NCERT Exemplar Solutions
Class 6 - Mathematics - Unit 1: Number System - Fill in the Blanks

Question 122

Why “division by zero” is not defined

1. Division asks: “What number times the divisor gives the dividend?”

   Example: \(12 \div 3 = 4\) because \(3 \times 4 = 12\).

2. Now try dividing by zero. Suppose \(5 \div 0 = x\).

   Then we must have \(0 \times x = 5\).

3. But for any number \(x\):

   \(0 \times x = 0\).

   It can never be 5.

4. 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 \(5 \times 0 = 0\).