To solve the problem [tex]\( 6 \div \frac{3}{8} \)[/tex], we need to understand the concept of dividing by a fraction. Dividing by a fraction is the same as multiplying by its reciprocal. Here's the step-by-step solution:
1. Identify the reciprocal of the fraction:
The given fraction is [tex]\( \frac{3}{8} \)[/tex]. The reciprocal of [tex]\( \frac{3}{8} \)[/tex] is obtained by flipping the numerator and the denominator, which results in [tex]\( \frac{8}{3} \)[/tex].
2. Convert the division into multiplication:
Instead of dividing [tex]\( 6 \)[/tex] by [tex]\( \frac{3}{8} \)[/tex], we multiply [tex]\( 6 \)[/tex] by the reciprocal of [tex]\( \frac{3}{8} \)[/tex].
[tex]\[
6 \div \frac{3}{8} = 6 \times \frac{8}{3}
\][/tex]
3. Perform the multiplication:
Now, multiply [tex]\( 6 \)[/tex] by [tex]\( \frac{8}{3} \)[/tex]:
[tex]\[
6 \times \frac{8}{3}
\][/tex]
4. Break down the multiplication:
First, multiply the whole number [tex]\( 6 \)[/tex] by the numerator [tex]\( 8 \)[/tex]:
[tex]\[
6 \times 8 = 48
\][/tex]
Next, divide the result by the denominator [tex]\( 3 \)[/tex]:
[tex]\[
\frac{48}{3} = 16
\][/tex]
The final result of dividing [tex]\( 6 \)[/tex] by [tex]\( \frac{3}{8} \)[/tex] is [tex]\( 16 \)[/tex], based on all the steps we took.
So, the correct answer is:
[tex]\[
\boxed{16}
\][/tex]
Finally, looking at the multiple-choice options provided:
A. [tex]\( \frac{1}{8} \)[/tex]
B. [tex]\( \frac{1}{4} \)[/tex]
C. 16
D. 48
The correct choice is:
[tex]\[
\boxed{C}
\][/tex]
