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Maths 3 Mark Question

Negative Numbers and Integers · Maharashtra Board STD 6 (MSBSHSE - Semi 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 × (-23) + 20 × 22
= 20 × (-23 + 22)
= 20 × (-1)
= -20
Now,
y = 11 + (-10) + 11 + (-10) + ... + (20 terms)
= 11 + 11 + ... + (10 terms) + (-10) + (-10) + ... + (10 terms)
= 11 × 10 + (-10) × 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.
  1. Write all the pairs of integers whose sum is 0.
  2. Is (-4) + (-2) = (-2) + (-4)?
  3. 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 -10 -8 -6 -4 -2 0 2
-6 -12 -10 -8 -6 -4 -2 0
  1. (+6, -6), (4, -4), (3, -3), (2, -2), (1, -1), (0, 0)
  2. Yes by commutativity of Addition:
(-4) + (-2) = (-2) + (-4)
  1. By existence of additive identity:
0 + (-6) = -6 [$\because$ 0 + a = a]
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