Question

what is the next fraction in this sequence? simplify your answer.
\frac{5}{13}, \frac{9}{26}, \frac{4}{13}, \frac{7}{26},...

Explanation:

Step1: Standardize denominators

Rewrite fractions with denominator 26:
$\frac{5}{13} = \frac{10}{26}$, $\frac{9}{26} = \frac{9}{26}$, $\frac{4}{13} = \frac{8}{26}$, $\frac{7}{26} = \frac{7}{26}$

Step2: Identify numerator pattern

Numerators: 10, 9, 8, 7 (decrease by 1 each term)
Next numerator: $7 - 1 = 6$

Step3: Form and simplify fraction

Next term: $\frac{6}{26} = \frac{3}{13}$

Answer:

$\frac{3}{13}$