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.
Basic arithmetic info
Operations
Four basic operations:
Note: Division by 0 is not defined. Rounding is applied according to the selected decimal places.
Examples
Formulas & properties
Addition
(Commutative)
(a + b) + c = a + (b + c)
(Associative)
Subtraction
Not commutative
a − (b − c) ≠ (a − b) − c
Multiplication
(Commutative)
(a×b)×c = a×(b×c)
(Associative)
Division
Not commutative
a ÷ (b ÷ c) ≠ (a ÷ b) ÷ c
Neutral & inverse
a + (−a)=0
a×1=a
a×(1/a)=1 (a≠0)
Distributive
(b + c)×a=b×a + c×a
Sign rules
(−a)×(−b)=+ab
(+a)×(−b)=−ab
(−a)×(+b)=−ab
Fractions
(a/b)/(c/d)= a×d / (b×c)
Example calculation
Example: 11 + 4
Addition – sum of two positive numbers.
Example: 11 ÷ 4
Division – quotient obtained by partitioning the dividend.
Calculation steps (11 × 4)
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.