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For example, (10 + 2) / 2 = (10 / 2) + (2 / 2). This works if the added terms are on the left side of the division side (or the numerator of a fraction).

Consider the distribution of multiplication over addition to be the fundamental rule; if you convert the division above to a multiplication, and later you convert the multiplication back to a division, it should be clear why the distributive property works in this case:

(10 + 2) / 2 = (10 + 2) x (1/2) = (10 x 1/2) + (2 x 1/2) = (10 / 2) + (2 / 2)

Please note that it does NOT work the other way round, that is, if the added terms are on the right of the division sign (denominator of a fraction).

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Q: Is there distributive for division over addition?
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