Before we begin, let’s clarify the problem: we need to multiply the fraction \( \frac{3}{13} \) by its reciprocal \( \frac{13}{6} \).
Understanding Reciprocals
- The reciprocal of a fraction \( \frac{a}{b} \) is obtained by flipping the numerator and denominator, resulting in \( \frac{b}{a} \).
- For \( \frac{3}{13} \), the reciprocal is \( \frac{13}{3} \). However, in this case, we are using \( \frac{13}{6} \) as given in the problem.
Multiplication of Fractions
- To multiply fractions, the rule is to multiply the numerators together and the denominators together.
- Thus, we calculate:
\[
\frac{3}{13} \times \frac{13}{6} = \frac{3 \times 13}{13 \times 6}
\]
Performing the Calculation
- Now, simplifying the expression:
\[
= \frac{39}{78}
\]
- Both the numerator and denominator can be simplified by dividing by their greatest common divisor (GCD), which is 39:
\[
= \frac{39 \div 39}{78 \div 39} = \frac{1}{2}
\]
Final Result
- The final answer after multiplying \( \frac{3}{13} \) by \( \frac{13}{6} \) is:
\[
\frac{1}{2}
\]
In conclusion, multiplying a fraction by its reciprocal involves straightforward multiplication and simplification, leading to the result of \( \frac{1}{2} \).