Yumi has a ribbon of length $\frac{5}{6}$ m. Her sister has a ribbon of length $\frac{4}{9}$ m. The question asks how many times longer Yumi's ribbon is compared to her sister's ribbon. In other words, we need to find $x$ such that $\frac{4}{9} \times x = \frac{5}{6}$.

1. Problem Description

Yumi has a ribbon of length $\frac{5}{6}$ m. Her sister has a ribbon of length $\frac{4}{9}$ m. The question asks how many times longer Yumi's ribbon is compared to her sister's ribbon. In other words, we need to find $x$ such that $\frac{4}{9} \times x = \frac{5}{6}$.

2. Solution Steps

To find how many times longer Yumi's ribbon is than her sister's, we need to divide the length of Yumi's ribbon by the length of her sister's ribbon.

So we need to calculate $\frac{5}{6} \div \frac{4}{9}$.

To divide by a fraction, we multiply by its reciprocal:

$\frac{5}{6} \div \frac{4}{9} = \frac{5}{6} \times \frac{9}{4}$

$\frac{5}{6} \times \frac{9}{4} = \frac{5 \times 9}{6 \times 4}$

We can simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor.

$\frac{5 \times 9}{6 \times 4} = \frac{5 \times (3 \times 3)}{(2 \times 3) \times 4}$

Cancel out the common factor of 3 in the numerator and denominator:

$\frac{5 \times 3}{2 \times 4} = \frac{15}{8}$

3. Final Answer

$\frac{15}{8}$ times