Question 12 Marks
Simplify:
$(-9) \times 6 + (-9) \times 4$
$(-9) \times 6 + (-9) \times 4$
Answer
View full question & answer→$(-9) \times 6 + (-9) \times 4$
$= (-54) + (-36)$
$= -54 - 36$
$= -90$
$= (-54) + (-36)$
$= -54 - 36$
$= -90$
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Question 22 Marks
The point $A$ is on a mountain which is $5700$ meters above sea level and the point $B$ is in a mine which is $39600$ meters below sea level. Find the vertical distance between $A$ and $B.$
Answer
View full question & answer→$5700 + 39600 = 45300$
So, the vertical distance between $A$ and $B$ is $45300$ metres.
So, the vertical distance between $A$ and $B$ is $45300$ metres.
Question 32 Marks
Use the number line and add the following integers:
$8 + (-8)$
$8 + (-8)$
Answer
View full question & answer→On the number line, we start from $0$ and move $8$ steps to the right to reach point $A$.
Now, starting from $A$, we move $8$ steps to the left to reach point $B$.
$B$ represents the integer $0$
Therefore, $8 + (-8) = 0$
Now, starting from $A$, we move $8$ steps to the left to reach point $B$.
$B$ represents the integer $0$
Therefore, $8 + (-8) = 0$
Question 42 Marks
Use the number line and add the following integers: $(-1) + (-3)$
Answer
View full question & answer→On the number line, we start from $0$ and move $1$ step to the left to reach point $A$.
Now, starting from $A$, we move $3$ steps to the left to reach point $B$.
$B$ represents the integer $-4$
Therefore, $(-1) + (-3) = -4$
Now, starting from $A$, we move $3$ steps to the left to reach point $B$.
$B$ represents the integer $-4$
Therefore, $(-1) + (-3) = -4$
Question 52 Marks
Use the number line and add the following integers: $(-4) + (-7)$
Answer
View full question & answer→On the number line, we start from $0$ and move $4$ steps to the left to reach point $A$.
Now, starting from $A$, we move $7$ steps to the left to reach point $B$.
$B$ represents the integer $-11$
Therefore, $(-4) + (-7) = -11$
Now, starting from $A$, we move $7$ steps to the left to reach point $B$.
$B$ represents the integer $-11$
Therefore, $(-4) + (-7) = -11$
Question 62 Marks
On a day Srinagar, the temperature at $6\ pm$ was $1^\circ C$ but at midnight that day, it dropped to $ -4^\circ C$. By how many degrees Celsius did the temperature fall?
Answer
View full question & answer→$1 - (-4) = 1 + 4 = 5$
So, the temperature fall $5^\circ C$.
So, the temperature fall $5^\circ C$.
Question 72 Marks
Find $34 - (-72)$ and $(-72) - 34$. Are they equal?
Answer
View full question & answer→$34 - (-72) = (-72) - 34$
$L. H. S.$
$34 - (-72)$
$= 34 + 72$
$= 106$
$R. H. S.$
$(-72) - 34$
$= -106$
So, it is not equal.
$L. H. S.$
$34 - (-72)$
$= 34 + 72$
$= 106$
$R. H. S.$
$(-72) - 34$
$= -106$
So, it is not equal.
Question 82 Marks
Simplify: $16 ÷ (-1)$
Answer
View full question & answer→$16\div(–1)$
$=\frac{16}{-1}$
$=\frac{16\times(-1)}{(-1)\times(-1)}$
{Multiplying the numerator and the denominator by $(–1)$}
$=16\times(-1)$
$=-16$
$=\frac{16}{-1}$
$=\frac{16\times(-1)}{(-1)\times(-1)}$
{Multiplying the numerator and the denominator by $(–1)$}
$=16\times(-1)$
$=-16$
Question 92 Marks
The sum of two integers is $-12$. If one of them is $34$, find the other.
