The product of a fractional number and its reciprocal is always equal to 1. Let's understand why this is the case.

Fractional numbers can be written in the form of a/b, where a and b are integers and b is not equal to zero. The reciprocal of a fraction is obtained by interchanging the numerator and denominator. So, the reciprocal of a/b is b/a.

To find the product of a fraction and its reciprocal, we multiply the fraction by its reciprocal:

(a/b) * (b/a)

Let's simplify this expression step by step:

Step 1: Multiply the numerators (a * b) and the denominators (b * a) separately:

(a * b) / (b * a)

Step 2: Simplify the expression by canceling out the common factors in the numerator and denominator:

(ab) / (ba)

Step 3: Notice that ab and ba are the same. When we multiply a number by its reciprocal, the result is always 1:

1

So, the product of a fractional number and its reciprocal is always equal to 1.

In other words, no matter what the values of a and b are (as long as b is not equal to zero), when you multiply a fraction by its reciprocal, the result is always 1.

For example, let's consider the fraction 2/3. Its reciprocal is 3/2. When we multiply 2/3 by 3/2, we get:

(2/3) * (3/2) = (2 * 3) / (3 * 2) = 6/6 = 1

Similarly, if we consider the fraction 5/8, its reciprocal is 8/5. When we multiply 5/8 by 8/5, we get:

(5/8) * (8/5) = (5 * 8) / (8 * 5) = 40/40 = 1

This pattern holds true for all fractional numbers. The product of a fraction and its reciprocal is always equal to 1.