**The Product of Two Rational Numbers: An Explanation with Examples**

**Introduction:**
In mathematics, rational numbers are numbers that can be expressed as a fraction of two integers, where the denominator is not zero. The product of two rational numbers refers to the result obtained when multiplying two rational numbers together.

**Example 1:**
Let's consider the product of two rational numbers, 2/3 and 3/4.

**Step 1:**
To find the product of these two rational numbers, we multiply the numerators and denominators separately.

- Numerator: 2 * 3 = 6
- Denominator: 3 * 4 = 12

**Step 2:**
The product of 2/3 and 3/4 is 6/12. However, we can simplify this fraction further by dividing both the numerator and denominator by their greatest common divisor (GCD), which is 6 in this case.

- Numerator: 6 ÷ 6 = 1
- Denominator: 12 ÷ 6 = 2

**Step 3:**
The simplified product of 2/3 and 3/4 is 1/2. This means that when we multiply 2/3 and 3/4 together, the result is 1/2.

**Example 2:**
Let's take another example with different rational numbers, 5/6 and 7/8.

**Step 1:**
Multiply the numerators and denominators separately:

- Numerator: 5 * 7 = 35
- Denominator: 6 * 8 = 48

**Step 2:**
Simplify the resulting fraction by dividing both the numerator and denominator by their GCD, which is 1 in this case.

- Numerator: 35 ÷ 1 = 35
- Denominator: 48 ÷ 1 = 48

**Step 3:**
The simplified product of 5/6 and 7/8 is 35/48.

**Conclusion:**
The product of two rational numbers is obtained by multiplying their numerators and denominators separately. After multiplication, the resulting fraction can be further simplified by dividing both the numerator and denominator by their GCD. This simplification ensures that the product is in its simplest form. The examples provided help illustrate the process of finding the product of two rational numbers.