Intuitively many students (and adults) think division by 0 produces an answer of 0. This is understandable because division by 0 occurs so seldom in real world situations.

Using Number Properties

Problem: “Make up a word problem for 0 ÷ 34 and solve it.”  (Possible answer: Marie thinks about dividing nothing into 34 pieces. Answer: 0.)

Examples: Work out: 0 x 456,  0 ÷ 89,  89 x 0,  0 ÷ 789 093,  345 x 567 x 0, 0 ÷ 834 ÷ 2 345

Understanding Number Properties:

If letters stand for any numbers, find:
a x b x 0,  0 ÷ a,  a x 0 ÷ b,  a x b x c ÷ d x 0

Hard Problem: “Find 34 ÷ 0 on a calculator. What does the “E” in the display indicate? Why is division by 0 impossible?”

(Brief answer: Consider this problem: There is a queue of people. Jill has 34 apples  and she gives out 0 apples to each person in the queue. So in a sense, she can give out  apples to an infinite number of people.  So 34 ÷ 0 = ∞ .Because mathematicians have a strong aversion to sayign 34 ÷ 0 = ∞, they prefer to say 34 ÷ 0 is undefined).