Division of a whole number by ____ is not defined.
0
Why “division by zero” is not defined
Division asks: “What number times the divisor gives the dividend?”
Example: \(12 \div 3 = 4\) because \(3 \times 4 = 12\).
Now try dividing by zero. Suppose \(5 \div 0 = x\).
Then we must have \(0 \times x = 5\).
But for any number \(x\):
\(0 \times x = 0\).
It can never be 5.
So there is no number \(x\) that works.
Therefore, division by zero is not defined.
Important notes
\(12 \div 0\) is not defined (no answer).
\(0 \div 0\) is also not defined (it is “indeterminate”).
But dividing zero by a non-zero number is fine:
\(0 \div 5 = 0\) because \(5 \times 0 = 0\).