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You (or they) have it backward. Someone might say, I am using Cherry 8/4 ("eight quarter") by 6".
Measuring in quarters indicates that they are using rough cut lumber. If the lumber was purchased finish planed, it would generally be listed in "inches", like 2 inch.
So, here's the oddity. If you run out and buy some "one by" finish planed material, it will not be one inch thick. It will usually be 3/4", though that varies according to how diligent the planer operator is. If you buy "four quarter" rough material, it should be one full inch thick, or a little over. Again, depends on how diligent the sawyer is.