Question

what is the next fraction in this sequence? simplify your answer. \\(\frac{22}{27}\\), \\(\frac{23}{27}\\), \\(\frac{8}{9}\\), \\(\frac{25}{27}\\), ...

Explanation:

Step1: Convert to common denominator

Rewrite $\frac{8}{9}$ as $\frac{24}{27}$ to match the denominator of other terms.
Sequence becomes: $\frac{22}{27}, \frac{23}{27}, \frac{24}{27}, \frac{25}{27}, ...$

Step2: Identify pattern

Each term increases by $\frac{1}{27}$.
$\frac{25}{27} + \frac{1}{27} = \frac{26}{27}$

Step3: Simplify (if needed)

$\frac{26}{27}$ is already in simplest form.

Answer:

$\frac{26}{27}$