What is the result of 7/8 ÷ 9/5?

To determine the result of dividing two fractions, such as ( \frac{7}{8} \div \frac{9}{5} ), you first recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the expression as:

[

\frac{7}{8} \times \frac{5}{9}

]

Now, perform the multiplication across the numerators and the denominators:

[

\frac{7 \times 5}{8 \times 9} = \frac{35}{72}

]

Thus, the result of the division ( 7/8 \div 9/5 ) simplifies perfectly to ( \frac{35}{72} ).

This is why the first choice is the correct answer. Understanding the process of converting division to multiplication using the reciprocal is crucial in operations involving fractions. The calculation maintains the integrity of the arithmetic operations as well as provides insight into how fractions interact with one another.

While the other options present different fractions, only ( \frac{35}{72} ) emerges from the proper application of fraction division. This exemplifies the importance of mastering fraction operations to achieve accurate results.