# The four operations

The four arithmetic operations are addition, subtraction, multiplication and division.

Addition ($$+$$) gives the **sum** of two numbers.

Subtraction ($$-$$) gives the **difference**. Order matters.

$$$\Tblue{10}-\Tgreen{3}=7,\qquad \Tgreen{3}-\Tblue{10}=-7 = -(\Tblue{10}-\Tgreen{3}).$$$

Addition and subtraction are inverse operations. In other words, adding a number $$B$$ to a number $$A$$ and then subtracting the number $$B$$ from the sum will yield the original number $$A$$.

$$$ (\Tgreen{18} - \Tblue{15}) + \Tblue{15} = 3 + \Tblue{15} = \Tgreen{18}.$$$ Multiplication ($$\times$$) gives the **product** of two numbers.

$$$\Tgreen{5} \times \Tblue{3} = \Tblue{3} \times \Tgreen{5} = 15.$$$

Division ($$\div$$) gives the **quotient** of two numbers. Order matters.

It is impossible to divide by zero.

Multiplication and division are **inverse operations**. In other words, multiplying a number $$A$$ by another number $$B$$ and then dividing the product by the number $$B$$ will yield the original number $$A$$.