What fraction results from simplifying 7/8 ÷ 9/5?

To simplify the expression ( \frac{7}{8} \div \frac{9}{5} ), we can use the rule that dividing by a fraction is the same as multiplying by its reciprocal. Thus, we rewrite the division as follows:

[

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

]

Next, we multiply the numerators and the denominators:

[

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

]

Now we've reached the fraction ( \frac{35}{72} ). To ensure it's fully simplified, we check if there are any common factors between the numerator and the denominator. Since 35 (which factors into 5 and 7) and 72 (which factors into 2, 2, 2, 3, and 3) have no common factors, ( \frac{35}{72} ) is indeed in its simplest form.

Therefore, the final result of simplifying ( \frac{7}{8} \div \frac{9}{5} ) is ( \