17-Apr-15Created by Mr. Lafferty Maths Dept Ordering integers Integers Add / Sub Mathematically Letters and Numbers Multiplying Integers.

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Dept

Ordering integers

IntegersIntegersw

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Add / Sub Mathematically

Letters and Numbers

Multiplying Integers

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Dividing Integers


Starter QuestionsStarter Questionsw

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Q2. How many Euros do I get for £20 if exchange rate is £1 1.5 €

Q3. The answer to the question is 90. What is thequestion.

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18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths DeptCreated by Mr. Lafferty Maths Deptww

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1.1. To be put integers in To be put integers in order of size.order of size.

1. To understand how to add positive and negative numbers using the thermometer as an aid.

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IntegersIntegers


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IntegersIntegersS33

Definition : An INTEGER is a negative or positive whole number, including 0.

e.g. -2, -1, 0, 5, 100

Note : -2.5, -1.2, 23.5 Are NOT INTEGERS

Write down 3 places where negative numbers are used

Temperature Sea Level

Coordinate Grid

Profit and Loss


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1

4

1211

10

7

98

65

32

0-1

-4

-12

-11-10

-7

-9-8

-6-5

-3-2

Negaive -

Positive +

12 > 4

-2 > -3

-4 < -1

Integers can be representedon a thermometer or number line.

IntegersIntegersS33

The further to the top a number isthe bigger it is.Greater

than

Less than

-3.5 < -2.8


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1 32 540

1

3

2

5

4

1 32 40

-2

1

-1

32

Plot the point(3,2)

(-2,2)x - axis

y - axis

x-coordinate is 3

y-coordinate is 2origin

-3

-4 -2-3 -1

Plot the point that makesshape a parallelogram.

Coordinate Grid

(-4,-2)

IntegersIntegersS33

18 Apr 202318 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Now try Exercise 2.1

Ch2 (page 23)

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IntegersIntegersS33



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Q2. How many euros do I get for £10 if exchange rate is £1 1.4 €

Q3. The answer to the question is 30. What is thequestion.

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1.1. To be able to write down To be able to write down mathematically the mathematically the addition and subtraction addition and subtraction of both positive and of both positive and negative integers.negative integers.

1. To explain how to write down mathematically addition and subtraction of negative integers.

Negative Negative NumbersNumbers

Addition & SubtractionS33


NegativeNumbers

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1

4

1211

10

7

98

65

32

0-1

-4

-12

-11-10

-7

-9-8

-6-5

-3-2

(a) 12 + 4 =

(b) 10 + ( - 8) =

(c) -7 – (- 10) =

2

3

16

Start at 12

Go up 4

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replace by single “-”

“- -” side by side

replace by single “+”

10 - 8 =

-7 + 10 =


= -4

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(1) 3 - 7

(2) 4 + (-9)

(3) -7 – (- 8)

(4) -2 + (-12)

(5) -5 – (-25)

(6) 8 + (-9)

Examples

= -5

= 1

= -14

= 20

= -1

Negative Negative NumbersNumbers

Remember

“+ -” = -

“- -” = +

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Now try Ex 3.1 to 4.2

Ch2 (page 26)

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IntegersIntegersS33



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-2

1. 21% of £ 300

2. True or f alse :

(a) -1 - (-1) = 2 (b) - 3 - (5 - (-4)) = - 6

(c) - 6 + 10 - ( - 3) = 7

3. Does 3.5 10 = 0.35

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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.

SubstitutionSubstitutionS33

18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Dept

1 If a = 2 and b = 14 evaluate

a + b

2 +14=

= 16

Sub in a=2Sub in b=14

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If a = 3 and b = -9 evaluate

a - bRemember “- -” replace by “+”

3 - (-9)=

= 3 + 9

2

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SubstitutionSubstitution

= 12

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3 If a = 3 and b = 9 evaluate

b2 – a2

Remember b2 means b x b

9x9 – 3x3

81

- 9== 72

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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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Now try Exercise 5.1

Ch2 (page 28)Q1 – Q4

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18 Apr 202318 Apr 2023 Created by Mr.Lafferty Maths DeptCreated by Mr.Lafferty Maths Deptww

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2.2. Be able to tidy up like Be able to tidy up like terms.terms.

