The Dow Jones Industrial Average (DJINDICES: ^DJI) just entered a new era. Three old Dow tickers got the boot on Monday, replaced by three brand-new members. You can argue all day for and against the merits of the changes, but one thing is for certain: The math behind the Dow changed dramatically overnight.

The Dow is a price-weighted index, which means that individual stock-price moves make a bigger difference if share prices are high. It's a somewhat controversial alternative to market-cap weighting, which is how the S&P 500 manages its total value.

What's the difference? Well, a company with a big share price but a small market cap carries a big stick on the Dow but hardly matters when calculating the S&P 500's total value. Grab a ticker with an outsized market cap but modest share prices instead, and the situation is reversed.

Let me help you visualize the situation with an interactive graph:

Two of the three newcomers to the Dow fit the first description to a "T." Visa (NYSE: V) and Goldman Sachs (NYSE: GS) bring in share prices comparable to former index king IBM. Thanks to this rebalancing action, IBM's Dow weight suddenly fell from 9.4% to 7.9%. Big Blue is still important, but it's not the totally dominating force it used to be.

But the newbies would need to combine their market caps to carry as much weight as Big Blue would wield in a cap-weighted index.

Nike (NYSE: NKE) is a different beast altogether. The sportswear veteran is smaller than the average Dow stock in terms of both share price and market cap. That being said, Nike's relatively modest share price is still 44% higher than the three departing tickers taken together.

The three new members account for nearly 18% of the Dow's total share prices, which translates to 18% of the weight applied to the premium index's total score. They also add up to 5.8% of the Dow's total market-cap value. Fair or not, that's the way the cookie crumbles.

The changes also made a big difference to the Dow divisor. Dow scores are calculated by adding up share prices and then dividing the result by this divisor, which in turn is modified whenever the composition of the actual index veers off. The Dow doesn't fall when its members pay out dividends, because the divisor changes to balance out these effects. And even though Nike, Goldman, and Visa increased the Dow's combined share prices by $385 on Monday, you didn't see the Dow itself soaring 20% higher. Thank the divisor for this stability.

The divisor value has been roughly 0.13 for the past few years, but it's time to learn a new number. Hello, 0.155715905! The Wall Street Journal can help you keep track of the current divisor on a daily basis.

The Dow's Blue Chips Still Look Tasty
The new Dow math doesn't change one basic truth: The Dow is packed to the rafters with high-quality stocks. If you're looking for some long-term investing ideas, you're invited to check out The Motley Fool's brand-new special report, "The 3 Dow Stocks Dividend Investors Need." It's absolutely free, so simply click here now and get your copy today.

Fool contributor Anders Bylund owns shares of Intel but holds no other position in any company mentioned. Check out Anders' bio and holdings or follow him on Twitter and Google+.

The Motley Fool owns shares of Walt Disney, Intel, and Microsoft. Motley Fool newsletter services have recommended buying shares of UnitedHealth Group, Nike, Coca-Cola, Home Depot, McDonald's, American Express, Johnson & Johnson, 3M, Procter & Gamble, Visa, Walt Disney, and Goldman Sachs Group. Motley Fool newsletter services have recommended creating a diagonal call position in Nike. Motley Fool newsletter services have recommended creating a synthetic long position in International Business Machines. Motley Fool newsletter services have recommended creating a write covered straddle position in American Express. Motley Fool newsletter services have recommended creating a bull call spread position in McDonald's. Motley Fool newsletter services have recommended buying calls on Johnson & Johnson. Motley Fool newsletter services have recommended creating a bull call spread position in Microsoft. Motley Fool newsletter services have recommended creating a bull call spread position in Wal-Mart Stores. Motley Fool newsletter services have recommended creating a diagonal call position in UnitedHealth Group. Motley Fool newsletter services have recommended creating a bull call spread position in Intel. Motley Fool newsletter services have recommended creating a buy leap calls position in Coca-Cola. Motley Fool newsletter services have recommended creating a diagonal call position in 3M. The Motley Fool has a disclosure policy.

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