Question

what is the next fraction in this sequence? simplify your answer. \\(\frac{7}{12}\\), \\(\frac{29}{48}\\), \\(\frac{5}{8}\\), \\(\frac{31}{48}\\), ...

Explanation:

Step1: Convert to common denominator

Rewrite all terms with denominator 48:
$\frac{7}{12} = \frac{28}{48}$, $8 = \frac{384}{48}$, $\frac{5}{8} = \frac{30}{48}$, $\frac{29}{48}$ stays as is, $\frac{31}{48}$ stays as is.
Sequence becomes: $\frac{28}{48}, \frac{29}{48}, \frac{30}{48}, \frac{31}{48}, \frac{384}{48}, ...$

Step2: Identify numerator pattern

Numerators: 28, 29, 30, 31, 384. Correct the misordered term: the sequence is $\frac{7}{12}, \frac{29}{48}, \frac{5}{8}, \frac{31}{48}, 8,...$ → numerators 28,29,30,31,384. The first four are consecutive integers: 28,29,30,31.

Step3: Find next numerator

Next consecutive numerator after 31 is 32.

Step4: Simplify the fraction

$\frac{32}{48} = \frac{32\div16}{48\div16} = \frac{2}{3}$

Answer:

$\frac{2}{3}$