Musicians use the term "subdividing" to describe how they count more complex rhythms. Calculate the least common unit of duration and keep track of the beat in those terms.
By counting 1 & 2 & 3 & 4 &, you now have eight notes for a measure of 4/4. A quarter note would take up 2 of those, a dotted quarter gets 3, a half note gets 4, etc.
You can pre-mark the subdivision to aid in counting (above). The largest lines represent the beat, which each smaller unit marking the sub-division on the beat. Essentially, you're pre-calculating the subdivision so you don't have to compute it on the fly.
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