Both sides of a market add up to more than 100%. The extra is the book's hold. Strip it out and you get the price the market actually believes — which is the number every other decision should be measured against.
A book posting -110 on both sides is not saying the game is a coin flip. Each -110 implies 52.38%, and 52.38 plus 52.38 is 104.76. That extra 4.76 points is the hold — the book's cut, baked into both prices.
Dividing each side by the book total scales them back to 100 and leaves the market's actual opinion. At -110/-110 that lands on an even 50/50, which is what you already suspected. It gets interesting when the prices are lopsided: -140/+120 does not mean what most people read it to mean.
This matters because every edge calculation compares your number to the market's number. If you compare against the priced number instead of the fair number, you'll count the book's cut as if it were your disagreement with the market, and you'll think you have an edge on games where you don't.
One caution worth stating plainly: this simple method splits the hold evenly across both sides, which is close enough for two-way markets near even money and gets less accurate on heavy favorites. It is a good tool, not a perfect one.
Math, not advice. 21+ where legal. If gambling stops being entertainment, call 1-800-GAMBLER.