To find the reciprocal of the mixed number \(5 \frac{1}{8}\), you first need to convert it into an improper fraction. 1. Convert \(5 \frac{1}{8}\) to an improper fraction: \[ 5 \frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \] 2. The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). Thus, the reciprocal of \(\frac{41}{8}\) is: \[ \frac{8}{41} \] So, the reciprocal of \(5 \frac{1}{8}\) is \(\frac{8}{41}\).

Reciprocal for 5 1/8

1 answer

To find the reciprocal of the mixed number \(5 \frac{1}{8}\), you first need to convert it into an improper fraction.

Convert \(5 \frac{1}{8}\) to an improper fraction: \[ 5 \frac{1}{8} = \frac{(5 \times 8) + 1}{8} = \frac{40 + 1}{8} = \frac{41}{8} \]
The reciprocal of a fraction \(\frac{a}{b}\) is \(\frac{b}{a}\). Thus, the reciprocal of \(\frac{41}{8}\) is: \[ \frac{8}{41} \]

So, the reciprocal of \(5 \frac{1}{8}\) is \(\frac{8}{41}\).