Use adaptive quiz-based learning to study this topic faster and more effectively.

# 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 $A$.

$$(\Tgreen{18} - \Tblue{15}) + \Tblue{15} = 3 + \Tblue{15} = \Tgreen{18}.$$
Addition and subtraction can be visualised using a number line.

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.

$$\Tblue{24} \div \Tgreen{6} = 4,\qquad\displaystyle\Tgreen{6} \div \Tblue{24} = \frac{1}{4} = \frac{1}{\Tblue{24} \div \Tgreen{6}}.$$

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 $A$.

$$(\Tblue{18}\div \Tgreen{6}) \times \Tgreen{6} = 3\times \Tgreen{6} = \Tblue{18}.$$