Basic arithmetic

Addition, subtraction, multiplication and division with real numbers

Basic arithmetic calculator

What is calculated?

This calculator performs a single operation between two real operands. Supported operations are addition (+), subtraction (−), multiplication (×), division (/) with optional rounding to a chosen number of decimal places.

Inputs
Result
Calculation: Expression = Operand1 (Operator) Operand2

Basic arithmetic info

Operations

Four basic operations:

Addition Subtraction Multiplication Division

Note: Division by 0 is not defined. Rounding is applied according to the selected decimal places.

Examples
Addition: 11 + 4 = 15
Subtraction: 11 − 4 = 7
Multiplication: 11 × 4 = 44
Division: 11 ÷ 4 = 2.75

Formulas & properties

Addition
a + b = b + a
(Commutative)
(a + b) + c = a + (b + c)
(Associative)
Subtraction
a − b ≠ b − a
Not commutative
a − (b − c) ≠ (a − b) − c
Multiplication
a × b = b × a
(Commutative)
(a×b)×c = a×(b×c)
(Associative)
Division
a ÷ b ≠ b ÷ a
Not commutative
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Neutral & inverse
a + 0 = a
a + (−a)=0
a×1=a
a×(1/a)=1 (a≠0)
Distributive
a×(b + c)=a×b + a×c
(b + c)×a=b×a + c×a
Sign rules
(+a)×(+b)=+ab
(−a)×(−b)=+ab
(+a)×(−b)=−ab
(−a)×(+b)=−ab
Fractions
a/b = a×1/b
(a/b)/(c/d)= a×d / (b×c)

Example calculation

Example: 11 + 4
11 + 4 = 15

Addition – sum of two positive numbers.

Example: 11 ÷ 4
11 ÷ 4 = 2.75

Division – quotient obtained by partitioning the dividend.

Calculation steps (11 × 4)
1. Repeated addition
2. 11 + 11 = 22
3. 22 + 11 = 33
4. 33 + 11 = 44

Multiplication as shortened addition.

Applications

Basic arithmetic underpins nearly all areas of mathematics and engineering:

General mathematics
  • Algebraic transformations
  • Fractions & percent calculations
  • Linear equations
  • Polynomial arithmetic
Computer science & engineering
  • Number encoding & bits
  • Algorithms & loops
  • Simulation & modeling
  • Signal processing
Education
  • Number sense
  • Calculation fluency
  • Mathematical thinking
  • Error analysis
Everyday & business
  • Budgeting & planning
  • Financial calculations
  • Consumption & statistics
  • Unit conversions

Mathematical context

Description

The four basic arithmetic operations form the foundation of arithmetic. Addition and multiplication are commutative and associative, whereas subtraction and division are not. Multiplication distributes over addition. Division by zero is undefined. In higher areas (e.g. algebra, analysis, number theory) these operations are extended and structurally generalized (groups, rings, fields).

Summary

Basic arithmetic connects elementary computation with universal laws. Their rules (commutativity, associativity, distributivity) are cornerstones for complex mathematical structures and applications in science, engineering and computer science.