Page 8 - SM inner class 7.cdr

Division of an Integer by ‘0’ is not Possible æ121 ö
= + ç ÷ = + 11
Division by zero is an operation for which we è 11 ø
cannot find the answer as shown below. (ii) (+ 169 ) (-13 )
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4 = W or 4 = W ´ 0 = -(169 13 ) (Unlike signs rule)
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0 æ169 ö
= + ç ÷ = -13
But no value would work for 0 ´ 4 = Work for è 13 ø
0 ´ 4 W because 0 time any number is 0. So,
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(iii) (-72 ) (+ 8 )
division of an integer by ‘0’ is not possible.
= -(72 ¸ ) (Unlike signs rule )
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Ex am ple 7 : Find the quo tient of the fol low ing: æ72 ö
(i) (-121 ) (-11 ) (ii) (+ 169 ) (-13 ) = - ç ÷ = -9
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ø
è 8
(iii) (-72 ) (+ 8 ) (iv) (+ 144 ) (+ 16 )
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(iv) (+ 144 ) (+ 16 )
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So lu tion :
= + (144 ¸16 ) (Like signs rule)
(i) (-121 ) (-11 ) æ144 ö
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= + ç ÷ = + 9
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= + (121 11 ) (Like signs rule) è 16 ø
E xercise 1.2
1. Solve the fol low ing :
(a) (-42 ) (-7 ) (b) (+ 36 ) (+ 9 ) (c) (+ 65 ) (+ 5 ) (d) (-27 ) (-3 )
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(e) (-126 ) (+14 ) (f) (+ 34 ) (-17 )
2. Fill the fol low ing boxes :
12 -16 W 30
(a) =W (b) = -2 (c) = - 4 (d) = - 6
3 W 5 W
W 169 8 -16
(e) =9 (f) =W (g) = 2 ´W (h) = ´W
2
-8 13 2 2
-27
(i) = ´W
3
-3
3. Find the quo tient of the fol low ing :
(a) (+ 252 ) (+18 ) (b) (-195 ) (+15 ) (c) (-480 ) (-120 )
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(d) (+196 ) (-28 ) (e) (-99 ) (+11 ) (f) (+ 2000 ) (-40 )
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Properties of Integers (iii) Clo sure prop erty un der mul ti pli ca tion:
Integers are closed under multiplication, i.e.,
1. Closure Property
for any two integers a and b, ab is an integer.
(i) Clo sure prop erty un der ad di tion:
)
(
)
;
(
For ex am ple : 5 ´ 6 = 30 - 9 ´ - 3 = 27
Integers are closed under addition, i.e. for any
two integers a and b, a + b is an integer. (iv) Clo sure prop erty un der di vi sion:
Integers are not closed under division, i.e., for
For ex am ple : 3 + 4 = 7; ( - 9 + 7 = - 2
)
any two integers a and b, a ¸ b may or not be an
(ii) Clo sure prop erty un der sub trac tion: integer.
Integers are closed under subtraction, i.e. for 1
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any two integers a and b, a – b is an integer. For ex am ple : (-2 ) (-4 ) =
2
8
=
For ex am ple : (-21 ) (-9 ) (-12 ); - 3 = 5
-
2. Commutative Property :
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Mathematics In Focus - 7