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# Multiplicative Identity|Definition & Meaning

## Definition

According to the concept of multiplicative identity, if a number is multiplied by 1, the outcome will be the original number. A number’s multiplicative identity is “1.”

Before exploring the concept of multiplicative identity let us first explore the **fundamental properties of numbers** and what is identity property. Commutative, associative, distributive, and identity are the four fundamental qualities that are deployed with numbers. As opposed to only individual numbers, these qualities apply to **groups** of numbers.

## Commutative Property

The term “**commutative**” originates from the term “**commute**,” which means “to move about.” Therefore, the “commutative feature” alludes to the ability to **rearrange** numbers within **numeric** sentences.

For instance, **adding** 2 and 3 results in the number 5, so if we rearrange the numbers such that 3 and 2 equal 5, we still obtain the correct answer. Likewise, the result of **multiplying** 6 by 4 is 24, just as the result of multiplying 4 by 6 is 24.

## Associative Property

According to the associative property, when you plus or multiply integers, it does not make a **difference** how you **group** the numbers.

This principle applies to **sequences** of integers that are enclosed in **brackets**. Calculations are enclosed in brackets if we require a person to carry out the **computation** in the bracket first.

When it comes to a collection of integers that require to be **added** together, it does not make a difference where the brackets are because the result will always be **similar**.

In a similar manner, when there is a set of integers that requires to be multiplied, the result will remain the same irrespective of the way the integers are put together.

## Distributive Property

The distributive property is a useful tool in mathematics that can be used to simplify difficult issues since it reduces **expressions** to either the **addition** or **subtraction** of two integers.

Under this property, if we multiply the sum of two integers by an integer, we will achieve a **similar** result as if we multiplied each integer by the number separately and then **added** the **products** together.

The distributive property teaches us how to **answer** statements of the following type **x (y + z)** by showing us how to multiply the integer directly outside the **parenthesis** with the numbers that are contained within the **brackets** and plus them into one.

Now, since the topic we are discussing here is multiplicative identity, let us first discuss what precisely is the identity property.

## Identity Property

An **integer** that you can multiply by, divide into, add to, subtract from, or divide into another number and not have its **identity altered** is referred to as an identity element. These actions do not alter the initial number. The other number is referred to as an identity element because the identity of the initial number is **preserved**.

## Identity Element

The identity elements are the following two numbers:

- Zero
- One

Varying operations make use of each of these above-mentioned **identity elements**. Use for the identity element **zero** is done in the following operations:

- Add
- Subtract

Use for the identity element **one** is done in the following operations

- Multiply
- Divide

## Multiplicative Identity

A mathematical notion known as “multiplicative identity” describes the **character** of a number being **identical** to itself whenever the number is multiplied by 1. To put in other words, multiplying an integer by one always results in the same result: the integer itself.

The term multiplicative identity is also referred to as the identity property of multiplication. Due to its use in numerous algebraic operations as well as its importance in **understanding** how integers respond when **multiplied**, this idea is crucial in **mathematics**.

## Zero as The Multiplicative Identity for All Non-Zero Numbers

The multiplicative identity of **zero **for all non-zero integers is one of the fundamental characteristics of the multiplication identity property. This indicates that any **nonzero **integer multiplied by zero would always give zero as an answer.

For instance, the outcome of 5 times 0 is **0**. Understanding this characteristic is **crucial **for us because it shows the way in which integers respond when they are multiplied by zero.

The fact that the number “**one**” is the multiplicative identity for every integer is another significant aspect of multiplicative identity. By extension, this indicates that multiplying any **integer **by 1 will always yield a **similar result**.

For instance, the result of multiplying 5 by 1 is **5**. It is crucial to comprehend this feature since it explains how one multiplies a number, which is a fundamental mathematical concept.

## Use of The Multiplicative Identity in Solving Equations

There are various **techniques** to solve equations using the multiplicative identity. **Eliminating** the **constant** that is multiplied by the equation’s variable is among the most popular applications of multiplicative identity in equation solving. As an illustration, think about the equation below:

3y = 9

The identity property of multiplication of **one-half** of the equation can be used to get rid of the constant of three that multiplies y and then solve the equation for y. To accomplish this, **divide** each side of the equation by three, as it is shown below.

3y / 3 = 9 / 3

That amounts to:

y = 3

In this manner, you can utilise the identity property of multiplication of one-half to find the answer of the variable y in the equation.

Eliminating constants that are **dividing** the equation’s **variable** would be another technique to solve equations using the identity property of multiplication. Take the equation below as an illustration:

y / 2 = 4

The identity property of multiplication of two can be used to get rid of the constant of two that is **dividing** y and then solve the equation for y. To achieve this, **multiply** each side of the equation by two as shown in the example below:

(y / 2) × 2 = 4 × 2

That amounts to:

y = 8

In this fashion, you may find the answer for the **variable** of y in the equation using the identity property of multiplication of two.

Thus, we can say that the multiplicative identity is a **helpful** technique for resolving equations since it gets rid of constants that are **multiplying** or **dividing** a particular equation’s variables. Equations can be made simpler, and the answer of a variable can be determined by utilizing the proper **multiplicative** identity.

In general, the identity property of multiplication is considered to be a core concept in the field of mathematics, with numerous applications in a variety of methods and areas. That perhaps is the reason why success in several mathematical disciplines depends on one’s ability to comprehend and use the multiplicative identity property.

## Example

Which of the following **mathematical Expressions** can be considered an Illustration of the **multiplicative** **identity**

1) 3 × 3 = 9

2) 3 × 1 = 3

3) 3 ÷ 3 =1

### Solution

Amongst the given expressions, **“3 × 1 = 3”** is an example of the multiplicative identity.

*All images/mathematical drawings were created with GeoGebra.*