Page 10 - SM inner class 7.cdr

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For ex am ple : (-4 ) ´ = ´ (-4 ) = -4
When an integer is multiplied by –1, the result is the integer with sign changed i.e., the additive
identity of the integer.
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For any integer a a, ´ - = - ´ a = - a
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E xercise 1.3

1. Fill in the blanks
(a) 18946 99´ - - 18946) =18946 …… (b) (-10 ) ´11 = …… (c) (-15 ) ´ ´ (-18 ) = ……
0
(
´
(d) (-12 ) (- = ……
)
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¸
2. Ver ify the fol low ing :
´
´
´
+
=
[
(
2
(
]
(
)
]
(a) 18 ´[ 7 + - 3 =[ 18 7 + [ 18 ´ - 3)] (b) (-21 ) [(-4 ) (-6 )] [(-21 ) (-4 )] + - ) ´ - )]
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(
1
3. Ver ify that a ¸( b c ¹( a b ¸ c for each of the fol low ing val ues of a b and c
)
)
¸
,
¸
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(a) a =12, b = -4, c =2, (b) a = -( 10 ), b = , c =3
Word Problems on Integers below the ground by a negative integer, then
an swer the fol low ing:
Example 8: In a class test containing 12
ques tions, 4 marks are given for ev ery cor rect (i) A lift descends into a mine shaft at the
answer and (–3) marks are given for every rate of 9 metre per minute. What will be
in cor rect answer. its position after half an hour?
(i) Gurpreet attempts all questions but only (ii) If it begins to descend from 15 m above
7 of her answers are correct. What is her the ground, what will be its position after
total score? 25 minutes?
(ii) One of her friends gets only 6 answers So lu tion :
correct. What will be her score? (i) Since the lift is going down, so the
So lu tion : distance covered by it will be represented by a
negative integer.
(i) Marks given for one correct answer = 4
Change in position of the elevator in one
So, marks given for 7 correct answers
minute = –9 m
= 4 ´ = 28
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Marks given for one incorrect answer = (– )3 Position of the elevator after 30 minutes
´
9
= (– ) 30 = –270 m, i.e., 270 m below ground
–
So, marks given for incorrect answers 5 = ( 12 7)
level.
= (–3) ´ 5 = –15 (ii) Change in position of the elevator in 25
Therefore, Gurpreet's total score
minutes = (– ) 25 = –225 m, i.e., 225 m
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´
+
= 28 (– 15) =13 below ground level.
(ii) Marks given for one correct answer = 4 So, the final position of the elevator = –225 15
+
So, marks given for 6 correct answers = –210 m, i.e., 210 m below ground level.
= 4 ´ = 24 Ex am ple 10. The prod uct of the two in te gers
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Marks given for one incorrect answer = (–3) is -300. If one integer is 25. find the other
So, marks given for 6 (12 – ) incorrect answers in te ger.
6
3
= (– ) ´ = –18 So lu tion : Let the other in te ger be x.
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Therefore, her friend’s total score 25 ´ x = - 300
= 24 + (– 18) = 6 300
x = - = -12
Ex am ple 9 : Sup pose we rep re sent the dis tance 25
above the ground by a pos i tive in te ger and that Hence, the required integer is -12
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Mathematics In Focus - 7