Question 12 Marks
Simplify:
(-9) × 6 + (-9) × 4
(-9) × 6 + (-9) × 4
Answer
View full question & answer→(-9) × 6 + (-9) × 4
= (-54) + (-36)
= -54 - 36
= -90
= (-54) + (-36)
= -54 - 36
= -90
Questions
2 Mark Question
Take a timed test
29 questions · self-marked practice — reveal the answer and mark yourself.
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.
= 45300
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
Therefore, 8 + (-8) = 0
Question 42 Marks
Use the number line and add the following integers:
(-1) + (-3)
(-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
B represents the integer -4
Therefore, (-1) + (-3) = -4
Question 52 Marks
Use the number line and add the following integers:
(-4) + (-7)
(-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
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 $5^{\circ} C$.
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)
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)
(-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 × (-12) + 7 × (-12)
8 × (-12) + 7 × (-12)
Answer
View full question & answer→8 × (-12) + 7 × (-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)
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
Question 132 Marks
Simplify:
[-13 - (-17) + [-22 - (-40)]
[-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
C represents the integer -6
Therefore, (-1) + (-2) + (-3) = -6
Question 152 Marks
Simplify:
(-15) × (-14) + (-15) × (-6)
(-15) × (-14) + (-15) × (-6)
Answer
View full question & answer→(-15) × (-14) + (-15) × (-6)
= 210 + 90
= 300
= 210 + 90
= 300
Question 162 Marks
Use the number line and add the following integers:
3 + (-2) + (-4)
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
C represents the integer -3
Therefore, 3 + (-2) + (-4) = -3
Question 172 Marks
Simplify:
(-24) × (68) + (-24) × 32
(-24) × (68) + (-24) × 32
Answer
View full question & answer→(-24) × (68) + (-24) × 32
= -(24) × (68 + 32)
= -24 × 100
= -2400
= -(24) × (68 + 32)
= -24 × 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
(-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
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 × (-33) + 43 × (-17)
43 × (-33) + 43 × (-17)
Answer
View full question & answer→43 × (-33) + 43 × (-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)
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
C represents the integer -3
Therefore, 5 + (-2) + (-6) = -3
Question 242 Marks
Simplify:
30 × (-22) + 30 × (14)
30 × (-22) + 30 × (14)
Answer
View full question & answer→30 × (-22) + 30 × (14)
= (-660) + 420
= -240
= (-660) + 420
= -240
Question 252 Marks
Simplify:
(-9) × 18 - (-9) × 8
(-9) × 18 - (-9) × 8
Answer
View full question & answer→(-9) × 18 - (-9) × 8
= -(9) × [18 - 8]
= -9 × 10
= -90
= -(9) × [18 - 8]
= -9 × 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) × (-16) + (-27) × (-14)
(-27) × (-16) + (-27) × (-14)
Answer
View full question & answer→(-27) × (-16) + (-27) × (-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)
(-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
B represents the integer -10
Therefore, (-2) + (-8) = -10