To find the reciprocal of the mixed number [tex]\(6 \frac{1}{5}\)[/tex], we need to follow a series of steps. Let's break it down:
1. Convert the mixed number to an improper fraction:
- A mixed number [tex]\(6 \frac{1}{5}\)[/tex] can be written as a sum of the whole part and the fractional part.
- Here, the whole part is 6, and the fractional part is [tex]\(\frac{1}{5}\)[/tex].
- Converting it to an improper fraction:
[tex]\[
6 + \frac{1}{5} = \frac{6 \times 5}{5} + \frac{1}{5} = \frac{30}{5} + \frac{1}{5} = \frac{31}{5}
\][/tex]
2. Calculate the numerical value of the improper fraction:
[tex]\[
\frac{31}{5} = 6.2
\][/tex]
3. Find the reciprocal:
- The reciprocal of a number [tex]\(x\)[/tex] is [tex]\(\frac{1}{x}\)[/tex].
- So, the reciprocal of [tex]\(6.2\)[/tex] is:
[tex]\[
\frac{1}{6.2} \approx 0.16129032258064516
\][/tex]
Therefore:
- The value of [tex]\(6 \frac{1}{5}\)[/tex] is [tex]\(6.2\)[/tex].
- The reciprocal of [tex]\(6.2\)[/tex] is approximately [tex]\(0.16129032258064516\)[/tex].
So, Eclat is indeed the reciprocal of [tex]\(6 \frac{1}{5}\)[/tex], which is [tex]\(0.16129032258064516\)[/tex].
