chapter module directed numbers
TRANSCRIPT
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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)
1.2 Combined Operations of Integers
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
1.2 Combined Operations of Integers
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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
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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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