Question

Which of the following statements is true?
(i) $\frac{-5}{0}$ is a negative rational number.
(ii) The reciprocal of $\frac{1}{a}$, if a=0 is $\frac{1}{0}$.
(iii) $1÷(-\frac{1}{4})=-4$
(iv) $x÷(y+z)=x÷y+x÷z$

• A. Both (i) and (ii)
• B. Only (iii)
• C. (i), (ii) and (iv)
• D. (ii), (iii) and (iv)

Answer 1

Answer: (B)

Only (iii)

Statement (i) : Division by zero is not defined. So, the statement is false.

Statement (ii) : Reciprocal of zero is not defined (same thing). So, the statement is false.

Statement (iii) : $1÷(-\frac{1}{4})=\frac{1}{(-\frac{1}{4})}=\frac{1\times 4}{-1}=-4$. So, the statement is true.

Statement (iv) : $x÷(y+z)=\frac{x}{y+z}\ne \frac{x}{y}+\frac{x}{z}$. So, the statement is false.

$\therefore$ only statement $\left(iii\right)$ is true here.

So, answer is $\left[B\right]$.