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- Definition
- Addition Operator (+)
- Example of the Addition Operator
- The Rules of Addition
- Subtraction Operator (-)
- Example of the Subtraction Operator
- The Rules of Subtraction
- Multiplication Operator (×)
- Example of the Multiplication Operator (×)
- The Rules of Multiplication
- Division Operator (÷)
- Example of the Division Operator (÷)
- The Rules of Division
- Significance of Operators
- Example

# Operator|Definition & Meaning

## Definition

The fundamental operations carried out on numbers and other mathematical objects are defined by math operators. The four fundamental operations in mathematics are addition, subtraction, multiplication, and division.

Mathematical problems contain **symbols** known as operators, each of which stands for an **operation** that must be performed. They **instruct** us on the action that should be carried out. All mathematical operations and procedures are built on **operators**, which can be thought of as the **fundamental** building blocks.

The operators reduce mathematics to the fundamentals that we make use of on a **daily basis**, regardless of whether or not we are aware of this fact. Following are the four fundamental operators used in mathematics.

- Addition
- Subtraction
- Multiplication
- Division

Let’s examine each of these four fundamental operators, including their **laws** and some **illustrations**, in further detail.

## Addition Operator (+)

The operator of addition is a mathematical operator that refers to the **process** of **combining** two or more **quantities**. The symbol for addition is a plus (+) sign, which indicates the operation of addition. The process entails integrating two or more **numerical** expressions into a single phrase.

When it comes to the addition operation, the order is irrelevant. This entails that the operation of adding is **commutative** in nature. It is possible for it to involve any kind of number, including **real** numbers, complex numbers, **fractions**, **decimals**, and so on.

## Example of the Addition Operator

We can illustrate the **addition** operator through the following example

5 + 6 = 11

The **summation** of numbers is another name for the operation of adding more than two **integers**, values, or elements, and it can involve any number from one to n number of terms.

## The Rules of Addition

Below is a list of the **rules** of addition that apply to **integers**.

- The result of adding two
**positive**numbers together is also a**positive** - The result of adding two
**negative**numbers together is another**negative** - When you are adding
**negative**and**positive**integers, you should first**minus**the integers and then utilise the sign of the integer number with the highest value.

## Subtraction Operator (-)

The difference among the two values can be determined by the use of the **subtraction** operator. The sign for subtraction is a **minus** sign, which looks like this (-). It is nearly identical to addition; however, it is the **inverse** of the second element. The operator works in the **opposite** direction of addition.

The concept of subtraction refers to the **process** of adding the **positive** number to the **negative number**. The **primary** goal of this method is to determine how many items are still available after others have been **eliminated**.

## Example of the Subtraction Operator

We can illustrate the **Subtraction** operator through the following example.

11 – 6 = 5

As discussed already, you can write the above expression in the following manner as well.

11 + (- 6) = 5

## The Rules of Subtraction

Below is a list of the **rules** of subtraction that apply to integers.

- If the signs of both of the numbers are
**positive**, then the result will be a**positive** - The result of any subtraction operation will be a
**negative**number if the signs of both of the numbers are**negative**. - In the case where the signs of the numbers are not the
**same**, minus the numbers, and then select the sign of the number that is**greater**among them.

## Multiplication Operator (×)

The operation of multiplication is equivalent to **adding** the same number together **repeatedly**. It is indicated by the symbol “×.” In addition to this, it can **combine** with any number of values to produce a single value.

The terms **multiplicand** and **multiplier** are involved in the multiplication operation. The **product** is the term used to refer to the end result that is obtained by multiplying the multiplicand with the multiplier.

## Example of the Multiplication Operator (×)

We can illustrate the **multiplication** operator through the following example.

3 × 4 = 12

In this case, the number “3” serves as the **multiplier,** whereas the number 4 serves as the **multiplicand**, while the result, “6,” is referred to as the **product** of the multiplication operation.

The outcome of multiplying two integers, denoted by ‘X’ and ‘Y,’ is a single value denoted by the term **‘XY,’ **in which ‘X’ and ‘Y’ are the factors of the resulting final value.

## The Rules of Multiplication

Below is a list of the **rules** of multiplication that apply to integers.

The **rules** for multiplying numbers are presented in the following paragraphs.

- A positive result is obtained when two
**positive**numbers are multiplied together. - A positive result is obtained when two
**negative**numbers are multiplied together. - A
**negative**result is obtained when a positive and a negative number are multiplied together.

## Division Operator (÷)

The operation of division, which is the **opposite** of multiplication, is typically represented by the symbol “÷.” It is composed of the two words **dividend** and **divisor**, with the dividend being the component that is divided by the divisor to produce the singular term value.

In case the dividend is higher than the divisor, then the quotient that is obtained is larger than 1, whereas if the divisor were higher, the **quotient** that is obtained is lower than 1.

## Example of the Division Operator (÷)

We can illustrate the **division **operator through the following example.

10 ÷ 5 = 2

In the above equation, “10” represents the dividend, “5” represents the divisor, and the outcome, “2,” is referred to as the quotient.

## The Rules of Division

Below is a list of the rules of division that apply to integers.

- The result of dividing a positive number by another positive number is also a
**positive** - If you divide two negative numbers together, you will get a
**positive**number - If you divide integers that have opposite signs from each other, you will get a
**negative**

## Significance of Operators

The use of operators, such as addition (+), Subtraction (-), multiplication (×), and division (÷), is a necessary component in the development of more **complicated** mathematical calculations and **algorithms**. They are utilized in a wide variety of disciplines, including the realms of **economics**, **engineering**, and **computer science**, to carry out fundamental calculations.

In addition, they are utilized in activities that are part of everyday living, such as determining how much of a tip to leave at a hotel or balancing a **checkbook**. For more sophisticated mathematical and **computational** tasks, it is vital to have a solid understanding of and facility with these fundamental **operators**.

## Example

Solve the following statements using mathematical operators.

- James purchased
**5 more**apples after having**6 already**. How many apples does James have now? - Of the total apples James had, he
**gave 3**to john. How many apples are left with James?

### Solution

According to the data given in statement (a):

Total apples James has = 6 + 5

**Total apples James has = 11**

Now, as mentioned in statement (b), James gave 3 apples to John. Thus:

Total apples left with James = 11 – 3

**Total apples left with James = 8**

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