### Main Difference

Mathematics and Arithmetic are sometimes considered to be the same terms having same meaning but actually both are somehow different from each other. Basically Arithmetic is the branch of Mathematics. Mathematics is a broad term covering Arithmetic. Mathematics is defined in many ways as it has vast scope. Mathematics can be defined as the branch of science dealing with the study of measurements and properties of quantities using numbers, quantities, shapes, symbols, structures and geometry. Arithmetic can be defined as the branch of Mathematics dealing with the study of numbers, their properties and operations including basic operations of division, multiplication, addition and subtraction. One of the major differences between Mathematics and Arithmetic is that the Mathematics is about theories but Arithmetic is related to the calculations and numbers. Arithmetic is the simple calculation while mathematics is the cognition.

### What is Mathematics?

Mathematics is a broad term and is used in almost every field of life. Mathematics is considered as the basic fundamental of science. Mathematics can be defined as the branch of science dealing with the study of measurements and properties of quantities using numbers, quantities, shapes, symbols, structures and geometry. Mathematics includes proofs of theorems for its principles. Pure Mathematics and Applied Mathematics are its main branches. It is further categorized as Algebra, Arithmetic, Calculus, Geometry and Trigonometry. Scope of Mathematics is vast as compare to the Arithmetic. Basically Mathematics is the cognition.

### What is Arithmetic?

Arithmetic is the most old and fundamental sub division of Mathematics. It covers the basic calculations regarding the numbers. Arithmetic is the simple calculation or computational discipline. Arithmetic can be defined as the branch of Mathematics dealing with the study of numbers, their properties and operations including basic operations of division, multiplication, addition and subtraction. Thus division, multiplication, addition and subtraction are the four fundamental operations of Arithmetic. It deals with real numbers, integers, fractions, decimals and complex numbers. It also deals in power computation and root extraction.

### Key Differences

- Arithmetic is the branch of Mathematics.
- “Mathematics” can be defined as the branch of science dealing with the study of measurements and properties of quantities using numbers, quantities, shapes, symbols, structures and geometry while “Arithmetic” can be defined as the branch of Mathematics dealing with the study of numbers, their properties and operations including basic operations of division, multiplication, addition and subtraction.
- Scope of Mathematics is vast as compare to the Arithmetic.
- Mathematics deals with the geometry but Arithmetic does not.
- Mathematics deals with Calculus but Arithmetic does not.
- Mathematics deals with the trigonometry but Arithmetic does not.
- Mathematics deals with the Algebra but Arithmetic does not.
- Mathematics has its main branches of Pure Mathematics and Applied Mathematics but Arithmetic does not have such branches.
- Mathematics covers the scope of Arithmetic.
- Arithmetic is the most old and fundamental sub division of Mathematics.
- Proofs of theorems are included in Mathematics but Arithmetic is not much elaborated.
- Mathematics is about theories but Arithmetic is related to the calculations and numbers.
- Arithmetic is the simple calculation while mathematics is the cognition.
- Arithmetic is basically the building block of Mathematics.