What is the difference between the whole number and the mixed number below?

[tex]\[ 8 - 3 \frac{2}{5} \][/tex]

A. [tex]\( 4 \frac{3}{5} \)[/tex]
B. [tex]\( 4 \frac{2}{5} \)[/tex]
C. [tex]\( 5 \frac{1}{5} \)[/tex]
D. [tex]\( 5 \frac{2}{5} \)[/tex]



Answer :

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]