Certainly! Let's solve the division of fractions step-by-step.
Given the problem:
[tex]\[ \frac{5}{7} \div \frac{8}{11} \][/tex]
To divide two fractions, we multiply the first fraction by the reciprocal (or the inverse) of the second fraction. The reciprocal of a fraction is obtained by swapping its numerator and denominator.
Step 1: Identify the reciprocal of the second fraction:
[tex]\[ \text{The reciprocal of } \frac{8}{11} \text{ is } \frac{11}{8}. \][/tex]
Step 2: Replace the division with multiplication by the reciprocal:
[tex]\[ \frac{5}{7} \div \frac{8}{11} = \frac{5}{7} \times \frac{11}{8} \][/tex]
Step 3: Multiply the numerators and the denominators:
[tex]\[ \frac{5 \times 11}{7 \times 8} = \frac{55}{56} \][/tex]
So, the result of the division is:
[tex]\[ \frac{5}{7} \div \frac{8}{11} = \frac{55}{56} \][/tex]
From the given options, the correct answer is:
[tex]\[ \boxed{\frac{55}{56}} \][/tex]
So, the correct answer is option D.
