Question

what is the next fraction in this sequence? simplify your answer.
\\(\frac{1}{6}\\), \\(\frac{2}{9}\\), \\(\frac{5}{18}\\), \\(\frac{1}{3}\\), ...

Explanation:

Step1: Find common denominator

Convert all fractions to eighteenths: $\frac{1}{6}=\frac{3}{18}$, $\frac{2}{9}=\frac{4}{18}$, $\frac{5}{18}=\frac{5}{18}$, $\frac{1}{3}=\frac{6}{18}$.

Step2: Identify pattern

Numerators: 3, 4, 5, 6. The pattern is +1 each time.

Step3: Calculate next numerator

Next numerator: $6 + 1 = 7$. Denominator remains 18. So the fraction is $\frac{7}{18}$.

Answer:

$\frac{7}{18}$