This is odd on the face of it. The term "ratio" when used in reference to flash typically refers to the relative intensity of flashes in a given setup. So, for example, a 2:1 ratio involves two lights one at (say) f/8 and the other at f/5.6. Bear with me if you are unfamiliar with using f-stop settings to refer to light intensity. The point is, one light emits twice as much light as the other. In a typical portrait situation, a main light, positioned at 45 degrees to the right of the subject and a fill at 45 degrees and to the left might be set in a 2:1 ratio where the main light illuminates and gives definition, while the fill light softens the image by adding light in the harsh shadows.
Your example is about mixing a controlled light source (the flash) with an uncontrolled one (ambient). Clearly, the more flash there is relative to the strength of the ambient, the less the ambient matters. Expressing this as a ratio, however, is unusual. But, the "more flash" part can be achieved by using flash exposure compensation to increase the output of the flash while using exposure compensation to reduce the effective amount of light reaching the sensor.
However... The most important factor governing the mixing (or not) of ambient light is the shutter speed. The higher the shutter speed, up to the flash sync speed, the less the ambient light will factor into the exposure. Say you have determined that a correct flash exposure is whatever your flash puts out at f/5.6. It could be that a correct exposure for ambient light is 1/30 sec at f/5.6. So, following along this example, if you expose at 1/30 of a second, the ambient light will be a major factor in your image. However, if you expose at 1/60, it will be half the factor, at 1/100 a quarter (fudging because cameras normally switch from 1/60 to 1/100 instead of 1/120). Anyhow, by the time you reach sync speed at about 1/200 second (depending on your flash), you will have reduced the influence of the ambient light to a fraction of what it would have been at the "correct" ambient exposure.
Note: The reason I cited only an aperture for the correct flash exposure is that the flash duration is so short that the shutter speed is irrelevant -- only that you keep it at or longer than the flash sync speed.
Having gone through all of this, I would say two things:
- Ratios among several lights can (are) important to understand. However, I don't think this is what you were talking about in your question.
- The most important thing to understand about mixing flash and ambient light is that faster shutter speeds reduce the effect of ambient light.
- How you reduce the shutter speed is up to you. My method is to set the camera on manual and decide for myself. This implies that I do one of two other things: Either meter the flash to help me decide (for studio strobes); or use TTL flash so a speedlight can adjust its output automagically (and, amazingly, it will!)
I hope I haven't overcomplicated this, but I would recommend not using FEC/EC just to jerk the camera into using different shutter speeds. That gives the camera more control than you want. Try M. You'll find yourself liking it.