Answer
View full question & answer→Let the integer be $x$
$\therefore$ $34 + x = -12$
$x = -12 - 34$
$x = -46$
Therefore, the other integer is $-46.$
$\therefore$ $34 + x = -12$
$x = -12 - 34$
$x = -46$
Therefore, the other integer is $-46.$
Question 102 Marks
Simplify: $(-147) ÷ (-21)$
Answer
View full question & answer→$(-147)\div (-21)$
$=\frac{-147}{-21}$
$=\frac{(-1)\times147}{(-1)\times21}$
$=\frac{(-1)}{(-1)}\times\frac{147}{21}$
$=7$
$=\frac{-147}{-21}$
$=\frac{(-1)\times147}{(-1)\times21}$
$=\frac{(-1)}{(-1)}\times\frac{147}{21}$
$=7$
Question 112 Marks
Simplify: $8 \times (-12) + 7 \times (-12)$
Answer
View full question & answer→$8 \times (-12) + 7 \times (-12) $
$= (-96) + (–84) $
$= -96 – 84$
$ = -180$
$= (-96) + (–84) $
$= -96 – 84$
$ = -180$
Question 122 Marks
Use the number line and add the following integers: $9 + (-6)$
Answer
View full question & answer→On the number line, we start from $0$ and move $9$ steps to the right to reach a point $A$.
Now, starting from $A$, we move $6$ steps to the left to reach point $B$.
$B$ represents the integer $3$ Therefore, $9 + (-6) = 3$
Now, starting from $A$, we move $6$ steps to the left to reach point $B$.
$B$ represents the integer $3$ Therefore, $9 + (-6) = 3$
Question 132 Marks
Simplify: $[-13 - (-17) + [-22 - (-40)]$
Answer
View full question & answer→$[-13 - (-17) + [-22 - (-40)] $
$= (-13 + 17) + (-22 + 40) $
$= 4 + 18 = 22$
$= (-13 + 17) + (-22 + 40) $
$= 4 + 18 = 22$
Question 142 Marks
Use the number line and add the following integers:
$(-1) + (-2) + (-3)$
$(-1) + (-2) + (-3)$
Answer
View full question & answer→On the number line, we start from $0$ and move $1$ step to the left to reach point $A$.
Now, starting from $A$, we move $2$ steps to the left to reach point $B$.
Again, starting from $B$, we move $3$ steps to the left to reach point $C$.
$C$ represents the integer $-6$
Therefore, $(-1) + (-2) + (-3) = -6$
Now, starting from $A$, we move $2$ steps to the left to reach point $B$.
Again, starting from $B$, we move $3$ steps to the left to reach point $C$.
$C$ represents the integer $-6$
Therefore, $(-1) + (-2) + (-3) = -6$
Question 152 Marks
Simplify: $(-15) \times (-14) + (-15) \times (-6)$
Answer
View full question & answer→$(-15) \times (-14) + (-15) \times (-6) $
$= 210 + 90 $
$= 300$
$= 210 + 90 $
$= 300$
Question 162 Marks
Use the number line and add the following integers: $3 + (-2) + (-4)$
Answer
View full question & answer→On the number line, we start from $0$ and move $3$ steps to the right to reach point $A$.
Now, starting from $A$, we move $2$ steps to the left to reach point $B$.
Again, starting from $B$, we move $4$ steps to the left to reach point $C$.
$C$ represents the integer $-3$ Therefore, $3 + (-2) + (-4) = -3$
Now, starting from $A$, we move $2$ steps to the left to reach point $B$.
Again, starting from $B$, we move $4$ steps to the left to reach point $C$.
$C$ represents the integer $-3$ Therefore, $3 + (-2) + (-4) = -3$
Question 172 Marks
Simplify: $(-24) \times (68) + (-24) \times 32$
Answer
View full question & answer→$(-24) \times (68) + (-24) \times 32 $
$= -(24) \times (68 + 32) $
$= -24 \times 100 $
$= -2400$
$= -(24) \times (68 + 32) $
$= -24 \times 100 $
$= -2400$
Question 182 Marks
The sum of two integers is $-13$. If one of the numbers is $170$, find the other.
Answer
View full question & answer→Let the other number be $m.$
Then,
$170 + m = (-13)$
$m = -13 - 170$
$m = -183$
So, the other number of the integers is $(-183).$
Then,
$170 + m = (-13)$
$m = -13 - 170$
$m = -183$
So, the other number of the integers is $(-183).$
Question 192 Marks
Use the number line and add the following integers: $(-3) + 7$
Answer
View full question & answer→On the number line, we start from $0$ and move $3$ steps to the left to reach point $A$.
