Odds for Hitting Outs on Turn AND River

[Mastershake73]

I am an Engineer and for some reason, having a terrible time understanding the odds for calculating outs on the turn and the river (2 cards to come).

I could just memorize the odds charts, but I won't be able to believe it until I understand the calculation.

Assuming 4 outs (gut shot straight) the chance of hitting that hand on the turn is 4 /(52-5) or 8.5%

If you miss on the turn and need to hit on the river, the chance of hitting is 4 / (52-6) or 8.7%

What I can't grasp is why those odds are not added to get the chance of hitting on the turn or the river.

I read that the difference is due to the times that you hit the card on both the turn and the river.

Could someone please explain this to me?