Question

what is the next fraction in this sequence? simplify your answer.\\(\frac{7}{15}, \frac{2}{5}, \frac{1}{3}, \frac{4}{15}, ...\\)

Explanation:

Step1: Make denominators equal

Convert all fractions to have denominator 15:
$\frac{7}{15}$, $\frac{2}{5}=\frac{6}{15}$, $\frac{1}{3}=\frac{5}{15}$, $\frac{4}{15}$.

Step2: Identify the pattern

Check the numerators: 7, 6, 5, 4. The pattern is subtracting 1 each time.

Step3: Find the next numerator

Next numerator: $4 - 1 = 3$.

Step4: Form the next fraction

Fraction: $\frac{3}{15}$, simplify to $\frac{1}{5}$.

Answer:

$\frac{1}{5}$