Should the quotient of an integer divided by a nonzero integer always be a rationalnumber? Why or why not?
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a rational number is defined as
a/b , where a and b are integers, with b≠0
when you divide two integers you get exactly that form
Yes, the quotient of an integer divided by a nonzero integer will always be a rational number.
To understand why, we need to recall that a rational number is defined as a number that can be expressed as the ratio of two integers, where the denominator is not zero.
When we divide an integer by a nonzero integer, we can express the result as the fraction of the numerator divided by the denominator. Both the numerator and denominator are integers, satisfying the definition of a rational number.
For example, let's consider dividing 10 by 2. The quotient is 5, which can be expressed as a fraction 5/1, where both the numerator and denominator are integers.
In general, dividing any integer by a nonzero integer will always yield a result that can be expressed as a ratio of two integers, making it a rational number.