Here's another attempt to make the math make sense.
Say you have 10 ml of 24 mg/ml nicotine. That means each mililiter of nicotine solution contains 24 mg of nicotine. Picture 24 little milligrams of nicotine floating around in 1 mililiter. Now, if you have 10 ml of that, you have 10 mililiters, each containing 24 mg of nicotine. So 10 ml x 24 mg/ml = 240 mg of nicotine floating around in those 10 ml.
Now, say you add 1 ml of flavor to those 10 ml of nicotine base. The flavor did not have any nicotine in it, so it doesn't add any nicotine, but it does add a ml of volume. So now you have 240 mg of nicotine, but it is now floating around in 11 ml of liquid. So... 240mg / 11 ml = 21.8mg/ml.
That's just a way to conceptualize what the numbers actually mean, which (IMO) helps figure out how to do the math.