Sure, let's solve the division of two fractions step-by-step.
The problem is to evaluate [tex]\(\frac{7}{8} \div \frac{7}{16}\)[/tex].
### Step 1: Understand Division of Fractions
When dividing by a fraction, you can multiply by its reciprocal. The reciprocal of [tex]\(\frac{a}{b}\)[/tex] is [tex]\(\frac{b}{a}\)[/tex].
### Step 2: Apply the Reciprocal
So, [tex]\(\frac{7}{8} \div \frac{7}{16}\)[/tex] can be rewritten as:
[tex]\[
\frac{7}{8} \times \frac{16}{7}
\][/tex]
### Step 3: Simplify the Expression
Now, we multiply the numerators together and the denominators together:
[tex]\[
\frac{7 \times 16}{8 \times 7}
\][/tex]
### Step 4: Cancel Common Factors
Notice that both the numerator and the denominator have a common factor of 7, which can be canceled out:
[tex]\[
\frac{16}{8}
\][/tex]
### Step 5: Simplify Further
Simplify [tex]\(\frac{16}{8}\)[/tex]:
[tex]\[
16 \div 8 = 2
\][/tex]
Thus, the result of [tex]\(\frac{7}{8} \div \frac{7}{16}\)[/tex] is 2.
### Conclusion
So, the answer is:
[tex]\[
\boxed{2}
\][/tex]
Therefore, the correct choice is:
b. 2
