Question

True or false? If True give an example or If false give counterexampleThe quotient of two integers is an integer.

Answer 1

Given the statement "the quotient of two integers is an integer", we could determine if it is true or false.

Let us consider two integers, say A and B. If the A divides B and the result (i.e. the quotient) divides evenly then, the statement is true. If A is 4 and B is 2, the quotient is as shown below

`(A)/(B)=(4)/(2)=2`

From the above example, the quotient is an integer

If A is 2 and B is 4, the quotient is as shown below

`(A)/(B)=(2)/(4)=(1)/(2)`

From the above example, the quotient is a fraction and not an integer.

Hence, the statement "the quotient of two integers is an integer" is FALSE based on the above examples.