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