3-jun-14created by mr.lafferty maths dept algebra tidying up terms number machine solving simple...

10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

AlgebraAlgebra

Tidying up terms

Number Machine

Solving Simple Equations

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Working with Expressions

Understanding Inequalities

Solving Harder Equations

Solving Simple Inequalities

MTH 3-14aMTH 3-15aMTH 3-15b


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


10 Apr 202310 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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2c c 4c+ + = 7c

2nd Row : + + =

2d 2d 3d+ + = 7d

Tidying TermsMTH 3-14aMTH 3-15aMTH 3-15b


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3f f 2f+ + = 6f

In Total we have

7c + 7d + 6f

CANNOTTIDY UP

ANYMORE

WE CAN ONLY TIDY UP “LIKE TERMS”



Tidying Termsw

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WE CAN ONLY TIDY UP “LIKE TERMS”

Tidy up the following:

Q1. 2x + 4x + 5y -3y + 18 =

Q2. 4a + 3b + 5a + 6 – b =

6x + 2y + 18

9a + 2b + 6



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Your turn !

Page 46 Exercise 1Q1 and Q2




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Q2. Calculate

Q3. Round to 1 decimal place.

Q4. 12.5 % as a fraction

2 of 84

3

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



Aim of the LessonAim of the Lessonw

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1. To build simple expressions.2. To UNDO simple expressions.

Number MachineNumber Machine



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simply follow the rules given:

aMultiply

By 44a+1Add 1

4a

7m7

MultiplyBy m

7m-2Subtract

2

Number MachineNumber MachineMTH 3-14aMTH 3-15aMTH 3-15b


3Multiple

by b?+9

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simply follow the rules given:

4Multiply

By 5?+3

2023

3b3b+9



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Your turn !

Page 93 Exercise 2Q1



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simply do the opposite of the rules given:

?Divide by

210-8

UNDO+8

1836

UNDOx2



?Divide by

414+9

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simply do the opposite of the rules given:

UNDO-9

520

UNDOx4



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Your turn !

Page 93 Exercise 2Q3 and Q4




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

I f there are 28 pieces of f ruit in total.

How many apples are there.

a a d a a d 1. Simplify

3. Find HCF of 8 and 18



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2.2. Solving expressions Solving expressions showing working.showing working.

1. To explain the process of working out expressions by substitution method.

1.1. Understand process of Understand process of substitution.substitution.

SubstitutionSubstitutionMTH 3-14aMTH 3-15aMTH 3-15b


1 If a = 3 and b = 9 evaluate

a + b

3 +9=

= 12

Sub in a=3Sub in b=9

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If a = 3 and b = 9 evaluate

ab

Sub in a=3Sub in b=9

Remember ab means a x b

a x b

3 x 9=

= 27

2

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3 If a = 3 and b = 9 evaluate

4b

Sub in b=9

Remember 4b means 4 x b

4 x b

4 x 9=

= 36

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If a = 5 and b = 6 evaluate1. a + b2. ab

3. 3a

4. b - a

5. 4b

6. 3ab

=11=30=15

=1

=24=90w

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If a = 5 and b = 3 evaluate2a +

4bSub in a=5Sub in b=3

Remember 2a means 2 x a

4

2xa + 4xb2x 5+4x3

=

=

= 10 + 12= 22

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If a = 5 and b = 3 evaluatea

Sub in a=5

Remember a2 means a x a

5

a x a

5x 5

=

=

= 25

2

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Remember a means a ÷ b b

If a = 15 and b = 3 evaluate

a

Sub in a=15

6

153

=

= 5

b

Sub in b = 3

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If a = 2 and b = 6 evaluate1) 4a +

3b2) a2

3) b2

5) 4a2

4) 5b – 3a

6) ba

=26=4=36

=24=16

=3

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Your turn !

Page 94 Exercise 3




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x x x x 1. Simplify

3. Find LCM of 6 qand 21



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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’.

EquationsEquationsLevel E Solving Equations



The rule “change side change sign”

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EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x

Level E Solving EquationsMTH 3-14aMTH 3-15aMTH 3-15b



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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





Now try Exercise 4Ch8 (page 96)

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EquationsEquationsLevel E Solving Equations




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y x x x xy 1. Simplify

3. Find HCF of 15 and 21



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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.



EquationsEquationsLevel E Harder Equations




ww

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EquationsEquations

Write down the opposite of the following :

+opposite is

x-÷opposite is

opposite is

opposite is- +÷ x

Level E Harder EquationsMTH 3-14aMTH 3-15aMTH 3-15b



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2 1 11x

2 10x 2 11 1 10x

Examples

EquationsEquations

+1 opposite

is -1

Check to see if correct !


105

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 !


369

4x




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EquationsEquationsLevel E Harder Equations




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a a b b ab 1. Simplify

3. Find LCM of 4 qand 7



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2.2. Solving simple Solving simple inequalities equations.inequalities equations.

1. To explain the various symbols for inequalities.

Level E Solving Inequalities

1.1. Know rule the 4 symbols Know rule the 4 symbols forforinequalities.inequalities.

InequalitiesInequalitiesMTH 3-14aMTH 3-15aMTH 3-15b


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Level E Solving Inequations

The equations you were solving were called equations because they contained an “=“ sign.

InequalitiesInequalities

greater than

less than

greater than or equal to

less than or equal to

There are 4 other Mathematical symbolsThey are called inequalities :



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Examples : Write in words what each mean.

5 > 3

-7 < -6

y ≤ -5

x ≥ 2

means 5 is greater than 3

means -7 is less than -6

means x can take the value2 or greatermeans y can take the value-5 or less

Arrow ALWAYS points to the

smallest number



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Examples : Write out an inequality for the numbers


(a) 14 and 6

(b) -2 and 1

(c) -3 and -7

(d) 34 and -35

14 > 6

-2 < 1

-3 > -7

34 > -35



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Examples : Choosing from -3, -2, -1, 0 , 1, 2, 3


(a) y < 0

(b) y > 2

(c) y ≤ -2

(d) y > 3

-3, -2, -1

3

-3, -2

No solution




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InequalitiesInequalitiesLevel E Solving Inequalities




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How many pears are there.

y y y y y 1. Simplify

3. Find LCM of 6 and 10



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2.2. Solving simple Solving simple inequalities equations.inequalities equations.

1. To solve simple inequalities using the same rules as for equations ‘‘change side change change side change sign’.sign’.

Level E Inequalities





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The Good News

Same rule as solving equations





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9 16x

25x 16 9x 19 10x

10 19x

9x

Examples


-9 opposite

is +9

+10 opposite

is -10


Level E Solving InequalitiesMTH 3-14aMTH 3-15aMTH 3-15b



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7 35y

5y

35

7y 36

9m

9 36m

4m

Examples





Level E Solving InequalitiesMTH 3-14aMTH 3-15aMTH 3-15b



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3-jun-14created by mr.lafferty maths dept algebra tidying up terms number machine solving simple...

Documents

b slide

substitution mth

b tidying terms mth

simple inequalities

q1 number machine mth

q4 number machine mth

q2 tidying terms mth

d tidying terms mth