What are the four basic arithmetic operations?

The four basic arithmetic operations are addition, subtraction, multiplication, and division. Addition combines quantities, subtraction finds the difference, multiplication is repeated addition, and division splits a quantity into equal parts or groups.

Does this calculator respect the order of operations?

Yes. In the expression mode, the calculator follows the standard order of operations: parentheses first, then multiplication and division, and finally addition and subtraction, evaluated from left to right within each level.

Can I use negative numbers and decimals?

You can enter both negative numbers and decimals in all fields, for example −3.5, 0.25, or 12.75. In the expression mode, you can use the minus sign either as a subtraction operator or as a sign for a negative number.

What happens if I divide by zero?

Division by zero is undefined in arithmetic. If you try to divide by zero, the calculator will warn you and will not produce a numerical result.

How can I move from basic arithmetic to more advanced topics?

Once you are confident with basic operations and the order of operations, you can move on to topics such as fractions, exponents, percentage error, remainder and modular arithmetic, prime factorization, and algebraic expressions. Those concepts build directly on basic arithmetic.

Basic Arithmetic Calculator – Add, Subtract, Multiply, Divide

Quickly perform the four basic arithmetic operations on two numbers or on a full expression. The tool supports whole numbers, decimals, negative values, standard order of operations, and shows clear, step-by-step explanations.

The four basic arithmetic operations

Arithmetic is the branch of mathematics that deals with numbers and the simplest operations we perform on them. The four basic operations are:

Addition ( + ) – combine quantities.
Subtraction ( − ) – find the difference between quantities.
Multiplication ( × ) – repeated addition of equal groups.
Division ( ÷ ) – sharing or splitting into equal groups.

Examples

Addition: \( 7 + 3 = 10 \)
Subtraction: \( 7 - 3 = 4 \)
Multiplication: \( 7 \times 3 = 21 \)
Division: \( 21 \div 3 = 7 \)

Order of operations (PEMDAS / BODMAS)

When an expression contains several operations, we must respect a standard order so that everyone gets the same result. A common mnemonic is PEMDAS:

P – Parentheses first.
E – Exponents (powers and roots).
MD – Multiplication and Division, from left to right.
AS – Addition and Subtraction, from left to right.

The expression calculator on this page follows this order. For example:

\[ 7 + 3 \times 2 = 7 + (3 \times 2) = 7 + 6 = 13, \] not 20.

Working with negative numbers and decimals

Arithmetic extends naturally beyond positive whole numbers:

Negative numbers represent quantities below zero (for example, debts or temperatures below freezing).
Decimals represent parts of a unit (for example, 0.5 as one half, 2.75 as two and three quarters).

The calculator accepts values like \(-3.5\), \(0.25\), or \(12.75\) in all fields and applies the usual rules—for example:

\((-3) + 5 = 2\)
\((-3) - 5 = -8\)
\((-3) \times 5 = -15\)
\((-15) \div 5 = -3\)

Checking your work with remainder and percentage error

Basic arithmetic is the foundation for more advanced tools:

Use the Remainder Calculator to see the quotient and remainder of a division and to understand division in more depth.
Use the Percent Error Calculator to compare a measured value with a reference value and quantify how accurate your arithmetic or experiments are.
Use Prime Factorization and GCF to simplify fractions and check mental calculations.

From basic arithmetic to algebra

Once you are comfortable with numbers and operations, the next step is to replace numbers with variables (letters like \(x\), \(y\)) and work with algebraic expressions. All the rules you learn in arithmetic carry over:

Adding like terms behaves like adding numbers.
Multiplication distributes over addition (for example, \(a(b + c) = ab + ac\)).
Division connects to fractions and rational expressions.

You can experiment with more advanced tools such as the Algebra Calculator or the Geometric Sequence Calculator once the basics feel solid.

Basic Arithmetic Calculator

Perform a basic arithmetic operation

Result

Expression result

The four basic arithmetic operations

Order of operations (PEMDAS / BODMAS)

Working with negative numbers and decimals

Checking your work with remainder and percentage error

From basic arithmetic to algebra

Related Core Math & Algebra tools