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Arithmetic Expressions in Mathematics: Types, Operators, and Applications
Publish Date: 08 Aug, 2023
Table of Content
Arithmetic expressions are important concepts in mathematics and computer programming. It involves mathematical operations such as addition, subtraction, multiplication, and division are used to denote mathematical equations.
Arithmetic expressions are used in more than a few different fields, as well as in mathematics, physics, engineering, and computer programming. It is an important part of any programming language, and understanding how to use it is key to writing effective code.
In this article, we will explore the basics of arithmetic expressions, including their types, operators, and applications,
Arithmetic Expressions
The mathematical expression that uses numbers, variables, and operators is called an arithmetic expression. Addition, multiplication, subtraction, and, division are the basic operators of arithmetic expressions. It is the sub-type of arithmetic.
Types of Arithmetic Expressions
The arithmetic expressions have 3 basic types,
- Simple arithmetic expression
- Complex arithmetic expressions
- Numeric arithmetic expressions
To gain a better handle on this we explain all types briefly with examples.
Simple Arithmetic Expressions
The arithmetic expressions, which have only one or two numbers and one operator, are called simple arithmetic expressions.
Example:
- 8 + 10
- 5 × 3
- 10 / 9
Complex Arithmetic Expressions
The arithmetic expressions, which have more than one or two numbers or operators, are called complex arithmetic expressions.
Example:
- 5 × 3 + 8
- 25 / 6-1
Numeric and Algebraic Arithmetic Expressions
The arithmetic expressions, which are, involved only numbers and operators are called numeric arithmetic expressions. while algebraic expressions are involved with variables, numbers, and operators.
Example:
- Numeric: (10 + 5) / 3
- Algebraic: (a + b -3c)
Further, algebraic arithmetic expressions are classified into more types which are defined below in the table,
Types | Definition | Examples |
Monomial | The algebraic expression which contains only one term is known as a monomial expression. | 2x, 5x, -3y, |
Binomial | The algebraic expression which contains two terms is known as a binomial expression. | 2x+5y, 4x3-9y |
Trinomial | The algebraic expression which contains three terms is known as a trinomial expression. | 4x+3y-5z, |
Polynomial | The algebraic expression which contains two or more terms is known as a polynomial expression. | -4x4 + 5x3 + 6x2
|
Operators in Arithmetic Expressions
The arithmetic expressions used different operators to represent the mathematical operations. The fundamental operators are,
- Addition (+)
- Subtraction (-)
- Multiplication (×)
- Division (÷)
These operations are known as arithmetic operations.
Variables in Arithmetic Expressions
In arithmetic expressions, variables are symbols that signify unknown values, with normally used letters like x, y, and z. The context in which a variable occurs within an expression affects the value of that variable. The basis of a lot of contemporary mathematics and science is this straightforward idea.
Difference between Arithmetic Expressions and Equations
In mathematics, equations and expressions have various meanings. Let's attempt to understand why they differ. Arithmetic expressions are types of mathematical expressions that employ variables, integers, and operators to represent mathematical expressions.
The fundamental operators used in mathematical expressions are addition, multiplication, subtraction, and division. In contrast, the mathematical statement has an equal sign called an equation. To better grip it, have a look at the following table
Arithmetic Expressions | Equations |
Arithmetic has contained only one side limit | Equations have contained two sides limits (left and right) |
Arithmetic expressions cannot find the unknown variables | Equations find the value of unknown variables |
Does not have an equal sign | Have equal sign |
8+9 | 2x+3 = 7 |
Applications of Arithmetic Expressions
Arithmetic expressions are commonly used in many fields such as science, computer science, and engineering, to solve mathematical problems and many other daily life fields. We discuss here only some applications of this.
Financial calculation
We use arithmetic expressions in financial calculations. Such as making interest rates, loan returns, and investment returns.
Programming
Arithmetic expressions are us in programming to control the flow of operations.
Examples of Arithmetic Expressions
To grasp this concept more fully let’s solve some examples of arithmetic expressions. These examples determine the step-by-step process of solving arithmetic expressions, considering the order of operations (parentheses, multiplication/division, and addition/ subtraction).
Example 1:
Solve the given arithmetic expression (20 + 13) – 15 × 15 / 5.
Solution:
Step 1:
Multiplication
15 × 15 = 225
Step 2:
Division
225 / 5 = 45
Step 3:
Addition
20 + 13 = 33
Step 4:
Subtraction
33 – 45 = -12
Therefore, the result of the arithmetic expression (20 + 13) – 15 × 15 / 5 = -12
Example 2:
Solve the given arithmetic expression (5 + 5) × (8 -2) / 6
Solution:
Step 1:
Addition
5 + 5 = 10
Step 2:
Subtraction
8 – 2 = 6
Step 3:
Multiplication
10 × 6 = 60
Step 4:
Division
60 / 6 = 10
Therefore, the result of the arithmetic expression (5 + 5) × (8 -2) / 6 = 10
Example 3:
Solve the given expression 45 / 5 + 3 × 4 – 7.
Solution:
Step 1:
Division
45 / 5 = 9
Step 2:
Multiplication:
3 × 4 = 12
Step 3:
Addition
9 + 12 = 21
Step 4:
Subtraction
21– 7 = 14
Therefore, the result of the arithmetic expression is 45 / 5 + 3 × 4 – 7. = 14
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