To find the difference between the whole number and the mixed number [tex]\( 8 - 3 \frac{2}{5} \)[/tex], we can follow these steps:
1. Convert the mixed number to an improper fraction:
- The mixed number presented is [tex]\( 3 \frac{2}{5} \)[/tex].
- To convert [tex]\( 3 \frac{2}{5} \)[/tex] to an improper fraction, we multiply the whole number part (3) by the denominator (5) and then add the numerator (2).
[tex]\[
3 \times 5 + 2 = 15 + 2 = 17
\][/tex]
- Thus, [tex]\( 3 \frac{2}{5} \)[/tex] becomes [tex]\( \frac{17}{5} \)[/tex].
2. Subtract the improper fraction from the whole number:
- The whole number is 8, and we need to subtract [tex]\( \frac{17}{5} \)[/tex] from it.
- First, convert the whole number 8 into a fraction with the same denominator (5).
[tex]\[
8 = \frac{8 \times 5}{5} = \frac{40}{5}
\][/tex]
- Now, we subtract [tex]\( \frac{17}{5} \)[/tex] from [tex]\( \frac{40}{5} \)[/tex].
[tex]\[
\frac{40}{5} - \frac{17}{5} = \frac{40 - 17}{5} = \frac{23}{5}
\][/tex]
3. Convert the resulting improper fraction back to a mixed number:
- Divide the numerator (23) by the denominator (5) to get the quotient and the remainder.
[tex]\[
23 \div 5 = 4 \text{ R } 3
\][/tex]
- The quotient (4) is the whole number part, and the remainder (3) is the numerator of the fractional part with the original denominator (5).
[tex]\[
\frac{23}{5} = 4 \frac{3}{5}
\][/tex]
So, the difference [tex]\( 8 - 3 \frac{2}{5} \)[/tex] is [tex]\( 4 \frac{3}{5} \)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{A. \ 4 \frac{3}{5}}
\][/tex]
