Divisibility Theorem (Sum)

Suppose x, y, and z are all counting numbers, and x + y = z. If two of these numbers are multiples of 7, is the third one also a multiple of 7? Show why or why not.


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The answer is yes; here’s why:

A multiple of 7 can be written 7k, or 7n, or whatever, where k, n, etc. are whole numbers.
So if x + y = z, and x and y are multiples of 7, we can say x = 7k and y = 7n.
Then x + y = z = 7k + 7n = 7(k + n), and z is also a multiple of 7.

The argument is the same for the other cases, since x = zy and y = zx.

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