First of all this is my first post here, I would like to say nice to meet you all here...!!!
I am confused about Router IP Addresses and Default Gateways. I know what both of them are, but still having problems to understand them well. I am new in Cisco world, I am going to an Academy course where our course material is "CCNA Discovery 4.0" and also I am at the semester CCNA1...
We are currently working with Cisco ISR or Linksys WRT300N, while entering default gateway and Internet IP's I cannot understand what's the point... Or at the other hand while playing with Packet Tracer 5.1 when I design somekind of a basic network, in one side of network I add one Linksys connect 3 wireless and 1 wired computer. At other side of the network I add a router (I know how to enable its ports whereas work somehow a bit with them "practised a bit") to the router I connect one Server where it acts as Web Server. Till' now everything is okay. The time comes for logically addressing them. At Linksys side think that I have a public address of (*144.22.63.2/16), at the Router IP Address I put some private IP Addresses (*192.168.150.10-20/24) with default gateway of (*192.168.150.1) I want to mention that I enabled the DHCP inside of the Linksys. But now at the Internet port side I am a bit confused, this happens also on real world, what to write?!
At the other side of the network think what the Server has a real IP of 82.122.44.4 and now what to configure at Router any clue would be very helpful.

Also thanks for viewing this topic and to ones who replay thanks 2x...!!!
- Onur