What is the reciprocal of 7 2/3

Question

?(1 point)

Answer 1

To find the reciprocal of \( 7 \frac{2}{3} \), first convert the mixed number to an improper fraction.

1. Convert \( 7 \frac{2}{3} \) to an improper fraction: \[ 7 \frac{2}{3} = \left(7 \times 3 + 2\right)/3 = (21 + 2)/3 = 23/3 \]

2. The reciprocal of a fraction \( \frac{a}{b} \) is \( \frac{b}{a} \). So the reciprocal of \( \frac{23}{3} \) is: \[ \frac{3}{23} \]

Thus, the reciprocal of \( 7 \frac{2}{3} \) is \( \frac{3}{23} \).