Zero times anything is zero.
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Division by a non-zero rational number is equivalent to multiplication by its reciprocal.
Dividing by a rational number (other than zero) is simply multiplication by its reciprocal.
Zero is a rational number and an integer.
Division by any non-zero number is the same as multiplication by its reciprocal.
A rational number can be expressed as a fraction or ratio of two integers. Zero is an integer. Therefore, zero is a rational number EXCEPT, that the denominator of a rational number cannot be zero. You can't divide by zero.