1. To explain the process of tidying up expressions.

1.1. Understand the term like Understand the term like terms.terms.

Tidying Up Like TermsTidying Up Like TermsS33


Tidying Termsw

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1, 3 , 5, -6, 8 are like terms simple numbers

x, 3x , -2x are like terms in x

x2, 3x2, -2x2 are like terms in x2

x is NOT the same as x2

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Tidying Termsw

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3a2 – 2a2 =a2

3x – 4y – x – 2y =2x – 6y

4x2 – x – y + 6x2 = 10x2 – x - y

Examples

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6p2 – q – 3q + 6p2 =12p2 – 4q



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1 3 11

2 4 4

1. Share 36 in the ratio 3:9

1 12. Calculate of

2 2

3. Does Explain ?

4. Explain how we solve - 3x +9 27

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1. Explain how to multiply positive and negative integers.

1. Understand how to multiply positive and negative integers.

IntegersIntegersMultiplication

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IntegersIntegers

1 1 xx (-2) = (-2) =


5 5 x x (-8) =(-8) =

(-3) (-3) xx 3 = 3 =

(-4) (-4) xx 5 = 5 =

(-2) (-2) xx (-1) = (-1) =

(- 2) (- 2) xx (-5) = (-5) =

(-5) (-5) x x (-5) =(-5) =

(-4) (-4) xx (-8) = (-8) =

Rules

+ve x -ve = -ve -ve x +ve = -ve


Multiplication

-ve x -ve = +ve +ve x +ve = +ve

-2-2

-20-20

-9-9

-40-40

22

1010

2525

3232

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IntegersIntegers

1 1 ++ (-2) (-2) xx (-10) = (-10) =


5 5 x x (-2)(-2)22 + 5 - 19= + 5 - 19=

8 – (-3)8 – (-3)22 = =

3 + (-5)3 + (-5)22 = =

Rules

+ve x -ve = -ve -ve x +ve = -ve


Multiplication

-ve x -ve = +ve +ve x +ve = +ve

2121

2828

-1-1

66

Remember BODMAS

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Now try MIA Ex 6.1Ch2 (page 31)

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IntegersIntegersMultiplication

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× =

1 3 16

3 7 21

2

1. Share 63 in the ratio 2:5

2. Decide which are true or f alse

(a) a a = 2a (b) 3b 5f = 8bf

(c) 2w w = 2w (d) 2xy 4y 8 xy

3. Does Explain ?

4. Write in sc

ientifi c notation and to 2 sig. fi g.

(a) 0.03465 (b) 4960000

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1. Explain how to divide positive and negative integers.

1. Understand how to divide positive and negative integers.

IntegersIntegersDivision

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IntegersIntegers

8 8 ÷÷ (-4) = (-4) =

Dividing Integers

16 16 ÷ ÷ (-2) =(-2) =

(-3) (-3) ÷÷ 3 = 3 =

(-24) (-24) ÷÷ 6 = 6 =

(-22) (-22) ÷÷ (-2) = (-2) =

(- 56) (- 56) ÷÷ (-7) = (-7) =

(-15) (-15) ÷ ÷ (-5) =(-5) =

(-4) (-4) ÷÷ (-8) = (-8) =

Rules

+ve ÷ -ve = -ve -ve ÷ +ve = -ve


Division

-ve ÷ -ve = +ve +ve ÷ +ve = +ve

-2-2

-4-4

-1-1

-8-8

1111

88

33

0.50.5

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IntegersIntegers

1 1 ++ (-20) (-20) ÷÷ (-10) = (-10) =

Division Integers

-48 -48 ÷ ÷ (6 - 2)(6 - 2)22 + 5 = + 5 =

100 - 36 100 - 36 ÷÷ (-3) (-3)22 = =

100 100 ÷÷ (-5) (-5)22 = =

Rules

+ve ÷ -ve = -ve -ve ÷ +ve = -ve


Division

-ve ÷ -ve = +ve +ve ÷ +ve = +ve

33

44

9696

22

Remember BODMAS

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Now try MIA Ex 8.1Ch2 (page 31)

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IntegersIntegersDivision

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17-Apr-15Created by Mr. Lafferty Maths Dept Ordering integers Integers Add / Sub Mathematically Letters and Numbers Multiplying Integers.

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