3.2. MULTIPLICATION AND DIVISION
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(6) Distributive Property of Multiplication over Addition
Let a, b, and c be any whole numbers. Then, provided b
a(b
c) = ab
c,
ac.
Proof.
Let b
c = n.
Then b = c + n (Missing addend).
ab = a(c + n).
ab = ac + an (distributive)
Thus ab
ac = an (missing addend)
But b
c = n.
So ab
ac = a(b
⇤
c).
Multiplication Property of Zero
For every whole number a,
a · 0 = 0 · a = 0.