Is playing a dotted quarter note, one eighth note tied with a quarter note, and then an eighth note the same as : a dotted quarter note, one eighth note, an eighth rest, one eighth note, and then a quarter note?

To determine whether two musical notations are the same, you need to understand the value of each note and rest involved. Here's how you can compare the two scenarios:

In the first scenario:
1. Start with a dotted quarter note, which is equivalent to three eighth notes.
2. Add one eighth note, which makes a total of four eighth notes.
3. Tie the last eighth note with a quarter note, making it a combined duration of one and a half beats.

In the second scenario:
1. Start with a dotted quarter note, equivalent to three eighth notes.
2. Add one eighth note.
3. Insert an eighth rest, which means there is silence for one eighth note duration.
4. Follow it with another eighth note.
5. Finally, include a quarter note, which lasts for one beat.

Comparing both scenarios, we find that they are not the same. In the first scenario, there is a tied note that extends to one and a half beats. However, in the second scenario, after the first eighth note, there is an eighth rest, which means there is silence for one eighth note duration before the following eighth note. Therefore, the two scenarios produce different rhythms.