A rational number is always the result of dividing an integer when the divisor is nonzero.
An integer is any number which can be either positive and negative but not a fractional number. It is also a whole number. Examples are -1,256, -589, -1, 0, 1, 569, 5,236. It is always a rational number. By definition, a rational number is the division of two integers, where the divisor is not zero. Since the divisor is 1 when the number is an integer, then all integers are rational.
Yes, the square of an integer is always an integer.
The square root of an integer is a CYCLOTOMIC integer.
Yes, by definition, the sum of two integers is always an integer. Likewise, the product and difference of two integers is always an integer.
Yes. The square of an integer is just the number times itself. For any two whole numbers that are multiplied, the answer is always an integer (i.e. no decimals).
No.
The opposite of a nonzero integer is found by changing its sign. For example, if you have a nonzero integer like +5, its opposite is -5. This relationship holds for any nonzero integer; the opposite will always be the same number with an inverted sign. Thus, the opposite of a nonzero integer ( x ) is simply ( -x ).
Yes, it is.
Yes.
Yes.
If ( p ) is an integer and ( q ) is a nonzero integer, then the expression ( \frac{p}{q} ) will always yield a rational number. Additionally, since ( q ) is nonzero, ( p ) cannot be divided by zero, ensuring the division is valid. Furthermore, ( p + q ) will also be an integer, as the sum of two integers is always an integer.
Yes, always. That is the definition of a rational number.
Yes, by definition.
Division by an integer is always defined only when the divisor is not zero
Because that is how a rational number is defined!
I had this name question for homework :| no
Because that is how a rational number is defined!