# Difference Between Arithmetic and Mathematics

## Core difference

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

## What is mathematics?

Mathematics is a broad term and is used in almost all fields of life. Mathematics is considered the basic foundation of science. Mathematics can be defined as the branch of science that deals with the study of the 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. Also, it is classified as Algebra, Arithmetic, Calculus, Geometry and Trigonometry. The scope of mathematics is vast compared to arithmetic. Basically, math is cognition.

What is arithmetic?

Arithmetic is the oldest and most fundamental subdivision of mathematics. Covers basic calculations regarding numbers. Arithmetic is the simple calculation or computational discipline. Arithmetic can be defined as the branch of mathematics that deals with the study of numbers, their properties, and operations, including the basic operations of division, multiplication, addition, and subtraction. Thus, division, multiplication, addition and subtraction are the four fundamental operations of arithmetic. These are real numbers, integers, fractions, decimals, and complex numbers. It also deals with power calculation and root extraction.

## Key differences

1. Arithmetic is the branch of mathematics.
2. “Mathematics” can be defined as the branch of science that deals with the study of the measurements and properties of quantities using numbers, quantities, shapes, symbols, structures, and geometry, while “Arithmetic” can be defined as the branch of mathematics that deals with the study of numbers, their properties, and operations, including the basic operations of division, multiplication, addition, and subtraction.
3. The scope of mathematics is vast compared to arithmetic.
4. Mathematics deals with geometry, but arithmetic does not.
5. Mathematics deals with calculus, but arithmetic does not.
6. Mathematics deals with trigonometry, but arithmetic does not.
7. Mathematics deals with algebra, but arithmetic does not.
8. Mathematics has its main branches of Pure Mathematics and Applied Mathematics, but Arithmetic has no such branches.
9. Mathematics covers the realm of arithmetic.
10. Arithmetic is the oldest and most fundamental subdivision of mathematics.
11. Proofs of theorems are included in Mathematics, but Arithmetic is not very elaborate.
12. Mathematics is about theory, but arithmetic is about calculations and numbers.
13. Arithmetic is simple calculation, while mathematics is cognition.
14. Arithmetic is basically the building block of mathematics.