Let's solve the problem step-by-step:
1. Multiply the whole number by the numerator of the fraction:
[tex]\[
3 \times 5 = 15
\][/tex]
2. The denominator remains the same:
[tex]\[
\frac{15}{6}
\][/tex]
3. Simplify the fraction [tex]\(\frac{15}{6}\)[/tex]:
- Find the greatest common divisor (GCD) of 15 and 6, which is 3.
- Divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{15 \div 3}{6 \div 3} = \frac{5}{2}
\][/tex]
4. Convert the improper fraction [tex]\(\frac{5}{2}\)[/tex] into a mixed number:
- The integer part is the quotient of the division of 5 by 2:
[tex]\[
5 \div 2 = 2 \quad \text{(quotient, integer part)}
\][/tex]
- The fractional part is the remainder over the original denominator:
[tex]\[
5 \mod 2 = 1 \quad \text{(remainder, numerator of the fractional part)}
\][/tex]
- This gives us:
[tex]\[
\frac{5}{2} = 2 \frac{1}{2}
\][/tex]
5. Compare this to the given options:
- Option A: [tex]\(1 \frac{2}{6} = 1 \frac{1}{3}\)[/tex] (not a match)
- Option B: [tex]\(\frac{15}{18}\)[/tex] does not simplify to [tex]\(\frac{5}{2}\)[/tex]
- Option C: [tex]\(2 \frac{3}{6} = 2 \frac{1}{2}\)[/tex] (this matches)
- Option D: [tex]\(\frac{5}{18}\)[/tex] does not simplify to [tex]\(\frac{5}{2}\)[/tex]
Thus, the correct answer is:
C. [tex]\(2 \frac{3}{6}\)[/tex]
