Question

Which of the following statements is always true?

• A. $\frac{x-y}{2}$ is a rational number between x and y.
• B. $\frac{x+y}{2}$ is a rational number between x and y.
• C. $\frac{x\times y}{2}$ is a rational number between x and y.
• D. $\frac{x÷y}{2}$ is a rational number between x and y.

Answer 1

The correct option is B $\frac{x+y}{2}$ is a rational number between x and y.

Consider, rational numbers 0 and 2, $\frac{0-2}{2}=\frac{-2}{2}=-1$, which does not lie between 0 and 2.

Consider, rational numbers -3 and -2, $\frac{-3\times -2}{2}=\frac{6}{2}=3$, which does not lie between -3 and -2.

Consider, rational numbers 1 and 2 , $\frac{1÷2}{2}=\frac{0.5}{2}=0.25$, which does not lie between 1 and 2 .

For any rational numbers x and y , $\frac{x+y}{2}$ is a rational number and it always lies between x and y.