Certainly! Let's work through this problem step-by-step:
1. Understanding the Problem:
- We are given two rational numbers whose product equals 2.
- One of the rational numbers is \(\( \frac{1}{7} \)\).
- Our goal is to find the other rational number.
2. Setting up the Equation:
- Let \(\( x \)\) be the other rational number we are looking for.
- According to the problem, the product of \(\( \frac{1}{7} \)\) and \(\( x \)\) equals 2.
- We can express this relationship with the equation:
\(\[
\frac{1}{7} \times x = 2
\]\)
3. Solving for \(\( x \)\):
- To isolate \(\( x \)\), we need to get rid of the fraction \(\( \frac{1}{7} \)\).
- We can do this by multiplying both sides of the equation by 7 (the reciprocal of \(\( \frac{1}{7} \)\)):
\(\[
7 \times \left( \frac{1}{7} \times x \right) = 7 \times 2
\]\)
- Simplifying the left side:
\(\[
x = 14
\]\)
4. Conclusion:
- The other rational number is \(\( 14 \)\).
Therefore, if the product of \(\( \frac{1}{7} \)\) and another rational number is 2, the other rational number is \(\( \boxed{14} \)\).
