The best replacement for long division is short division.

The best alternatives to long division are rated as following:
★★★★★  short division
★★★★  synthetic division
  division

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Speaking about long division, one probably shouldn't forget about decimals.

Other search terms related to long division and their ratings are:
★★★★★ decimals
★★★★★ polynomials
★★ remainder
dividing
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long division
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