

Given the following information find the values of :-

a = 3 ; b = 4 and c = -1

2a2 + 3b + 30c

= 2x(3)2 + 3x4 + 30x(-1)

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= 18 + 12 - 30

= 0

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Evaluating Expressions – number for letter

Now try Exercise 4

Ch2 (page 51)

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Created by Mr. Lafferty Maths Dept.

### Starter Questions

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Created by Mr. Lafferty Maths Dept.

Algebra

Factorising – The Common Factor

Learning Intention

Success Criteria

1. Understand the term factorising.

• 1. We are learning the process of factorising’.

2. Apply previous knowledge to recognise the HCF for a set of values.

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3. Analysis answer to validate it is correct.

Created by Mr. Lafferty Maths Dept.

Factorising

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorise 3x + 15

Example

1. Find the HCF for 3x and 15

3

2. HCF goes outside the bracket

3( )

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• To see what goes inside the bracket
• divide each term by HCF

15

3x

3( x + 5 )

= x

= 5

3

3

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Factorising

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorise 4x2 – 6xy

Example

1. Find the HCF for 4x2 and 6xy

2x

2. HCF goes outside the bracket

2x( )

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• To see what goes inside the bracket
• divide each term by HCF

6xy

4x2

2x( 2x - 3y )

= 2x

= 3y

2x

2x

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Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Simply find the HCF for a given set of data

and write the data using brackets :-

8a – 12b

6x – 12

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= ( )

= ( )

4

2a

- 3b

6

x

- 2

Created by Mr. Lafferty Maths Dept.

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Simply find the HCF for a given set of data

and write the data using brackets :-

9f – 6f2

am + an

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= ( )

= ( )

3f

3

- 2f

a

m

+ n

Created by Mr. Lafferty Maths Dept.

Factorising

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorise the following :

= ( )

3

x

+ 2

• (a) 3x + 6
• 4xy – 2x
• 6a + 7a2
• (d) y2 - y

= ( )

2x

2y

- 1

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= ( )

a

6

+ 7a

= ( )

y

y

- 1

Created by Mr. Lafferty@mathsrevision.com

Algebra

MTH 3-14a

MTH 4-14a

MTH 4-14b

Factorising – The Common Factor

Now try Exercise 5

Ch11 (page 54)

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Created by Mr. Lafferty Maths Dept.