Division is by zero is undefined.

8 ÷ 8 = 1. Another way to state this is: 1 x 8 = 8

8 ÷ 4 = 2. Another way to state this is: 2 x 4 = 8

8 ÷ 2 = 4. Another way to state this is: 4 x 2 = 8

8 ÷ 1 = 8. Another way to state this is: 8 x 1 = 8

8 ÷ 0 = ?. Another way to state this is: ? x 0 = 8

Since there is no number that can be multiplied by zero to get eight, ? is given the label undefined.

Given: You have 8 blocks and would like to separate them into equal groups.

8 ÷ 8 = 1: To separate eight blocks into eight equal groups, there must be one block in each group.

8 ÷ 4 = 2: To separate eight blocks into four equal groups, there must be two blocks in each group.

8 ÷ 2 = 4: To separate eight blocks into two equal groups, there must be four blocks in each group.

8 ÷ 0 = ?: To separate eight blocks into zero equal groups, how many blocks must be in each group?

There isn't a number that makes a solution to this question possible, therefore 8 ÷ 0 = Undefined

Observe what happens when a number (eight) is divided by POSITIVE numbers that get closer and closer to zero, and also observe what happens when the same number (eight) is divided by NEGATIVE numbers that get closer and closer to zero.

Recall that when one number is left of a second number on a number line, the first number is less than the second number. [MORE: (Comparision of number positions on a number line to number magnitudes)]

When the divisor is POSITIVE and gets closer to zero, the result gets LARGER and LARGER.

When the divisor is NEGATIVE and gets closer to zero, the result gets SMALLER and SMALLER.

When presented with an expression that has division by zero, we say that the result is undefined as we don't know whether the result is infinitely large or infinitely small.