22-Aug-15Created by Mr.Lafferty Maths Dept Algebra Tidying up terms Multiplying terms Solving Simple Equations Multiplying out Brackets

19 Apr 202319 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

AlgebraAlgebra

Tidying up terms

Multiplying terms

Solving Simple Equations

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Multiplying out Brackets

Solving Equations with Brackets

Solving Harder Equations

Two sided equations

General


Starter QuestionsStarter Questionsw

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266 % of £ 270

3Q1. Calculate

Q2. Convert 60% to fraction and simplify.

Q3. Convert

Q4. What is the time difference 09:28 and 10:50

45

to a percentage.

Q5. The answer to the question is 90. What is thequestion.


Aim of the LessonAim of the Lessonw

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1. Tidying up expressions.2. Show steps when tidying up.

a+2b+3a+b

Tidying Terms

19 Apr 202319 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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General

First Row : + + =2c c 4c+ + = 7c

2nd Row : + + =

2d 2d 3d+ + = 7d

Tidying Terms


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3rd Row : + + =

3f f 2f+ + = 6f

In Total we have

7c + 7d + 6f

CANNOTTIDY UP

ANYMORE

WE CAN ONLY TIDY UP “LIKE TERMS”

Tidying Terms


Tidying Termsw

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WE CAN ONLY TIDY UP “LIKE TERMS”

Tidy up the following:

Q1. 2x + 4x + 5y - 3y

Q2. 4a + 3b + 5a - b

Q3. 10f + 15g + 5f + g

6x + 2y

9a + 2b

15f + 16g


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General

Chapter 7Page 85

Ex 1 Q1 and Q2

Tidying Terms



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2y+3x+4x+10Q1. Tidy up the expression

Q2. Calculate

Q3. Round to 1 decimal place.

Q4. Write 4 x 4 in terms of powers

2 of 84

3

(a) 2.34 (b) 10.25(c) 3.23


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1. To explain how to multiply terms.

1.1. Understand process of Understand process of multiplying terms.multiplying terms.

GeneralMultiplying TermsMultiplying Terms


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2

8

3

4

6

5

Find the area of each square in terms of powers

2 x 8 = 16 3 x 4 = 12 6 x 5 = 30

2

y2 x y =2y b7 x b = 7b

7


= 2w

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Bracket EquationsBracket EquationsSolve the following equations:

(1) 2 x w

(2) 4 x 2y

(3) 3a x 3b

(4) 5h x 5g

(5) 9e x 4m

(6) 8p x a

Examples

= 8y

= 9ab

= 25gh

= 36em = 8ap

Always put letters inalphabetical order !


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3

3

5

5

8

8

Find the area of each square in terms of powers

32 52 82

y

yy2 bb2

b


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Bracket EquationsBracket EquationsSolve the following equations:

(a) 2 x d

(b) 3 x 2y

(c) 5a x 4b

(d) d x d

(e) 6e x 3e

(f) 2p x 3p x 4p

= 2d

= 6y

= 20ab

= d2

= 18e2

= 24p3


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Your turn !Chapter 7

Page 86 Exercise 2

Multiplying TermsMultiplying Terms



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2. 70 % of 150

3. Find two numbers that add to give 15 and divide to give 2.

General

19 Apr 2023 Created by Mr.Lafferty Maths Dept

Removing brackets (1)

3(b + 5) =3b

This means 3 times b



3(b + 5) =3b +15+

This means 3 times 5



5(8 - f) = 40



5(8 - f) = 40 - 5f

Tip: Draw lines to keep you right.

5(8 – f) = 40

- 5f



4(3b + 2) =12b

4 x 3b= 4 x 3 x b= 12 x b= 12b



4(3b + 2) =12b+8+



3(7a – 2b) =21a



3(7a – 2b) =21a - 6b



c(3c + b) = 3c²

c x 3c = 3c x c = 3c²



c(3c + b) = 3c²+bc

Tip: Remember to draw lines to keep you right.

c(3c + b)

= 3c²+ bc



6(5e + 3f - 2) =30e



6(5e + 3f - 2) =30e+ 18f



6(5e + 3f - 2) =30e+ 18f- 12

Careful!

Tip: Remember to draw lines to keep you right.

6(5e + 3f -2)

= 30e

+ 18f

- 12


Simplifying (1)

4(3a + 5) - 8 =12a


Simplifying (1)

4(3a + 5) - 8 =12a+ 20

This is not inside the bracketsSo don’t multiply!

