- How many hours does it take for the average child to memorize the $10\times 10$ addition table?
- How many school years does it take for the average child to memorize the $10 \times 10$ addition table?
- How many hours does it take for the average child to memorize the $10\times 10$ multiplication table?
- How many school years does it take for the average child to memorize the $10 \times 10$ multiplication table?
Assuming that the German "Kerncurriculum" (actually, there are 16 of them, one for each federal state. I'm referring to the one from Lower Saxony) for primary school is at least somewhat tailored for the "average person": at most two years, because at the end of second grade, pupils are supposed to
state the addition table (up to 10) and confidently derive the inverse operations
state the multiplication table (up to 10), confidently derive the inverse operations and the results of further problems.
While I have no idea what the last part ("further problems") is supposed to mean, the additions "derive inverse operations" is a hint that the tables should be thoroughly memorized by the end of second grade. Because I think that the memorization does not start straightaway from day one, less than two years is a reasonable estimate.
Sources for the translated expectations:
Die Schülerinnen und Schüler geben die Zahlensätze des kleinen 1 + 1 automatisiert wieder und leiten deren Umkehrungen sicher ab.
Die Schülerinnen und Schüler geben die Kernaufgaben des kleinen 1 x 1 automatisiert wieder und leiten deren Umkehrungen und die Ergebnisse weiterer Aufgaben ab.
Kerncurriculum für die Grundschule, Mathematik, Niedersachsen, 2006.
When/where I grew up in California, ordinary second-graders (7 - 8 year-olds) were expected to learn the times tables well enough to answer randomly chosen problems without writing anything down or looking anything up; but 100 percent accuracy was more of a hope than an expectation. Flashcards, mental shortcuts, and other memorization aids were used.
By the end of fourth grade (10 year-olds), above-average students were expected to be able to see, recognize, and write down the correct answer to randomly chosen times table problems in 2 - 3 seconds with 97 - 100 percent accuracy. The problems were randomly chosen between 0 x 0 and 12 x 12.