The problem requires simplifying each fraction in the given sequence: $\frac{6 \times 9}{3}, \frac{9 \times 7}{8}, \frac{12 \times 5}{13}, \frac{15 \times 3}{18}$.

1. Problem Description

The problem requires simplifying each fraction in the given sequence: $\frac{6 \times 9}{3}, \frac{9 \times 7}{8}, \frac{12 \times 5}{13}, \frac{15 \times 3}{18}$.

2. Solution Steps

First fraction: $\frac{6 \times 9}{3}$

We can simplify by dividing 6 by 3:

$\frac{6 \times 9}{3} = \frac{2 \times 3 \times 9}{3} = 2 \times 9 = 18$

Second fraction: $\frac{9 \times 7}{8}$

$9 \times 7 = 63$, so the fraction is $\frac{63}{8}$. This fraction cannot be simplified further.

Third fraction: $\frac{12 \times 5}{13}$

$12 \times 5 = 60$, so the fraction is $\frac{60}{13}$. This fraction cannot be simplified further.

Fourth fraction: $\frac{15 \times 3}{18}$

$15 \times 3 = 45$, so the fraction is $\frac{45}{18}$.

We can simplify this fraction by dividing both numerator and denominator by 9:

$\frac{45}{18} = \frac{5 \times 9}{2 \times 9} = \frac{5}{2}$.

3. Final Answer

The simplified sequence of fractions is: $18, \frac{63}{8}, \frac{60}{13}, \frac{5}{2}$.