In Analog to Analog conversion , why we multiply instead of adding?
Adding two signals together doesn't give the right result. What you want with AM is the audio signal moved up in frequency to around the carrier frequency so that many AM channels can co-exist and be individually tuned to by a radio receiver.

If you added 1 MHz with an audio source the resultant specturm is plain ordinary 1 MHz and unaltered 20Hz to 20 kHz.

What you get with modulation (i.e. multiplying) is plain ordinary 1MHz (as before) and two side bands containing the audio information centred around 1MHz. Lower sideband is 0.98000 MHz to 0.99998 MHz and upper sideband is 1.00002 MHz to 1.02000 MHz: -



Depending on how you amplitude modulate you may also get a suppressed carrier frequency i.e. no content at 1 MHz.

Now, all the audio information is pushed up into a band of frequencies between 0.98 MHz and 1.02MHz. The AM receiver will centre its filters at this area and reject all other transmissions because the filters have high rejection when not perfectly aligned. This allows a radio receiver to tune into a wanted AM transmission whilst rejecting unwanted radio transmissions.