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Why is the quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Should the quotient of an integer divided by a non zero integer always be a rational number?
Yes, that is how a rational number is defined.
What is the difference between division and integer division?
In integer division, you expect the result to be an integer. Anything left over will be quoted as a remainder. The more commonly used division (not integer division) will continue calculating decimals, up to the desired accuracy.
Is integer division another name for integer division?
It looks to be the same name.
Why the definition of a fraction restricts the denominator to being a nonzero integer?
Because division by zero is not defined and if the denominator were zero, we would be dividing by zero.
Is a quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Why is the quotient of an integer divided by a nonzero integer always a rational number?
Because that is how a rational number is defined!
Should the quotient of an integer divided by a non zero integer always be a rational number?
Yes, that is how a rational number is defined.
Is the reciprocal of an integer always less than the integer?
No. In fact, the reciprocal of 0 is not defined.
What is the difference between division and integer division?
In integer division, you expect the result to be an integer. Anything left over will be quoted as a remainder. The more commonly used division (not integer division) will continue calculating decimals, up to the desired accuracy.
Is integer division another name for integer division?
It looks to be the same name.
Why the definition of a fraction restricts the denominator to being a nonzero integer?
Because division by zero is not defined and if the denominator were zero, we would be dividing by zero.
Will the square of an integer always be an integer?
Yes, the square of an integer is always an integer.
How is an integer defined?
An integer is a positive or negative whole number.
What happens with the numbers when you multiply and divide integers?
If you multiply integers the results is an integer. If you divide integers (with one exception) the result is a rational number which, in some cases, may be an integer. However, the exception is that division by 0 is not defined.
Which statement is true the square root of an integer will always be an integer or the square of an integer will always be an integer?
the square of an integer will always be an integer
Is 37 squared a rational or irrational number?
372 = 1,369 is an integer; therefore, it is a rational number. In fact, the square of any integer is always an integer; this is because the sum or product of any two integers is an integer. And every integer is a rational number; this is because a rational number is defined as the quotient obtained by dividing one integer into another; and because every integer is the quotient obtained by dividing that integer by the integer 1.
