Table of Contents

## What is Multiplication by Zero?

Multiplication by zero is a mathematical operation that produces the result of zero. When multiplying any number by zero, the result is always zero.

## Fundamental Properties of Zero

Zero is a number that has unique and fundamental properties. It is the only number that is both additive and multiplicative identity. Additive identity means that when zero is added to any number, the result is the original number. For example, 5 + 0 = 5 and 9 – 3 = 6. Multiplicative identity means that when zero is multiplied by any number, the result is the original number. For example, 2 x 0 = 2 and 3 ÷ 0 = 3.

Zero is also the only number that is both a perfect square and a perfect cube. A perfect square is a number that is the result of multiplying a number by itself. For example, 4 is a perfect square because 4 x 4 = 16. A perfect cube is a number that is the result of multiplying a number by itself three times. For example, 8 is a perfect cube because 8 x 8 x 8 = 512.

Another unique property of zero is that it is the only number that is neither positive nor negative. Positive numbers are numbers that are greater than zero, while negative numbers are numbers that are less than zero. Zero is the only number that is located in the middle of the number line, between the positive and negative numbers.

## Ways to Represent Multiplication

There are a few ways to represent multiplication. One way is to use the multiplication symbol, which is an asterisk (*). Another way is to use parentheses, such as (2×3), to show that the parentheses represent multiplication. Another way is to use the dot operator, which is a period (.). The dot operator is most commonly used when working with fractions.

## Division of Zero

A division of zero is an undefined operation in mathematics. This means that the result of dividing two numbers by zero is not a number, but rather a symbol that represents an undefined mathematical operation.

## Dividing With Zero

When dividing by zero, the result is undefined. This means that the answer cannot be determined because there is no known value that could be produced.

## on Zero Property of Multiplication

For all real numbers a, b, and c,

a(b + c) = ab + ac.