Question

find the reciprocals of the numbers below.
the reciprocal of \\(\frac{1}{5}\\) is \\(\square\\).
the reciprocal of 18 is \\(\square\\).

Explanation:

Step1: Recall the definition of reciprocal

The reciprocal of a number \( a \) (where \( a
eq 0 \)) is \( \frac{1}{a} \) such that \( a\times\frac{1}{a} = 1 \). For a fraction \( \frac{b}{c} \) (where \( b
eq0,c
eq0 \)), its reciprocal is \( \frac{c}{b} \) because \( \frac{b}{c}\times\frac{c}{b}=1 \).

Step2: Find the reciprocal of \( \frac{1}{5} \)

Using the rule for the reciprocal of a fraction, if we have the fraction \( \frac{1}{5} \), we swap the numerator and the denominator. So the reciprocal of \( \frac{1}{5} \) is \( \frac{5}{1}=5 \).

Step3: Find the reciprocal of \( 18 \)

First, we can write \( 18 \) as a fraction \( \frac{18}{1} \) (since any integer \( n \) can be written as \( \frac{n}{1} \)). Then, using the rule for the reciprocal of a fraction, we swap the numerator and the denominator. So the reciprocal of \( \frac{18}{1} \) is \( \frac{1}{18} \).

Answer:

The reciprocal of \( \frac{1}{5} \) is \( 5 \).
The reciprocal of \( 18 \) is \( \frac{1}{18} \).