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.

The answer is yes; here’s why:

A multiple of 7 can be written 7*k*, or 7*n*, 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* = 7*k* and *y* = 7*n*.

Then *x* + *y* = *z* = 7*k* + 7*n* = 7(*k* + *n*), and *z* is also a multiple of 7.

The argument is the same for the other cases, since *x* = *z* – *y* and *y* = *z* – *x*.