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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Numbers do not have a distributive property. The distributive property is an attribute of one arithmetical operation over another. The main example is the distributive property of multiplication over addition.
The distributive property OF MULTIPLICATION over addition is a*(b + c) = a*b + a*c for any numbers a, b and c.
No. But multiplication is distributive over addition. This means that for any numbers A, B, and C A x (B + C) = (A x B) + (A x C). If addition were distributive over multiplication, that would mean that A + (B x C) = (A + B) x (A + C) which is not true.
The distributive property of multiplication over addition states that a*(b + c) = a*b + a*c
The distributive property of multiplication over addition.