First, rewrite [tex]$\frac{19}{20}$[/tex] and [tex]$\frac{14}{15}$[/tex] so that they have a common denominator. Then, use [tex]$\ \textless \ $, $=$, or $\ \textgreater \ $[/tex] to order [tex]$\frac{19}{20}$[/tex] and [tex]$\frac{14}{15}$[/tex].

[tex]\[
\begin{array}{c}
\frac{19}{20}=\frac{\square}{\square} ; \frac{14}{15}=\frac{\square}{\square} \\
\frac{19}{20} \square \frac{14}{15}
\end{array}
\][/tex]

To compare the fractions [tex]$\frac{19}{20}$[/tex] and [tex]$\frac{14}{15}$[/tex] by rewriting them with a common denominator, follow these steps:

1. Identify the least common multiple (LCM) of the denominators:
- The denominators are 20 and 15.
- The LCM of 20 and 15 is 60. This is the smallest number that both 20 and 15 can divide without leaving a remainder.

2. Convert each fraction to have the common denominator (60):
- For [tex]$\frac{19}{20}$[/tex]:
- Determine what number you need to multiply 20 by to get the LCM (60).
[tex]\[
\frac{60}{20} = 3
\][/tex]
- Multiply both the numerator and the denominator of [tex]$\frac{19}{20}$[/tex] by 3:
[tex]\[
\frac{19}{20} = \frac{19 \times 3}{20 \times 3} = \frac{57}{60}
\][/tex]

- For [tex]$\frac{14}{15}$[/tex]:
- Determine what number you need to multiply 15 by to get the LCM (60).
[tex]\[
\frac{60}{15} = 4
\][/tex]
- Multiply both the numerator and the denominator of [tex]$\frac{14}{15}$[/tex] by 4:
[tex]\[
\frac{14}{15} = \frac{14 \times 4}{15 \times 4} = \frac{56}{60}
\][/tex]

3. Compare the fractions:
- We now have [tex]$\frac{57}{60}$[/tex] and [tex]$\frac{56}{60}$[/tex].
- Since both fractions have the same denominator, you only need to compare the numerators.
[tex]\[
57 > 56
\][/tex]

Therefore, [tex]$\frac{19}{20} > \frac{14}{15}$[/tex].

To summarize:
[tex]\[
\frac{19}{20} = \frac{57}{60}, \quad \frac{14}{15} = \frac{56}{60}
\][/tex]
[tex]\[
\frac{19}{20} > \frac{14}{15}
\][/tex]