Chapter Module Directed Numbers

8/2/2019 Chapter Module Directed Numbers

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Multiplication andDivision of Integers

CombinedOperations ofIntegers

FractionsDecimals

Directed Numbers

(-3.2) X (-2.5) =

- 3 2 - ( - 1 5 ) =3 6

Maths

Form 2

Chapter1

DIRECTED NUMBERS

Prepared By:

Norisah bt

Mustaffa


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1.1 Multiplication and Division of Integers

When multiplying ordividing two integers ofthe same signs, theanswer is positive (+).

(+) x (+) = +

(-) x (-) = +

(+) (+) = +(-) (-) = +

When multiplying or

dividing two integersof different signs,the answer isnegative (-).

(+) x (-) = -

(-) x (+) = -

(+) (-) = -

(-) (+) = -


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1.1 Multiplication and Division of Integers

Solve the problems of the following

(a) A typist can type 60words every minute.Find how many wordscan be typed in 45

minutes.

= 60 x 45

= 2700 words.

(b) A participant wasdeducted 57 marks for 19questions answered

wrongly. How many markswere deducted for eachquestion answeredwrongly?

= 57 19

= 3 marks


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1.2 Combined Operations of Integers

4 -(-5)+(-10)= 4+5 10

= 9

10= - 1

Example

To perform computations

with more than oneoperations.

1. Do all calculationsinside brackets first.

2. Multiply and divide inorder from left to theright.

3. Add and subtract inorder from left to theright.


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a) - 9 - 12 + (-25) c) - 30 + 4 x (-6)

b) 24 x (-8) 6 d) -120 (- 4) x (11)


Simplify the following

= - 9 - 12 - 25

= - 21 - 25= - 46

= - 30 + (-24)

= - 30 - 24= - 54

= (24 x 8) 6

= 192 6

= 32

= (120

4) x 11= 30 x 11

= 330


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Solve the problems of the following

(a) The price of a computerdrops RM120 each year. Ifthe original price wasRM2 700. what is the price

of the computer after 2years?

= 2700 (120 x 2)

= 2700 240

= RM 2 460

(b) The temperature of a liquidat 7.00a.m was 9C. If its

temperature at 1.00p.m. was -3C, what was the rate ofchange in the temperature ofthe liquid per hour?

= (- 3 - 9 ) 6

= -12 6

= -2C per hour



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1.3 FractionsAddition and Subtraction Involving Fraction:a) 2 1 (- 2 1)

5 3

c) 1 + ( - 5 )

3 7

b) 4 1 3 33 8

d) 2 (- 5 3 )5 8

= -11 + 75 3

= -33 + 35 = 2

15 15

= -13 - 273 8

= -104 - 81 = -18524 24

= 1 - 53 7

= 7 - 15 = -8

21 21 21

= 2 + 435 8

= 16 + 215 = 23140 40


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1.3 FractionsMultiplication and Division Involving Fraction:

a) 3 3 x 2

4 5

c) 2 ( - 4 )

9 3

b) 2 (- 1 1 )3 6

d) 2 2 (- 2 1 )3 9

= -15 x 24 5

= -32

1

3 1

2

= - ( 2 x 3 )9 4

= -16

1

3 2

1

= + (2 x 6 )3 7

= 47

1

2

= - ( 8 x 9 )3 19

= - 2419

1

3
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a) 0.95 + (- 4.8) c) 9.8 x ( - 0.9)

b) - 14.3 + ( - 3.76 ) d) 0.284 (- 0.4)

= 0.95 4.8

= - 3.85

= - 14.3 3.76= - 18.06

= - (9.8 x 0.9)

= - 8.82

= - (0.284

0.4)= - 2.84 4= - 0.71

The addition, subtraction,multiplication and division on

decimals are similar to the

four operations of integers.

1.4 Decimal


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1.5 Directed NumbersIntegers, fractions and decimals are directednumbers. The computation of directed numbersis the same as that for whole numbers.

a) -5.62 + (- 1 )8

c) 129 (- 3 )5

b) 3 2 (- 2.7)

5

d) 3.42 + 2.18 0.02

= - 5.62 - 0.125

= - 5.745

= - 3.4 + 2.7= - 0.7

= - (129 x 5 )

3= - 215

1

43

= - 3.42 + (218 2)= - 3.42 + 109= 105.58


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Calculate:1) -10 + 6 x (-3) + (- 4) 5) -0.16 (0.04) 9) -3.15 + 1.2 x (- 0.1)

2) -36 + (- 4)x(-3) (-4) 6) -9 x (-3)10

10) 1.21 + 0.1 x (-1.5)0.11

3) 48 (-3) x (-3) + 10 7) 3 - 6 (-3) x (-6) 11) 1.99(-1.01)x4 (-2)5

4) -0.8 x (-0.07) 8) 0.01 + (-3.01 + 5)-0.02

12) 7 + (- 1 3) x 4.55

= -10 + (-18) 4= -10 18 4= - 28 4= - 32

= - 36 + (12) (- 4)= - 36 + (- 3)

= - 36 3= - 39

= 48 - (9) + 10= 39 + 10

= 49

= +(0.8 x 0.07)= 0.056

= - (0.16 0.04)= -16 4

= - 4

= +(9 x 3)10

= 27 = 2 710 10

= 3 (- 2) x (- 6)= 3 (+12)

= 3

12= - 9

= 0.01 + 1.99 = 2.00 = - 200- 0.02 - 0.02 2

= - 100

= - 3.15 + (- 0.12)

= - 3.15

0.12= - 3.27

= -11 + (- 0.15)

= - 11 0.15= - 11.15

= -1.99 +1.01x 4x ( 5)2

= -1.99 + 1.01 x ( 10)= - 1.99 - 10.1 = -8.11

= 7 + (- 8 x 4.5)5

= 7 +(- 7.2)= 7 7.2 = - 0.2


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Chapter Module Directed Numbers