The number on the bottom of a fraction is called the denominator. The number on the top is called the numerator. The denominator is the number by which you are dividing the numerator. The line separating the numerator and denominator actually means "divided by." To divide is to split into equal parts.
In a fraction, you are actually separating the numerator into the number of equal parts designated by the denominator. You can take a cake and divide it into four equal pieces; each piece is ¼ of the whole cake. But you cannot take a cake and divide it into 0 pieces. Rod Pierce, editor of "Math is Fun," explains that you can take 12 pieces of gum and divide them equally by 3 friends, 12/3. Each friend will get four pieces. If you take the same 12 pieces of gum and attempt to divide them by 0 people, what will happen? That doesn't make sense. You can't share with 0 people, and you can't divide by zero, so it cannot function at the bottom of a fraction.
The number 1 can be represented with any number of fractions. Simply place the same number in the numerator as the denominator. For example, 3/3 is equal to one. This fraction, 3/3, can multiply times any number and give the same results as one times the number. Pierce suggests trying the same thing with zero. Place 0/0 and attempt to multiply it times another number, say 4. Right off you notice that it does not behave like a normal number, because any number times zero is zero: "0 X 4= 0." That is a problem because it leaves you with 0/0, not 4 as expected. With zero in the denominator, the fraction does not act like a normal number.
Math's greatest feature is its definitive answer. Four times two is always eight. That never changes. Two-thirds times three equals two, no matter how you work the problem. "2/3 X 3 = 2" is equivalent to "2 x 3/3 = 2" and results in the same answer. Imagine 0 was a defined denominator, presses Pierce. Multiply 1/0 times 0. What is the result? "0 x 1/0 = 0" Any number times zero equals zero. However, the equation that should be equivalent yields "0/0 X 1 = 1." This makes no sense; you can't get two different answers to equivalent problems. Math does not allow for duplicity, so zero at the bottom of a fraction is undefined.