To convert the improper fraction [tex]\(\frac{15}{4}\)[/tex] into a mixed number, follow these steps:
1. Divide the numerator by the denominator:
Divide 15 by 4. The quotient is the integer part of the mixed number.
[tex]\[
15 \div 4 = 3 \quad \text{(remainder 3)}
\][/tex]
2. Identify the remainder:
The remainder when 15 is divided by 4 is 3.
[tex]\[
15 \div 4 = 3 \text{ with a remainder of } 3
\][/tex]
3. Form the fractional part:
The fractional part is given by the remainder over the original denominator.
[tex]\[
\text{Fractional part} = \frac{3}{4}
\][/tex]
4. Combine the integer part and the fractional part:
Thus, the mixed number is:
[tex]\[
3 \frac{3}{4}
\][/tex]
5. Convert the fractional part to a decimal for the mixed number:
Convert [tex]\(\frac{3}{4}\)[/tex] to a decimal.
[tex]\[
\frac{3}{4} = 0.75
\][/tex]
6. Combine the integer and decimal parts:
Adding the integer part (3) and the decimal part (0.75) gives:
[tex]\[
3 + 0.75 = 3.75
\][/tex]
Therefore, the improper fraction [tex]\(\frac{15}{4}\)[/tex] can be written as the mixed number 3.75.
Among the given choices, the correct one is:
[tex]\(\boxed{3.75}\)[/tex]
