By what number should 1365 be divided to get 31 as quotient and 32 as remainder?

Which of the following statement is true / false?

**(i)** \(\dfrac{ 2 }{ 3} – \dfrac{4 }{ 5}\) is not a rational number.

**(ii) **\( \dfrac{ -5 }{ 7}\) is the additive inverse of \( \dfrac{ 5 }{ 7}\)

**(iii)** 0 is the additive inverse of its own.

**(iv) **Commutative property holds for subtraction of rational numbers.

**(v) **Associative property does not hold for subtraction of rational numbers.

**(vi)** 0 is the identity element for subtraction of rational numbers.

If x = \( \dfrac{4 }{ 9}\), y =\( \dfrac{-7 }{ 12}\) and z = \( \dfrac{-2 }{ 3}\), then verify that x – (y – z) ≠ (x – y) – z

If x = \(\dfrac{ – 4 }{ 7}\) and y = \( \dfrac{2 }{ 5}\), then verify that x – y ≠ y – x

Subtract the sum of \(\dfrac{ – 5 }{ 7} and\dfrac{ – 8 }{ 3}\) from the sum of \(\dfrac{5 }{ 2} and \dfrac{– 11 }{ 12}\)