Question

what is the next fraction in this sequence? simplify your answer. \\(\frac{52}{55}\\), \\(\frac{48}{55}\\), \\(\frac{4}{5}\\), \\(\frac{8}{11}\\), ...

Explanation:

Step1: Simplify given fractions

$\frac{52}{55}$ (already simplified), $\frac{48}{55}$ (already simplified), $\frac{4}{5} = \frac{44}{55}$, $\frac{8}{11} = \frac{40}{55}$

Step2: Identify numerator pattern

Numerators: 52, 48, 44, 40. Each term decreases by 4.
Next numerator: $40 - 4 = 36$

Step3: Keep denominator consistent

Denominator remains 55 for the unsimplified next term: $\frac{36}{55}$

Step4: Check if fraction simplifies

36 and 55 share no common factors besides 1, so it is in simplest form.

Answer:

$\frac{36}{55}$