Answer:

Step-by-step explanation:

We will be using the concept of the division of integers to solve the given questions.

To check: a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c) ------------- (1)

a) a = 12, b = -4, c = 2

Take L.H.S, a ÷ (b + c)

Putting the values of a, b and c, we get

= a ÷ (b + c)

= 12 ÷ (-4 + 2)

= 12 ÷ (-2)

= 12 × 1 / (-2)

= -6

Now take R.H.S, (a ÷ b) + (a ÷ c)

= [12 ÷ (-4)] + (12 ÷ 2)

= [12 × (-1/4) ] + (12 × 1/2)

= -3 + 6

= 3

Putting the values of L.H.S and R.H.S in equation (1), we get

a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

-6 ≠ 3

L.H.S ≠ R.H.S

Hence verified

b) a = -10, b = 1, c = 1

Take L.H.S, a ÷ (b + c)

Putting the values of a, b and c, we get

= a ÷ (b + c)

= -10 ÷ (1 + 1)

= -10 ÷ (2)

= -10 × 1/2

= -5

Now take R.H.S, (a ÷ b) + (a ÷ c)

= [-10 ÷ (1)] + (-10 ÷ 1)

= (-10 × 1/1) + (-10 × 1/1)

= -10 + (-10)

= -20

Putting the values of L.H.S and R.H.S in equation (1), we get

a ÷ (b + c) ≠ (a ÷ b) + (a ÷ c)

-5 ≠ -20

L.H.S ≠ R.H.S

Hence verified