We have, [ 16 \(\div\) 4 ] \(\div\) 4 \(\div\) 0
First integer (x) = 16
Second integer (y) = 4
Third integer (z) = 0 \(\Rightarrow\) \(\frac { x }{ y } =\frac { 16 }{ 4 } \) \(\Rightarrow\) \(\frac { { x }/{ y } }{ y } =\frac { 4 }{ 4 } \) = 1 \(\Rightarrow\) \(\frac { { \left( { x }/{ y } \right) }/{ y } }{ z } =\frac { 1 }{ 0 } =\infty \)

Let the pair be 17 and 5.
\(\therefore\) Difference = 17 - 5 = 12, which is greater than only one of the integers.

18 - (-24)
​​​​​​​Forsubtraction 18 - (-24) = 18 + 24                      [\(\because\) (-)(-) = (+)]
= 42                                             [\(\because\) higher integer sign is (+)]
Verification First integer (x) = 18           [given]
Second integer (y) = (-24)             [given]
For closure property x - y = 18 - (-24) = 18+ 24 = 42 (integer) i.e. subtraction is closed.

We have, LHS = 39 + (-24) -15 = 39 - 39 = 0
and RHS = 36 + (-52) - (-36)
= 36 - 52 + 36 = 72 - 52 = 20
Since, 0 < 20
39 + (-24) -15 < 36 + (-52) - (-36).

10 + (-4) = 10 - 4 = +6 or 6  [\(\because\) difference = 6, higher integer sign is' +']

As per the given information, the product of two integers is -216.
First integer = - 6 and second integer = x (say).
So, their product,
(-6) \(\times\) x = -216
\(\therefore\) x = -216/-6 = 36
Hence, the other integer is 36.

Given, a = -11, b = -12, c = - 3
Taking LHS,
(a x b) x c = [(-11) x (-12)] x (-3)
= [(11 x 12) x (-3)] = 132 x (-3) = - 396
Now, taking RHS
a x (b x c) = (-11) x [( -12) x (-3)]
= (-11) x [(12 x 3)] = (-11) x 36 = - 396
Hence, (a x b) x c=a x (b x c)

Number line with all numbers is shown below:

We know that a place whose temperature is highest, will be the hottest place and the place whose temperature is lowest, will be the coldest place.
Here, the temperature of hottest place (Bangalore) = 22° C and temperature of coldest place (Lahulspiti) = - 8° C
\(\therefore\) Temperature difference between the hottest and coldest places = Temperature of Bangalore - Temperature of Lahulspiti.
= 22 - (- 8) = 22 + 8 = 30
Hence, the temperature difference between the hottest and the coldest places is 30°C.

(i) 49
(ii) 28

As per the given information, we can draw the given diagram.

Let A be the point above the sea level and B be the point below the sea level.
\(\therefore\) Vertical distance between points A and B = Distance between point A and sea level + Distance between point B and sea level.
= AO + OB = 8848 + 10911 = 19759 m

(i) We know that, 3 \(\div\) 1= 3, so 3 \(\div\) (- 1)= - 3
On comparing with a \(\div\) b = - 3, we get a = 3 and b = -1
Hence, the required pair of integers is (3, -1).
(ii) We know that, 12 \(\div\) 4 = 3, so 12 \(\div\)(- 4) = - 3
On comparing with a \(\div\) b = - 3, we get a = 12 and b = -4
Hence, the required pair of integers is (12, - 4).
(iii) We know that, 9 \(\div\) 3 = 3, so 9 \(\div\) (- 3) = - 3
On comparing with a \(\div\) b = - 3, we get a = 9 and b = -3
Hence, the required pair of integers is (9, - 3).
(iv) We know that,12 \(\div\) 4 = 3, so (-12) \(\div\) 4 = -3
On comparing with a \(\div\) b = - 3, we get a = -12 and b=4
Hence, the required pair of integers is (-12, 4).
(v) We know that, 15 \(\div\) 5 = 3, so 15 + (- 5) = -3
On comparing with a \(\div\) b = - 3, we get a = 15 and b = -5
Hence, the required pair of integers is (15, - 5).