Dividing By Zero: Definition & Concept

Instructor: Jennifer Beddoe
In mathematics, division by zero is undefined. Learn why according to the arithmetic and algebraic definitions of dividing by zero in this lesson. Then take a quiz to test your knowledge.

The Number Zero

Zero is the integer just before the number 1. It is an even number (-4, -2, 0, 2, 4) and is neither positive or negative. In fact, it's the only natural number (also called counting numbers) that is not positive. The value of the number zero is nothing.

History of the Number Zero

The use of zero as a number, and not just as empty space, is attributed to ancient India. The 9th-century Indians performed all mathematical calculations with zero and gave it the properties of a number instead of just treating it as a placeholder or not dealing with it at all as had been done in the past.

The ancient Greeks had mostly philosophical questions about zero. 'How can nothing be something?' This led to much discussion and religious arguments. By 130 AD, the Greeks had a symbol for zero and were using it in calculations regularly.

Dividing by Zero, Arithmetically Speaking

The basic definition of division is the breaking up of something into smaller parts. For example:

12/4 means dividing 12 into 4 equal parts.

For example, if there are 12 pieces of pizza and four people, each person would get 3 pieces of pizza.

However, if you try the same example with zero as the divisor, you end up with something that cannot be explained. Take the same 12 pieces of pizza, how many pieces would each person get if there were zero people? You can't evenly distribute 12 things to nobody. In mathematical terms, any number divided by zero is undefined.

12/0 = undefined

Any number divided by zero is undefined.

Dividing by Zero, Using Algebra

Algebraically speaking, division is the opposite of multiplication. Let's look at division by zero in these terms.

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