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

1. $-13, 2, -123, -3, 11, 0$
• Answer: $-123, -13, -3, 0, 2, 11$
2. $143, -317, -1, 19, -63, -19$
• Answer: $-317, -63, 19, -1, 19, 143$

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

1. $17, 0, -5, 69, -124, -1$
• Answer: $69, 17, 0, -1, -5, -124$
2. $-3, -77, 2, -345, -49, -617$
• Answer: $2, -3, -49, -77, -345, -617$

1. $64 + (-27) = 37$
2. $(-89) + 16 = -73$
3. $(-46) + (-38) = -84$
4. $(-47) + 85 + (-6) = 32$
5. $348 + (-121) + (-765) = -538$
6. $(-248) + (414) + (-8) + (77) + (-19) = 216$

Question 4: Find the additive inverse of:

1. $-987$
• Answer: $-987+a=0$ Therefore additive inverse is $987$
2. $0$
• Answer: $0+a=0$ Therefore additive inverse is $0$
3. $1428$
• Answer: $1428+a=0$ Therefore additive inverse is $-1428$

Question 5: Find the successor of the following integers:

1. $-1009$
• Answer: $-1009 + 1 = -1008$
2. $0$
• Answer: $0 + 1 = 1$
3. $-1$
• Answer: $-1 + 1 = 0$
4. $4321$
• Answer: $-4321 + 1 = -4320$

Question 6: Find the predecessor of the following integers:

1. $-1009$
• Answer: $-1009 - 1 = -1010$
2. $0$
• Answer: $0 - 1 = -1$
3. $-1$
• Answer: $-1 + 1 = 0$
4. $2094$
• Answer: $-2094 + 1 = -2093$

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: $155 \ km$

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 $= 523 - 507 = Rs. \ 16$

Question 9: Find an integer such that:

1. $a+ (-7) = 0$ Answer: $a = 7$
2. $(-4) + a = 0$ Answer: $a = 4$
3. $a + 12 = 0$ Answer: $a = -12$
4. $21 + a = 0$ Answer: $a = -21$

Question 10: Subtract:

1. $3715$ from $(-468)$
• Answer: $(-468) - (3715) = -4183$
2. $(-329)$ from $0$
• Answer: $0 - (-329) = 329$
3. $(-2347)$ from $1543$
• Answer: $1543 - (-2347) = 3890$
4. $(-4682)$ from $(-419)$
• Answer: $(-419) - (4682) = 4263$
5. $(-76)$ from the sum of $(-813)$ and $248$
• Answer: $(-813) + 248 - (-76) = -489$
6. The sum of $(-66)$ and $619$ from the sum of $597$ and $(-184)$
• Answer: $\{ (597) + (-184) \} - \{ (-66) + 619 \} = (413) - (553) = -140$

Question 11: Simplify:

$\{ (-78) - (-92) \}+ \{ (-54) - (-21) \}$

$= (-78 + 92)+ (-54 + 21)$

$= 14 + (-33)$

$= -19$

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

$= (92 + 53) - (76 + 132)$

$= 145 - 208$

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

Answer: Let one integer $= a$

$a + 182 = -29$

$a = -29-(182)$

$= -211$

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

$a - (-37) = -14$

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

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

Average day temperature – average night temperature

$= 37 - (-4)$

$= 41^o \ C$

Question 15: Find the products

1. $16 \times 25 = 400$
2. $(-34) \times 76= -2584$
3. $26 \times (-496)= -12896$
4. $(-289) \times (-173)=49997$
5. $(-25) \times 17 \times (-42)=17850$
6. $31 \times 13 \times (-23)= -9269$

Question 16: Divide

1. $893$ by $19$
• Answer: $839 / 19=47$
2. $(-629)$ by $37$
• Answer: $(-629) / 37= -17$
3. $224$ by $(-14)$
• Answer: $224 / (-14)= -16$
4. $(-423)$ by $(-47)$
• Answer: $(-423) / (-47)=9$

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.