Eat an elephant one bite at a time.
I am looking for an alternative to this idiom that expresses the same idea.
The idea expressed: If a big task is given, tackle it piece by piece
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There are probably lots of similar sayings, but the common one that springs to mind is:
slow and steady wins the race
Although it doesn't specifically mention breaking a task into pieces, this commonly used proverb is about being methodical with respect to both speed and accuracy.
A longer version of the proverb is said less often:
Slow and steady wins the race, not the person who wants to climb the whole stairs in one stride.