That’s essentially what I do though. Frequently enough that I don’t need to think much about what 1/12th or such of common intervals are. The gulf between 1/3 in, 1/2, and 1/3 to go is rough.
If I’m really suffering I’ll chop the end off an interval and start the mental math over again. Usually only doing that on the last minute or a VO2 interval though.
This is also what I do. I’m a clock watcher on the turbo. I’ve never got the whole timing music to workouts.
When the interval (in minutes) is not easily divisible by 10, I’ll calculate the number of second st which I reach each 5%, 10%, 15%, etc. mostly keeps me distracted. Important that each step be less than 2 minutes or I lose focus on the distraction. 
I like to compute gear ratio to the third digit over and over again. Also, I split longer intervals in ratios I find appealing. I usually count up so that it gets “easier” (85 % done, just 15 % to go) and count down for the last one or two. I’m glad I’m not along
The last two days I’ve done 2x40. But I set the 40 minute intervals up as 8 5-minute intervals. So instead of 2x40, I’m doing 2x8 
I always break the intervals into 5% increments. i.e., Six minute intervals get broken into 18 second chunks. 5% down, 10, 15…40% – 40% is basically the exact same thing as half way! This keeps going until 90 seconds (one minute left). The last minute oscillates between percentages and “a few more seconds”.
I notice a significant benefit when using increasingly closer landmarks to mark my progress during max efforts.
At least for me, I have a harder time with math games for shorter intervals (e.g., 3 minute) than I do for longer (like the 40 minute I’ve been doing). The shorter just hurt more.
I count down the last minutes of an interval in ten second blocks. That means each minute is actually six 10 second blocks - I can do anything for 10 seconds (or do I tell myself) and there are only six of them. Hope that makes sense!
I tried something like that but I always end up counting too fast. Lol, For me I find counting to 100 equates roughly to 60s and sometimes when its actually takes more than 60s to count to 100 I am pleasantly surprised 
If I am really desperate for the end of an interval it’s just 1 to 12 or 14 repeatedly
Who are you and why can you read my mind? I do that all the time
Ok my other most recurrent bike math repetitive thought is: I am riding at, say, 35 an hour and I’ve got 5 km to arrive. My train of thought is:
“1 km at 40 an hour is a minute and a half, and at 30 an hour it takes 2 minutes. So, at 35 an hour it must be 1:45, which makes these 5 km something like 8:45 minutes to go”. Sometimes the fractions get messy and the calculation is repeated every time the speed changes, etc… For some reason I like estimating the time of arrival.
I do exactly this - its pretty easy on round numbers, but still challenges me for weird durations like 7 or 21 minutes
My math is generally based on song length. So, if I have a 3-minute interval (for example), I say to myself “this interval is going to be over before the song ends”. Or, on a long interval, I look at the playlist and say “ok, I got this… one by Katy Perry, one by Ava Max, and I get to finish the interval with Selena Gomez!”
I know what you’re thinking: whoa, that @Jack_Russell_Racing dude is a weirdo.
I like to count the number of deep breaths I take during a long interval and calculate my respiratory rate
I focus on pedal revolutions. I do 100 groups of 3 revolutions counting off the right foot and then 100 off the left. I focus on form and only let my concentration drop when I know the interval will be over before the next 100 finishes. For some reason it has to be groups of 3. I tried 2 and 4 but it just wasn’t floating my boat.