Question

If x & y are two non zero positive rational number which of the statement is always true
• x-y /2 is a rational number between x & y
• x×y /2 is a rational number between x & y
• x+y /2 is a rational number between x & y
• x÷y /2 is a rational number between x & y

Answer 1

Step-by-step explanation:

If x & y are two non zero positive rational number which of the statement is always true

• (x+y) /2 is a rational number between x & y

is TRUE

Answer 2

Answer: The correct option is C.

x+y/2 is a rational number between x and y.

Rational Number: A rational number is a sort of real number in mathematics that takes the form p/q, where q is not equal to zero. Any fraction whose denominators are not 0 is a rational number. Some instances of rational numbers include 1/2, 1/5, 3/4, etc.

Step-by-step explanation:

Let us take two arbitrary value for x = $\frac{1}{2}$ and y = $\frac{1}{4}$ such that they are rational numbers.

• Option A is incorrect because

         $\frac{x-y}{2} = \frac{\frac{1}{2}-\frac{1}{4}}{2}\\\frac{x-y}{2} = \frac{1}{8} = 0.125$

        0.125 don't lie between 0.25 and 0.5

• Option B is incorrect because

         $\frac{x*y}{2} = \frac{\frac{1}{2}*\frac{1}{4}}{2}\\\frac{x*y}{2} = \frac{1}{16} = 0.0625$

           0.0625 don't lie between 0.25 and 0.5

• Option C is correct because

        $\frac{x+y}{2} = \frac{\frac{1}{2}+\frac{1}{4}}{2}\\\frac{x+y}{2} = \frac{3}{8} = 0.375$

       0.375 lie between 0.25 and 0.5

• Option D is incorrect because

         $\frac{x/y}{2} = \frac{\frac{1}{2}/\frac{1}{4}}{2}\\\frac{x/y}{2} = \frac{2}{2} = 1$

       1 don't lie between 0.25 and 0.5

Therefore, x+y/2 is a rational number between x and y.

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