Question 1: Write the following integers in an ascending order:

(i) -13, 2, -123, -3, 11, 0      (ii) 143, -317, -1, 19, -63, -19

Answer:

(i) -123, -13, -3, 0, 2, 11

(ii) -317, -63, 19, -1, 19, 143

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Question 2: Write the following integers in an descending order:

(i) 17, 0, -5, 69, -124, -1      (ii) -3, -77, 2, -345, -49, -617

Answer:

(i) 69, 17, 0, -1, -5, -124

(ii) 2, -3, -49, -77, -345, -617

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Question 3: Add the following:

(i) 64 + (-27)      (ii) (-89) + 16       (iii) (-46) + (-38) 

(iv) (-47) + 85 + (-6)      (v) 348 + (-121) + (-765)      

(v) (-248) + (414) + (-8) + (77) + (-19)

Answer:

(i) 64 + (-27) = 37      (ii) (-89) + 16 = -73      (iii) (-46) + (-38) = -84

(iv) (-47) + 85 + (-6) = 32      (v) 348 + (-121) + (-765) = -538

(v) (-248) + (414) + (-8) + (77) + (-19) = 216

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Question 4: Find the additive inverse of:

(i) -987      (ii) 0      (iii) 1428

Answer:

(i) -987+a=0 Therefore additive inverse is 987

(ii) 0+a=0 Therefore additive inverse is 0

(iii) 1428+a=0 Therefore additive inverse is -1428

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Question 5: Find the successor of the following integers:

(i) -1009     (ii) 0      (iii) -1      (iv) -4321

Answer:

(i) -1009 + 1 = -1008      (ii) 0 + 1 = 1     (iii) -1 + 1 = 0 (iv) -4321 + 1 = -4320

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Question 6: Find the predecessor of the following integers:

(i) -1009      (ii) 0      (iii) -1     (iv) -2094

Answer:

(i) -1009 - 1 = -1010      (ii) 0 - 1 = -1      (iii) -1 + 1 = 0      (iv) -2094 + 1 = -2093

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Question 7: A bus starts from the terminal and moves 188 \ km to the EAST and then \ 343 km to the west. How far is the bus from the terminal?v21

Answer: 155 \ km

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Question 8: A shopkeeper purchased a book for Rs. \ 345 , a pencil box for Rs. \ 62 , a note book for Rs. \ 21 and a pen for Rs. \ 79 . He sold the book for Rs. \ 376 , pencil for Rs. \ 55 , notebook for Rs. \ 25 and a pen for Rs. \ 67 . What is his gain or loss?

Answer:

Total Cost in Rs. = 345 + 62 + 21 + 79 = 507

Total Sales in Rs. = 376 + 55 + 25 + 67 = 523

Gain = Total Sales – Total Cost = 523 - 507 = Rs. \ 16

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Question 9: Find an integer such that:

(i) a+ (-7) = 0    (ii) (-4) + a = 0    (iii) a + 12 = 0    (iv) 21 + a = 0

Answer:

(i) a+ (-7) = 0 \Rightarrow a = 7    (ii) (-4) + a = 0 \Rightarrow a = 4

(iii) a + 12 = 0 \Rightarrow a = -12    (iv) 21 + a = 0 \Rightarrow a = -21

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Question 10: Subtract:

(i) 3715 from (-468)    (ii) (-329) from 0    (iii) (-2347) from 1543

(iv) (-4682) from (-419)    (v) (-76) from the sum of (-813) and 248

(vi) The sum of (-66) and 619 from the sum of 597 and (-184)

Answer:

(i) (-468) - (3715) = -4183    (ii) 0 - (-329) = 329    (iii) 1543 - (-2347) = 3890

(iv) (-419) - (4682) = 4263    (v) (-813) + 248 - (-76) = -489

(vi) \{ (597) + (-184) \} - \{ (-66) + 619 \} = (413) - (553) = -140

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Question 11: Simplify:

(i) \{ (-78) - (-92) \}+ \{ (-54) - (-21) \}    (ii) \{ 92 -  (-53) \} - \{ 76 - (-132) \}

Answer:

(i) \{ (-78) - (-92) \}+ \{ (-54) - (-21) \} = (-78 + 92)+ (-54 + 21) = 14 + (-33) = -19

(ii) \{ 92 -  (-53) \} - \{ 76 - (-132) \} = (92 + 53) - (76 + 132) = 145 -  208

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Question 12: The sum of the two integers is -29 . If one of the integer is 182 , find the other.

Answer: Let one integer = a

a + 182 = -29 \Rightarrow  a = -29-(182) = -211

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Question 13: The difference of an integer a and -37 is -14 . Find the value of a .

Answer:

a - (-37) = -14    \Rightarrow a = -14 + (-37) = -51

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Question 14: During a month, the average temperature of desert region was 37^o C and the average night temperature was -4^o C . Find the difference between the average day temperature and the average night temperature

Answer:

Ave. day temperature – Avg. night temperature   = 37 - (-4)   = 41^o \ C

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Question 15: Find the products:

(i) 16 \times 25    (ii) (-34) \times 76    (iii) 26 \times (-496)

(iv) (-289) \times (-173)    (v) (-25) \times 17 \times (-42)    (vi) 31 \times 13 \times (-23)

Answer:

(i) 16 \times 25 = 400    (ii) (-34) \times 76= -2584

(iii) 26 \times (-496)= -12896    (iv) (-289) \times (-173)=49997

(v) (-25) \times 17 \times (-42)=17850    (vi) 31 \times 13 \times (-23)= -9269

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Question 16: Divide

(i) 893 by 19    (ii) (-629) by 37    (iii) 224 by (-14)     (iv)  (-423) by (-47)

Answer:

(i) 839 / 19=47     (ii) (-629) / 37= -17

(iii) 224  / (-14)= -16     (iv) (-423) / (-47)=9

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Question 17: In an examination consisting of 20 questions, 5 marks are awarded for each correct question, (-2) marks are awarded for each incorrect answer and 0 for each question left un-attempted.  Aditya answered 10 questions correctly and 2 questions incorrectly. While Cyrus answered 12 questions correctly and 8 questions incorrectly. Who scored more marks and what was his score.

Answer:

Aditya’s Marks =10 \times 5+2 \times (-2)=46

Cyrus’s Marks  =12 \times 5+8 \times (-2)=44

Therefore Aditya scored more marks and his score was 46 marks.