Question

what is the next fraction in this sequence? simplify your answer.
\\(\frac{3}{5}\\), \\(\frac{1}{2}\\), \\(\frac{2}{5}\\), \\(\frac{3}{10}\\), ...

Explanation:

Step1: Rewrite integers as fractions

$\frac{3}{5}, \frac{1}{2}, \frac{2}{5}, \frac{3}{10}, ... = \frac{3}{5}, \frac{5}{10}, \frac{4}{10}, \frac{3}{10}, ...$

Step2: Standardize denominators to 10

$\frac{6}{10}, \frac{5}{10}, \frac{4}{10}, \frac{3}{10}, ...$

Step3: Identify numerator pattern

Numerators decrease by 1: $6, 5, 4, 3, ...$

Step4: Find next numerator and simplify

Next numerator: $3-1=2$, fraction: $\frac{2}{10} = \frac{1}{5}$

Answer:

$\frac{1}{5}$