Questions: What is the reciprocal of 3 4/5? A. 3 4/5 B. -3 4/5 C. -5/19 D. 5/19

Solution Steps

To find the reciprocal of a mixed number, first convert the mixed number to an improper fraction. Then, take the reciprocal of that fraction by swapping the numerator and the denominator.

To find the reciprocal of \(3 \frac{4}{5}\), we first convert the mixed number to an improper fraction.

\[ 3 \frac{4}{5} = \frac{3 \times 5 + 4}{5} = \frac{15 + 4}{5} = \frac{19}{5} \]

The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). Therefore, the reciprocal of \(\frac{19}{5}\) is:

\[ \frac{5}{19} \]

Final Answer