Four operations, one number system.
Arithmetic studies how numbers combine and how quantities change. Four basic operations form the foundation for much of the mathematics you will encounter later.
Addition
Combines quantities to find their total. Example: 8 + 4 = 12.
Subtraction
Finds a difference or the amount remaining. Example: 12 − 4 = 8.
Multiplication
Represents repeated equal groups. Example: 3 × 4 = 12.
Division
Splits a quantity into equal groups. Example: 12 ÷ 3 = 4.
These operations are connected. Multiplication can be viewed as repeated addition, while division can reverse multiplication when the division is exact.
Understanding those connections helps you estimate answers, spot mistakes, and choose an efficient way to calculate.
The order of operations matters.
When an expression contains several operations, you need a consistent order. A common convention is to evaluate parentheses first, then powers, then multiplication and division from left to right, and finally addition and subtraction from left to right.
Do not simply calculate every operation from left to right.
6 + 2 × 5Multiplication takes priority over addition.
6 + 10The final answer is twelve.
6 + 10 = 16Correction to watch for: the worked example above should end with 16, because \(6 + 10 = 16\). This is a useful reminder to check every step instead of memorising a result.
Explore the operations yourself.
Choose an operation and enter two numbers. Watch how the result and calculation change. Try negative numbers and decimals, too.
Arithmetic explorer
A simple live calculator that shows the expression and explains the selected operation.
Put your reasoning to work.
Try these questions without using the calculator first. Use a hint if you need help choosing the right operation.
Calculate: 9 + 6
Enter your answer.
Take the next step.
Arithmetic provides the foundation for fractions, geometry, algebra, and more advanced mathematics. Practise until the operations feel natural, then move on to expressions that contain unknown values.