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

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

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

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

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

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

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

(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) $1428$

(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) $-4321$

(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) $-2094$

(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?

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?

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) $21 + a = 0$

(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 $(-184)$

(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) $\{ 92 - (-53) \} - \{ 76 - (-132) \}$

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

(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 $a$.

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

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Question 14: During a month, the average temperature of the 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

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) $31 \times 13 \times (-23)$

(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) $893 \text{ by } 19$        (ii) $(-629) \text{ by } 37$        (iii) $224 \text{ by } (-14)$         (iv)  $(-423) \text{ by } (-47)$

(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.

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.