How many rational numbers exist between

To determine the number of rational numbers between two given numbers, we need to consider the properties of rational numbers.

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers.

Let's assume we have two rational numbers, a/b and c/d, where a, b, c, and d are integers and b and d are not equal to zero.

To find the number of rational numbers between a/b and c/d, we need to find the number of fractions that lie between these two fractions.

One way to do this is by finding a common denominator for the fractions a/b and c/d. Let's say the common denominator is k.

Now, we can rewrite the fractions a/b and c/d with the common denominator k as ak/bk and ck/dk.

To find the number of rational numbers between a/b and c/d, we need to find the number of fractions that lie between ak/bk and ck/dk.

This can be done by subtracting the numerators of the fractions and finding the absolute value of the difference. Let's call this difference m.

The number of rational numbers between a/b and c/d is equal to m - 1.

Therefore, the number of rational numbers between a/b and c/d is m - 1.