NCERT Exemplar Solutions
Class 7 - Mathematics - Unit 1: Number System - Multiple Choice Questions

Question 25

Why is the answer (a) (a div 0)?

Key idea of division: Saying “(a div b = x)” means “(b imes x = a)”. We’ll check each option using this idea.

1. (a div 0) (with (a eq 0))

   (a div 0 = x ;;Longleftrightarrow;; 0 imes x = a)

   But for any number (x),

   (0 imes x = 0)

   We need it to be (a) (and (a eq 0)). This is impossible. So division by zero is not defined.

2. (0 div a) (with (a eq 0))

   (0 div a = x ;;Longleftrightarrow;; a imes x = 0)

   This is true when

   (x = 0)

   So (0 div a) is defined and equals 0.

3. (a div 1)

   (a div 1 = x ;;Longleftrightarrow;; 1 imes x = a)

   That gives

   (x = a)

   So (a div 1 = a). It’s defined.

4. (1 div a) (with (a eq 0))

   (1 div a = x ;;Longleftrightarrow;; a imes x = 1)

   That gives

   (x = rac{1}{a})

   So (1 div a) is defined and equals ( frac{1}{a}).

Conclusion: Only (a div 0) is not defined. Hence, option (a).