Division By Zero

Division by zero with any number is undefined. The word division means splitting something into equal parts or groups so that it is shared evenly among everyone. Whereas the value of zero as a number is nothing. It is placed before 1, is an even number that is neither positive nor negative. Let us learn more about division by zero and solve a few examples.

Division by zero is considered as undefined where zero is the denominator or the division and is expressed as a/0, a being a number or numerator or dividend. In other words, dividing zero with any number will always give us a zero not matter with multiplication or division. Since multiplication and division go hand in hand, the division of zero can also mean multiplying with zero. For example, 7/0 = x or 0 × x = 5. Here x has no value or number to complete the equation. Hence, division by zero of any number is undefined.

One divided by zero is also considered as undefined. According to mathematicians, any non-zero number either positive or negative divided by zero is undefined because there is no value. For instance, let us try to define 1/0. If we divide a non-zero number with a small positive number we do derive at a value. The small positive number is close to zero but not zero.

1/0.1 = 10 , 1/0.01 = 100, 1/0.000001 = 1000000

Hence, as we divide one by smaller and smaller positive numbers we get larger and larger positive numbers. Therefore, 1/0 = + infinity. When we divided negative numbers that are close to zero, we get:

1/-0.1 = -10 , 1/-0.01 = -100, 1/-0.000001 = -1000000

One divided by a negative number closer to zero brings in a different result that is closer to negative infinity. Therefore, 1/0 = -infinity. Hence, one divided by zero has no answer which results in being undefined.

Given below are some facts about division and zero.

• Any number divided by 1(the quotient equals the dividend), gives the answer the same as the dividend. In other words, 1 is the divisor and the quotient will be equal to the dividend. For examples: 25 ÷ 1 = 25.
• A number cannot be divided by 0 and the result is thus undefined. Example: 78 ÷ 0 = undefined (but 0 ÷ 78 = 0).
• When the dividend equals the divisor, which means the same numbers but not 0, then the answer is always 1. For examples: 36 ÷ 36 = 1.
• Zero is a real number, an integer, a rational number, and a whole number.
• Zero is always neutral i.e. zero is never written like +0 or -0.
• The power of any number that is raised by zero is always one.

Related Topics

Listed below are a few interesting topics related to division by zero. Take a look:

• Long Division
• Zero Property of Multiplication
• Division Formula
• Division of Fractions

What is Meant by Division By Zero?

Division by zero means when any non-zero, positive, or negative number is divided by zero the result is always undefined. For example 4/0 = infinity or undefined.

Can You Divide a Number By Zero?

Any number divided by zero is considered undefined. When we divide zero over 1 that equals zero, when we divide zero over zero its is equal to undefined, and when 1 is divided by zero it is equal to undefined.

Why Division By Zero is Not Possible?

Division by zero is not possible as there is no definite answer when any number is divided by zero. Hence, the result is undefined.

What is Division By Zero Called?

In mathematics, division by zero has no meaning since any number divided by zero is considered undefined. Multiplication and division go hand-in-hand and when a number is multiplied with zero the result is a zero itself. While in division, it is undefined. 

What is the Quotient of 0 Divided by 8?

The quotient of 0 divided by 8 is 0. 0 ÷ 8 = 0.