Question

what is the next fraction in this sequence? simplify your answer. $\frac{1}{6}$, $\frac{11}{36}$, $\frac{4}{9}$, $\frac{7}{12}$, ...

Explanation:

Step1: Convert to common denominator

Rewrite all fractions with denominator 36:
$\frac{1}{6} = \frac{6}{36}$, $\frac{11}{36} = \frac{11}{36}$, $\frac{4}{9} = \frac{16}{36}$, $\frac{7}{12} = \frac{21}{36}$

Step2: Identify numerator pattern

Observe numerators: 6, 11, 16, 21. Each increases by 5.
Next numerator: $21 + 5 = 26$

Step3: Simplify the new fraction

New fraction is $\frac{26}{36}$, simplify by dividing numerator and denominator by 2:
$\frac{26 \div 2}{36 \div 2} = \frac{13}{18}$

Answer:

$\frac{13}{18}$