Since Mathematics

Since Mathematics is a language, I like to compare it to learning to read and write a foreign language:

Arithmetic = learning the alphabet

Algebra = starting to understand how the alphabet comes together in the new language

Geometry = putting words together

Trigonometry = making and understanding some sentences and phrases

Calculus = speaking and understanding the language.

One can do arithmetic without doing algebra:

1+1 = x

but one cannot do algebra without doing arithmetic:

solve for x: x+1 = 2

Algebra is about manipulating symbols and numbers using arithmetic to discover the value of the symbols. An arithmetic equation has all of the algebra worked out!

Arithmetic doesn't have any variables

Ex. 5+3=8

Algebra is full of variables

Ex. 5x +2 = 6

ARITHMETIC - A branch of mathematics usually concerned with the four operations (adding, subtracting, multiplication and division) of positive numbers.

eg:- 2+2=4, 3-2=1, 5*5=25, 49/7=7.

Arithmetic or arithmetics (from the Greek word αριθμός = number) is the oldest and most elementary branch of mathematics, used by almost everyone, for tasks ranging from simple day-to-day counting to advanced science and business calculations. In common usage, the word refers to a branch of (or the forerunner of) mathematics which records elementary properties of certain operations on numbers. Professional mathematicians sometimes use the term (higher) arithmetic when referring to number theory, but this should not be confused with elementary arithmetic.

Basic arithmetic addressing the four operations with integers, rational and real numbers and including measurement, geometry and base ten.

ALGEBRA - Algebra is the branch of mathematics that uses letters, symbols, and/or characters to represent numbers and express mathematical relationships. Those symbols are called variables.

eg:- 5m+6m=11m.

Algebra is a branch of mathematics concerning the study of structure, relation and quantity. The name is derived from the treatise written by the Persian[1] mathematician, astronomer, astrologer and geographer, Muhammad bin Mūsā al-Khwārizmī titled (in Arabic الكتاب الجبر والمقابلة ) Al-Kitab al-Jabr wa-l-Muqabala (meaning "The Compendious Book on Calculation by Completion and Balancing"), which provided symbolic operations for the systematic solution of linear and quadratic equations.

Together with geometry, analysis, combinatorics, and number theory, algebra is one of the main branches of mathematics. Elementary algebra is often part of the curriculum in secondary education and provides an introduction to the basic ideas of algebra, including effects of adding and multiplying numbers, the concept of variables, definition of polynomials, along with factorization and determining their roots.

Algebra is much broader than elementary algebra and can be generalized. In addition to working directly with numbers, algebra covers working with symbols, variables, and set elements. Addition and multiplication are viewed as general operations, and their precise definitions lead to structures such as groups, rings and fields.

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