- 8

\


Simplifying (1)

4(3a + 5) - 8 =12a+ 20 - 8

This can be tidied up

= 12a + 12


Simplifying (2)

3b + 2(5b – 6) = 10b3b +

This is not inside the bracketsSo don’t multiply!


Simplifying (2)

3b + 2(5b – 6) = 10b3b + - 12

Careful!


Simplifying (2)

3b + 2(5b – 6) = 10b3b + - 12

This can be tidied up

= 13b - 12


Now try Exercise 3Ch7 (page 86)

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Structured DiagramsStructured Diagrams



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2. A scale model of a train is 1cm : 5m. The height of the model train is 10cm.

What is the real height of the train.

3. 80 % of 350

General


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2.2. Solving simple algebraic Solving simple algebraic equations.equations.

1. To solve simple equations using the rule ‘‘change side change change side change sign’.sign’.

1.1. Know ruleKnow rule‘‘change side change side

change sign’.change sign’.

EquationsEquationsSolving Equations

General


The rule “change side change sign”

ww

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EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x

Solving EquationsGeneral



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5 11x

16x 11 5x 8 8x

8 8x

0x

Examples

EquationsEquations

-5 opposite

is +5

+8 opposite

is -8

Check to see if correct ! Check to see if correct !




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3 18y

6y

18

3y 72

8m 8 72m

9m

Examples

EquationsEquations

times by 3

opposite is divide

by 3

times by 8

opposite is divide

by 8

Check to see if correct ! Check to see if correct !




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General



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2. The ratio of apples to pears is 4:5.

I f there are 72 pieces of f ruit in total.

How many apples are there.

y x x x xy 1. Simplify

3. Find HCF of 15 and 21

General


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2.2. Solving harder algebraic Solving harder algebraic equations by using rule equations by using rule repeatedly.repeatedly.

1. To solve harder equations using the rule ‘‘change side change change side change sign’.sign’.repeatedly.repeatedly.

1.1. Know ruleKnow rule‘‘change side change side

change sign’.change sign’.


General



ww

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EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x




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2 1 11x

2 10x 2 11 1 10x

Examples

EquationsEquations

+1 opposite

is -1

Check to see if correct !

times by 2

opposite is divide

by 2105

2x




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4 6 30x

4 36x 4 30 6 36x

Examples

EquationsEquations

-6 opposite

is +6

Check to see if correct !

times by 4

opposite is divide

by 4369

4x




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General



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What is my shape?

3 12. Calculate of

4 8

3. Remove brackets 4(5k - 8)

General


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1. To show how to solve equations with brackets .

1. Multiply out brackets.

2. Apply ‘change side change sign’ rule.

Equations with Brackets

Bracket EquationsBracket EquationsGeneral


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Apply ‘change side change sign’ rule

2(2 3) 18x 4 6 18x

Example

4 12x 12 4 3x




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5(3 2) 20x 15 10 20x

Example

15 20 10x

30 15 2x 15 30x





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EquationsEquationsGeneral

Bracket Equations



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2. The ratio of apples to pears is 6:7.

I f there are 52 pieces of f ruit in total.

How many apples are there.

a a b b ab 1. Simplify

3. Find LCM of 4 qand 7

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2.2. Solving two sided Solving two sided equationsequations

1. To explain how to solve two sided equations using knowledge we already have

1.1. Know the ruleKnow the rulechange side change signchange side change sign

GeneralEquationsEquations

Two sided equation


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Both Sides Both Sides EquationsEquations

4m - 3m = 12 - 8

(1) letters to one side

m = 4

(2) Solve as normal

Check correct answer !

4m+8 =3m+12


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7h – 3h = 7 + 9

(1) letters to one side

h = 16 ÷ 4

(2) Solve as normal

Check correct answer !

7h- 9 =4h + 7

4h = 16

h = 4


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Solve the following equations:

(b) 12x - 4 = 4x + 12

(a) 3x - 5 = 2x + 1

(c) 5x + 6 = 3x + 20

x = 6

x = 2

x = 7




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EquationsEquationsGeneral

Two sided equation

Documents

22-Aug-15Created by Mr.Lafferty Maths Dept Algebra Tidying up terms Multiplying terms Solving Simple Equations Multiplying out Brackets