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Division: Help & Review9 chapters | 48 lessons

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.

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.

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.

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**.

Any number divided by zero is undefined.

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

When you think about it, there is no number you can substitute for A that will make this a true statement. There is nothing that when multiplied to zero will equal 5 (or any other number, for that matter).

Therefore, the answer to any equation where a number is divided by zero is undefined.

This is also true for algebraic expressions.

For example:

(x-5)/0 would be undefined

or

Solve (x + 2)/(x - 7)

For this expression, x would be undefined at 7 because if x were equal to 7, the denominator would be zero and therefore undefined.

Zero is the number that doesn't quite act like any other number. Its value is nothing, but it's more than a place holder. If you divide any number by zero, the answer you get is undefined. That is because you can't divide anything into zero parts.

You should have the ability to do the following after this lesson:

- Describe the history of the number zero
- Explain why division by zero is undefined, both arithmetically and algebraically

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Division: Help & Review9 chapters | 48 lessons

- What are the Different Types of Numbers? 6:56
- How to Perform Division: Steps & Examples 3:56
- Performing Long Division with Large Numbers: Steps and Examples 9:12
- Dividing By Zero: Definition & Concept
- Quotient: Definition & Meaning 3:23
- Remainder in Math: Definition & Example 5:30
- Go to Introduction to Division: Help & Review

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