Question

what is the next fraction in this sequence? simplify your answer. $\frac{3}{4}$, $\frac{1}{2}$, $\frac{1}{3}$, $\frac{2}{9}$, ...

Explanation:

Step1: Find common denominator

Rewrite fractions with denominator 36:
$\frac{3}{4}=\frac{27}{36}$, $\frac{1}{2}=\frac{18}{36}$, $\frac{1}{3}=\frac{12}{36}$, $\frac{2}{9}=\frac{8}{36}$

Step2: Analyze numerator pattern

Check ratio between consecutive numerators:
$\frac{18}{27}=\frac{2}{3}$, $\frac{12}{18}=\frac{2}{3}$, $\frac{8}{12}=\frac{2}{3}$

Step3: Calculate next numerator

Multiply last numerator by $\frac{2}{3}$:
$8 \times \frac{2}{3} = \frac{16}{3}$

Step4: Form next fraction & simplify

Next fraction: $\frac{\frac{16}{3}}{36} = \frac{16}{3 \times 36} = \frac{16}{108} = \frac{4}{27}$

Answer:

$\frac{4}{27}$