title: Instructions per second equation
body: <p>This should be a simple question.</p>
  
  <p>Say we have a 3.0 gHz processor with a CPI of 1.5 How many instructions per second does it execute? Just thinking logically, it would be the number of cycles per second times the number of instructions per cycle...which is...</p>
  
  <p>3&times;10<sup>9</sup> cycles/second &times; 1.5 instructions/cycle = 4.5&times;10<sup>9</sup> instructions/second</p>
  
  <p>Makes sense. Okay, so this is a question from my book and I look up the solutions just to make <em>sure</em> I understand and got it right. Well the solution says that it's:</p>
  
  <p>3&times;10<sup>9</sup>/1.5 = 2&times;10<sup>9</sup> instructions/sec</p>
  
  <p><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7469aa30bc5b52815ab09cb9fb192d434a3302a6" alt="hi"></p>
  
  <p>This answer comes from the clock rate/CPI part, but I am really failing to grasp how...if you sub in clock rate/cpi like this:
  (clock cycles/sec)/(instructions/clock cycle), it's basically the opposite of the original equation because you divide cycles by instructions instead of multiplying them...and the units don't even cancel out, you end up with a unit of cycles<sup>2</sup>/instructions&times;seconds. I have to be missing something totally obvious here/botching basic math, but my pea brain is not getting it.</p>