Question

how many rational numbers between 1 by 4 and 1 by 7​

Answer 1

Answer:

Step-by-step explanation:

Infinite rational numbers exist between any two rational numbers

Answer 2

Answer:

Infinite number of rational numbers between

$\frac{1}{4}$ and $\frac{1}{7}$

Step-by-step explanation:

There are an infinite number of rational numbers between two given (non-equal) numbers.

Let m and n be any two numbers with n > m. Let d = n-m. Let t be any positive integer greater than or equal to 2. Then m < m+d/t < n. Since there are an infinite number of possible values for t, each of which gives a different value of m+d/h, and each value of m+d/h is a rational number (the sum of two or more rational numbers is itself always a rational number), this gives an infinite number of rational numbers greater than or equal to m and less than n. Of course, this does not give all rational numbers greater than or equal to m and less than or equal to n, but it is enough to prove that there are an infinite number of rational numbers greater than or equal to m and less than or equal to n.

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