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MATHS 3 Marks Question

Negative Numbers and Integers · Rajasthan Board (RBSE) STD 6 (Rajasthan - English Medium). 5 questions.

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Question 13 Marks
Simplify: $(-145) + 97 + (-365) + (-71) + 8.$
Answer
$(-145) + 97 + (-365) + (-71) + 8$
$= (-145) + 97 + (-365) - (71 - 8)$
$= (-145) + 97 + (-365) - 63$
$= (-145) + 97 - (365 + 63)$
$= (-145) + 97 - 428$
$= (-145) - (428 - 97)$
$= (-145) - 331$
$= -(145 + 331)$
$= -476$
Hence, $(-145) + 97 + (-365) + (-71) + 8 = -476.$
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Question 23 Marks
If $x = (-23) + 22 + (-23) + 22 + ..... + (40$ terms$)$ and $y = 11 + (-10) + 11 + (-10) + ..... + (20$ terms$)$, then find $y - x.$
Answer
$x = (-23) + 22 + (-23) + 22 + ... + (40$ terms$)$
$= (-23) + (-23) + ... + (20$ terms$) + 22 + 22 + ... + (20$ terms$) $
$= 20 \times (-23) + 20 \times 22 $
$= 20 \times (-23 + 22) = 20 \times (-1) = -20$
Now, $y = 11 + (-10) + 11 + (-10) + ... + (20$ terms$) = 11 + 11 + ... + (10$ terms$) + (-10) + (-10) + ... + (10$ terms$)$
$= 11 \times 10 + (-10) \times 10 = 110 - 100 = 10$
Therefore, $y - x = 10 - (-20) = 10 + 20 = 30$
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Question 33 Marks
Evaluate: $-36 - 40 + 43 - (-29) + 18 - (-74)$
Answer
$-36 - 40 + 43 - (-29) + 18 - (-74) $
$= -36 - 40 + 43 - (-29) + 18 + 74 $
$= -36 - 40 + 43 - (-29) + 92$
$= -36 - 40 + 43 + 29 + 92 $
$= -36 - 40 + 43 + 121 $
$= -36 - 40 + 164$
$ = -(36 + 40) + 164 $
$= -76 + 164 $
$= 164 - 76 $
$= 88$
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Question 43 Marks
Find the value of: $38 - (-25) - 58 + (-15) + 23 - (-8)$
Answer
$38 - (-25) - 58 + (-15) + 23 - (-8)$
$ = 38 - (-25) - 58 + (-15) + 23 + 8 $
$= 38 - (-25) - 58 + (-15) + 31$
$ = 38 - (-25) - 58 + (31 - 15) $
$= 38 - (-25) - 58 + 16 $
$= 38 - (-25) - (58 - 16)$
$ = 38 - (-25) - 42 $
$= 38 + 25 - 42 $
$= 38 - (42 - 25)$
$ = 38 - 17 $
$= 21$
Hence, $38 - (-25) - 58 + (-15) + 23 - (-8) = 21$
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Question 53 Marks
Complete the following table:
$+$ $-6$ $-4$ $-2$ $0$ $2$ $4$ $6$
$6$           $10$  
$4$              
$2$             $8$
$0$ $-6$            
$-2$              
$-4$           $0$  
$-6$       $-6$      
From the above table.
$i.\ $Write all the pairs of integers whose sum is $0.$
$ii.\ $Is $(-4) + (-2) = (-2) + (-4)?$
$iii.\ $Is $0 + (-6) = -6?$
Answer
$+$ $-6$ $-4$ $-2$ $0$ $2$ $4$ $6$
$6$ $0$ $2$ $4$ $6$ $8$ $10$ $12$
$4$ $-2$ $0$ $2$ $4$ $6$ $8$ $10$
$2$ $-4$ $-2$ $0$ $2$ $4$ $6$ $8$
$0$ $-6$ $-4$ $-2$ $4$ $2$ $4$ $6$
$-2$ $-8$ $-6$ $-4$ $-2$ $0$ $2$ $4$
$-4$ $-40$ $-8$ $-6$ $-4$ $-2$ $0$ $2$
$-6$ $-12$ $-10$ $-8$ $-6$ $-4$ $-2$ $0$
$i.\ (+6, -6), (4, -4), (3, -3), (2, -2), (1, -1), (0, 0)$
$ii.\ $Yes by commutativity of Addition:
$(-4) + (-2) = (-2) + (-4)$
$iii.\ $By existence of additive identity:
$0 + (-6) = -6$ $[$$\because$ $0 + a = a]$
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