Use divisibility rules for 2, 3, 4, 5, 6, 8, 9.
Number Framework Stage 7.
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).