If a = 24 , b = 8 , c = 4 verify that a ÷ ( b + c ) ≠ ( a ÷ b ) + ( a ÷ c )

Given, a = 24 , b = 8 , c = 4 To verify: a ÷ b + c ≠ a ÷ b + a ÷ c Consider L.H.S a ÷ b + c = 24 ÷ 8 + 4 = 24 ÷ 12 = 2 Consider R.H.S a ÷ b + a ÷ c = 24 ÷ 8 + 24 ÷ 4 = 3 + 6 = 9 Since L.H.S ≠ R.H.S Hence Verified.

Write four pair of integers ( a , b ) such that a ÷ b = - 4

We are given to write a pair of integers a , b such that a ÷ b = - 4 . We have, a ÷ b = - 4 ⇒ a b = - 4 ⇒ a = - 4 b Thus, we observe that there could be infinitely many integral values of b , each for each integral value of a . Hence, there are infinitely many pairs of integers a , b . We are given to write only one pair of integers. So, for b = 1 , we have a = - 4 × 1 = - 4 . For b = 2 , a = - 4 × 2 = - 8 For b = 3 , a = - 4 × 3 = - 12 Therefore, - 4 , 1 , ( - 8 , 2 ) , ( - 2 , 8 ) , ( - 12 , 3 ) are four pairs of integers a , b such that a ÷ b = - 4 .

Give three examples to prove that, if p and q are two integers, then p ÷ q is not necessarily an integer

Given, If p and q are two integers, then p ÷ q is not necessarily an integer. Example 1 : p is 2 and q is 5 but p / q i.e., 2 5 is not an integer Example 2 : p is - 2 and q is 5 but p q i.e., - 2 5 is not an integer Example 3 : p is - 3 and q is - 4 but p q i.e., - 3 - 4 is not an integer. If p and q are two integers, the p ÷ q is not necessarily an integer. Hence, it is proved.