Question

I want explanation of this question.​

Answer 1

Question - Find two rational numbers between 5/7 and 11/13.

There are countless (infinite) rational numbers between any two rational numbers. Whenever we are asked to find rational numbers between any two numbers, first make sure that the two numbers have the same denominator.

Why both the numbers should have the same denominator?

To find rational numbers between them

For e.g., if you are asked to find two rational numbers between 2/3 and 7/6, you would not know which rational numbers lie between them. But after taking L.C.M. and making the denominators same (like we make when we have to arrange them in ascending order), the numbers become 4/6 and 7/6. 4/6 is equal to 2/3. And now, we can easily find two rational numbers between them. Obviously by looking, we can say that 5/6 and 6/6 lie between 4/6 and 7/6. Here if we consider the numerators, 5 and 6 lie between 4 and 6. We do not have to worry about the denominators as they are same.

So now let's solve your question.

First take L.C.M. and make the denominators same. (* means multiply)

L.C.M of 7 and 13 = 91

$\frac{5*13}{7*13} and \frac{11*7}{13*7}$

$\frac{65}{91} and \frac{77}{91}$

Now, the denominators are same. So, we can easily find two rational numbers.

66/91, 67/91, 68/91, 69/91, 70/91, 71/91, 72/91, 73/91, 74/91, 75/91, 76/91

All these numbers lie between 65/91 and 77/91, i.e., 5/7 and 11/13.

So pick any two numbers as your answer.