The importance of brackets

I was making good progress on the purple top I'm making but something didn't quite feel right about it.  At first I couldn't put my finger on it, I looked at my plans and they seemed reasonable, but still, something was off.  Then it began to be obvious that the sleeves had started with too many stitches (it's a top-down raglan), and I thought and thought about my math and the top, and I rechecked my gauge and math and still, I couldn't figure out what the issue was.

Tuesday night I was knitting and hanging out with friends and suddenly it hit me.  The order of operations, I had accidentally done the math in the wrong order and this was why everything was wonky.  Yesterday I re-did the math, confirming exactly what the issue was and ripped out to the start. It wasn't as demoralizing as I thought it would be.  

I was at row 26 when I ripped back and am back to row 18, and things are looking much better.  They're also going much faster since there are considerably fewer stitches for each sleeve.