Sure, let's solve the given expression step-by-step.
We start with the expression:
[tex]\[ 3 \frac{1}{4} \times \frac{1}{16} \][/tex]
1. Convert the mixed number to an improper fraction:
[tex]\[ 3 \frac{1}{4} = 3 + \frac{1}{4} \][/tex]
To convert this to an improper fraction:
Convert the whole number part:
[tex]\[ 3 = \frac{12}{4} \][/tex]
Combine it with the fractional part:
[tex]\[ 3 + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} \][/tex]
2. Multiply the fractions:
Now multiply [tex]\(\frac{13}{4}\)[/tex] by [tex]\(\frac{1}{16}\)[/tex]:
[tex]\[ \frac{13}{4} \times \frac{1}{16} = \frac{13 \times 1}{4 \times 16} = \frac{13}{64} \][/tex]
3. Simplify the fraction if possible:
The fraction [tex]\(\frac{13}{64}\)[/tex] is already in its simplest form since 13 is a prime number and does not share any common factors with 64.
Therefore, the simplified result of the expression [tex]\(3 \frac{1}{4} \times \frac{1}{16}\)[/tex] is:
[tex]\[ \frac{13}{64} \][/tex]
Among the given options, the correct one is:
C) [tex]\(\frac{13}{64}\)[/tex]
