Question

what is the next fraction in this sequence? simplify your answer.
\\(\frac{2}{7}\\), \\(\frac{5}{14}\\), \\(\frac{3}{7}\\), \\(\frac{1}{2}\\), ...

Explanation:

Step1: Convert to common denominator

Convert all fractions to fourteenths: $\frac{2}{7}=\frac{4}{14}$, $\frac{5}{14}=\frac{5}{14}$, $\frac{3}{7}=\frac{6}{14}$, $\frac{1}{2}=\frac{7}{14}$.

Step2: Identify the pattern

The numerators are 4, 5, 6, 7, so the next numerator is 8. The denominator remains 14.

Step3: Simplify the fraction

$\frac{8}{14}$ simplifies to $\frac{4}{7}$.

Answer:

$\frac{4}{7}$