Mathematics# Distributive property

## What is distributive property?

## What is distributive property for?

## History

## Distributive property of the sum

## Of the division

## Of multiplication

## Radication

## Potentiation

## Examples

**Distributive property** is a very deep mathematical principle that helps mathematics work. It is the rule that allows you to expand the parentheses, so it is very important to understand if you want to be good at simplifying math additions. It is a term widely used in the field of algebra. The distributive property is a property of multiplication that is applied to additions and subtractions. This characteristic tells us that two or more terms found in an addition or subtraction are equal to the addition or subtraction of the multiplication of each of the terms of the addition or subtraction by the number. To understand the distributive property, we can say that it is a digit multiplied by the sum of two summands which is identical to the sum of the products of each of the summands by that number.

**Related topics**

**Distributive property** is a **mathematical** property that can be applied to additions and subtractions. It is the multiplication of a number by an addition equal to the **sum** of the multiplications of that number by each of the **summands**.

The **distributive property** of **multiplication** is a very useful property that allows you to **simplify** expressions in which you are multiplying a number by a sum or difference. The distributive property of multiplication over addition can be used when you multiply a number by an addition. The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can **subtract** the numbers and then **multiply** them, or you can **multiply** and then **subtract**. This is known as *“distributing the multiplier”*.

**Properties** have always been present in **mathematics** and have probably been used since **antiquity**; for example, any method of multiplying digit by digit uses the **distributive** property. But it is important to ask who first recognized these properties worldwide. Then, it is known that the term arose in the early 1800s, when mathematicians began to **analyze** different types of more abstract objects than numbers, such as **quaternions** and their functions, and needed to talk about what the **properties of numbers** were. These properties were not carefully researched until **mathematics** reached a peak in its development, where properties that had previously been assumed had to be clearly discussed in order to make algebra rigorous and allow the study of alternative types of “algebra”.

It is important to remember that the **sum** is the **combination** of the values of two or more numbers in order to obtain a **total**. The distributive property is one of the mathematical laws related to addition and multiplication and tells us that the sum of two numbers multiplied by a third number is equal to the sum of each addition multiplied by the third number. This property can be represented as follows:

(a + b) x c = (axc) + (bxc)

This property can only be applied in division, only if the algebraic sum is found in the dividend and, each of the terms that form it, are divisible by the divisor. It is very important to point out that this mathematical Law only takes place within the division if the dividend is first broken down into equal parts. As a result, every division will lead us to the same quotient, whether it is done directly or by applying the distributive property, we choose to decompose the dividend into equal parts, in order to divide it each time by the divisor, and then add up their respective results.

The **distributive property** consists in **decomposing** one of the factors of multiplication in the addition or subtraction of two others and multiplying each part of this decomposition by the other factor and then, adding or subtracting the products, this will allow us to solve in a mental way and with greater comfort without altering the **result**.

When we refer to mathematics, the term **radication** is known as the operation performed to obtain the **root** of a figure or a number. In other words, radication is the process that, knowing the **index** and the **radicand**, allows us to find the root of a given number. This will be the figure that, when we manage to elevate it to the index, will give us the radicand as a result.

The **potentiation** is a term that is used when it is necessary to raise a number to a determined **potency**, this operation is carried out starting from a **base** and an **exponent**; this base is raised the exponent.

- 8 x (13 – 1) = 8 x 13 – 8 x 1 = 8 x 13 – 8
- 2 x (1 + 3) = 2 x 1 + 2 x 3 = 5
- 10 x (5 – 2) = 10 x 5 – 10 x 2 = 30

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Distributive property*. Recovered on 27 October, 2023, de Euston96: https://www.euston96.com/en/distributive-property/