Basics of Mathematics: Arithmetic, Geometry, Algebra & Words
The word mathematics means knowledge and it is learned as a language or skill and not as a subject. The basics of mathematics have four components such as arithmetic, geometry, algebra, and words. These components can be represented in everything that is learned in math.
Civilizations in China, India, and Egypt contributed to mathematics initially with the counting system being the first that was developed. After which mathematicians developed the basics of math i.e. arithmetic. Basic operations like addition, subtraction, multiplication, and division were developed which is the foundation of math. Over the years, when construction and fashion came into play, mathematicians started to develop the concept of geometry that deals with areas, volumes, and shapes. Algebra came into motion soon after a few years where mathematicians were solving linear equations.
Let us look at all four components in detail.
Arithmetic  Numbers and Operations
The word arithmetic was originated from the Greek word arithmos. It is a branch of mathematics that consists of the study of counting numbers and their properties. Arithmetic is a foundation of mathematics where we learn the most important aspects of arithmetic operations which are addition, subtraction, multiplication, and division. it also deals with advanced operations such as percentage, square roots, powers, exponents, trigonometric functions, and much more.
The main properties of arithmetic operations are  Commutative Property, Associative Property, Distributive Property, and Additive Identity. For the simplification of the arithmetic operations  addition, subtraction, multiplication, and division, the PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction) or BODMAS (Brackets, Exponents, Division, Multiplication, Addition, and Subtraction) rule is followed. For example  3 x 5 ÷ (9  2) is considered as an example for PEMDAS.
Geometry  Shapes
Geometry is considered the study of shapes where we can calculate the area, volume, lengths, widths, and much more. Geometry can into existence in the very beginning along with numbers in the form of diagrams and shapes. The study of shapes can be divided into two types  Plane Geometry and Solid Geometry. Plane Geometry deals with the study of 2D shapes such as squares, circles, triangles, etc. Whereas solid geometry deals with the study of 3D shapes such as cube, cone, sphere, etc.
Algebra  Expression and Equations
The branch of mathematics that deals with variables, numbers, and the representation of these variables is called algebra. This form of mathematics is used in our daytoday life. The study of algebra includes algebraic expressions where a combination of variables and constants are connected with the arithmetic operations  addition, subtraction, multiplication, and division to form an expression. An algebraic expression is defined by the sum, difference, product, and quotient of the constants and variables.
For example  5x + 1 is considered as an algebraic expression that contains the arithmetic operation  addition, variables, and constants.
Words  Mathematical Statement
Mathematical statements help in understanding the concepts better. The words used to define the different mathematical concepts simply for everyone to understand. Words also help in differentiating every concept from the other such as addition can be called as the sum, subtraction can be called as difference, the product can be related to multiplication, and quotient can be related to division. These words play an important role in understanding math better.
Related Topics
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Solved Examples

Example 1: Match the following words with the appropriate mathematical concept
Sum, difference, product, and quotient Geometry Area, Volume, and Perimeter Algebraic Expression Constants and Varibles Algebra 8 ÷ (4  8 x 9) PEMDAS 8x + 4 Arithmetic Solution:
Sum, difference, product, and quotient Arithmetic Area, Volume, and Perimeter Geometry Constants and Varibles Algebra 8 ÷ (4  8 x 9) PEMDAS 8x + 4 Algebraic Expression 
Example 2: Find the sum, difference, product, and quotient of these two numbers 32 and 60.
Solution: Let us find all 4 individually.
The word sum means addition. Hence, 32 + 60 = 92
The word difference means subtraction. Hence, 60  32 = 28
The word product means multiplication. Hence, 32 x 60 = 1920
The word quotient means division. Hence, 60 ÷ 32 = 1.875
Frequently Asked Questions (FAQs)
What are the Four Main Arithmetic Operations in Math?
The four main arithmetic operations in math are addition, subtraction, multiplication, and division. These four operations play as the base foundation in math that is learned at a very young age and are used in different aspects of mathematics. In real life, these operations are essential.
What are the Branches of Basic Mathematics?
Mathematics is not a subject but a language that is learned just like any other language like English or French. The main branches of basic mathematics are algebra, arithmetic, geometry, and words. These four branches are interlinked with each other.
How are the Arithmetic Operations Beneficial in Algebraic Expression?
Algebraic expressions deal with numbers and variables for solving problems. These expressions used to solve problems in daytoday life. The use of addition and subtraction proves to be beneficial in these expressions as it helps in defining the variable accurately. In the earlier days, people used to write words to express the operation.
What are the Basic Skills required for Geometry?
The basic skills required for geometry are visual skills, logical skills, and drawing skills. The skills used in geometry are very helpful in our daytoday life and help in problemsolving also. Students need to use the appropriate geometry materials such as a scale, protractor, compass, and a sharp pencil, to draw the basic geometric shapes like circles, triangles, and so on.
What is the Most Important Math Skill?
Mathematics is not only a subject but a skill that is thought to children at a young age. Students learn the basic arithmetic operations  addition, subtraction, multiplication, and division at the beginning of their journey which also marks as the base foundation for children that develops in the future. The most important skill in math is problemsolving that children develop over a period of time and enables them to also think analytically.
What is an Example of Mathematical Statements?
A mathematical statement is neither true nor false but should be descriptive in nature. For example, the square root of 6 is 9 which is false but the use of words in the statement makes it a mathematical statement. Maths as a subject is very precise but used differently for different situations.
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