Now, starting from $A$, we move $7$ steps to the right to reach point $B$.
$B$ represents the integer $4$ Therefore, $(-3) + 7 = 4$
Now, starting from $A$, we move $7$ steps to the right to reach point $B$.
$B$ represents the integer $4$ Therefore, $(-3) + 7 = 4$
Question 202 Marks
From the sum of $33$ and $-47$, subtract $-84.$
Answer
View full question & answer→$= [ 33 + (-47)] - (-84) $
$= 33 - 47 + 84 $
$= (33 + 84) - 47$
$ = 117 - 47$
$ = 70$
$= 33 - 47 + 84 $
$= (33 + 84) - 47$
$ = 117 - 47$
$ = 70$
Question 212 Marks
Subtract the sum of $-1050$ and $813$ from $-23.$
Answer
View full question & answer→$= -23 - (-1050 + 813)$
$= 1050 - (23 + 813)$
$= 1050 - 836$
$= 214$
$= 1050 - (23 + 813)$
$= 1050 - 836$
$= 214$
Question 222 Marks
Simplify:
$43 \times (-33) + 43 \times (-17)$
$43 \times (-33) + 43 \times (-17)$
Answer
View full question & answer→$43 \times (-33) + 43 \times (-17)$
$= (-1419) + (-731)$
$= -1419 – 731$
$= -2150$
$= (-1419) + (-731)$
$= -1419 – 731$
$= -2150$
Question 232 Marks
Use the number line and add the following integers: $5 + (-2) + (-6)$
Answer
View full question & answer→On the number line, we start from $0$ and move $5$ steps to the right to reach point $A.$
Now, starting from $A$, we move $2$ steps to the left to reach point $B.$
Again, starting from $B$, we move $6$ steps to the left to reach point $C.$
$C$ represents the integer $-3$ Therefore, $5 + (-2) + (-6) = -3$
Now, starting from $A$, we move $2$ steps to the left to reach point $B.$
Again, starting from $B$, we move $6$ steps to the left to reach point $C.$
$C$ represents the integer $-3$ Therefore, $5 + (-2) + (-6) = -3$
Question 242 Marks
Simplify: $30 \times (-22) + 30 \times (14)$
Answer
View full question & answer→$30 \times (-22) + 30 \times (14)$
$ = (-660) + 420$
$ = -240$
$ = (-660) + 420$
$ = -240$
Question 252 Marks
Simplify: $(-9) \times 18 - (-9) \times 8$
Answer
View full question & answer→$(-9) \times 18 - (-9) \times 8 $
$= -(9) \times [18 - 8] $
$= -9 \times 10 $
$= -90$
$= -(9) \times [18 - 8] $
$= -9 \times 10 $
$= -90$
Question 262 Marks
The sum of two integers is $65$. If one of the integers is $-47$, find the other.
Answer
View full question & answer→Let the other number be $m.$
Then, $(-47) + m = 65 m = 65 - (-47) m = 65 + 47 m = 112$
So, The other number is $112.$
Then, $(-47) + m = 65 m = 65 - (-47) m = 65 + 47 m = 112$
So, The other number is $112.$
Question 272 Marks
Simplify: $(-27) \times (-16) + (-27) \times (-14)$
Answer
View full question & answer→$(-27) \times (-16) + (-27) \times (-14) $
$= 432 + 378 $
$= 810$
$= 432 + 378 $
$= 810$
Question 282 Marks
Simplify:
$[37 - (-8)] + [11 - (-30)]$
$[37 - (-8)] + [11 - (-30)]$
Answer
View full question & answer→$[37 - (-8)] + [11 - (-30)]$
$= (37 + 8) + (11 + 30)$
$= 45 + 41$
$= 86$
$= (37 + 8) + (11 + 30)$
$= 45 + 41$
$= 86$
Question 292 Marks
Use the number line and add the following integers: $(-2) + (-8)$
Answer
View full question & answer→On the number line, we start from $0$ and move $2$ steps to the left to reach point $A.$
Now, starting from $A$, we move $8$ steps to the left to reach point $B.$
$B$ represents the integer $-10$ Therefore, $(-2) + (-8) = -10$
Now, starting from $A$, we move $8$ steps to the left to reach point $B.$
$B$ represents the integer $-10$ Therefore, $(-2) + (-8) = -10$