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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 quotient of two integers is not always an integer?
The quotient of two integers is not always an integer because division may result in a non-integer value when the numerator is not evenly divisible by the denominator. For example, dividing 5 by 2 gives 2.5, which is not an integer. Only when the numerator is a multiple of the denominator will the quotient be an integer.
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!
Is a 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 quotient of two integers is not always an integer?
The quotient of two integers is not always an integer because division may result in a non-integer value when the numerator is not evenly divisible by the denominator. For example, dividing 5 by 2 gives 2.5, which is not an integer. Only when the numerator is a multiple of the denominator will the quotient be an integer.
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.
What statements is true p is and integer and q is a nonzero integer?
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.
Can you divide an integer by another integer?
Yes, you can divide an integer by another integer, but the result may not always be an integer. If the divisor is a factor of the dividend, the result will be an integer. However, if the divisor does not evenly divide the dividend, the result will be a fraction or a decimal. Additionally, division by zero is undefined and cannot be performed.
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.
