Sure! Let's work through the subtraction of the mixed numbers [tex]\(8 \frac{1}{5} - 4 \frac{2}{5}\)[/tex] step by step.
1. Convert the mixed numbers to improper fractions:
For [tex]\(8 \frac{1}{5}\)[/tex]:
[tex]\[
8 \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{40 + 1}{5} = \frac{41}{5}
\][/tex]
For [tex]\(4 \frac{2}{5}\)[/tex]:
[tex]\[
4 \frac{2}{5} = \frac{4 \times 5 + 2}{5} = \frac{20 + 2}{5} = \frac{22}{5}
\][/tex]
2. Subtract the improper fractions:
Since both improper fractions have the same denominator, subtract the numerators:
[tex]\[
\frac{41}{5} - \frac{22}{5} = \frac{41 - 22}{5} = \frac{19}{5}
\][/tex]
3. Convert the result back to a mixed number:
Divide the numerator by the denominator:
[tex]\[
\frac{19}{5} = 3 \text{ remainder } 4
\][/tex]
So, the mixed number is:
[tex]\[
3 \frac{4}{5}
\][/tex]
This means we have 3 as the whole number part and [tex]\( \frac{4}{5} \)[/tex] as the fraction part.
Thus, the simplified answer, written as a mixed number, is:
[tex]\[
3 \frac{4}{5}
\][/tex]
So, the correct answer is:
[tex]\[
\boxed{3 \frac{4}{5}}
\][/tex]
