# A counterexample that shows when the statement is false. Show all work to verify that the counterexample really makes the statement false.For all integers a, b and c, if a = b,then a/c = b/c.

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### 1 Answer

For any real numbers a, b, and c, if a=b and c is not a zero, then a/c=b/c. A counterexample that shows when the statement is false would be when c equals zero. The denominator of any fraction must not be zero. If the denominator of a fraction is zero, the expression is not a legal fraction because its overall value cannot be defined.

Fractions are expressions of something being divided into groups of equal size. The denominator is the total number of groups you make. Having a zero in the denominator doesn't make sense because you can not take something and divide it and have no groups.

Easier,

ex) 5/0 = x means that 0 * x = 5.

There is no value that satisfies x because zero time any number equals zero.