Operations with Brackets

Using the rules for order of operations, anything in brackets is calculated first. If there are brackets inside other brackets then the inner brackets are calculated first, then the outer brackets.

Example 1      $(3+2)\times 4$

Here the expression in the brackets is calculated first, then the multiplication: $$\begin{align*} {\color{red}{(3+2)}}\times 4&={\color{red}{5}}\times 4\\ &=20 \end{align*}$$

Example 2      $50-(3+2)\times 4$

In this case we first calculate the expression in the brackets, then complete the multiplication and finally the subtraction: $$\begin{align*} 50-{\color{red}{(3+2)}}\times 4&=50 -{\color{blue}{ {\color{red}{5}} \times 4}}\\&=50-{\color{blue}{20}}\\&=30 \end{align*}$$

Example 3      $60-\left(3+(70\div 10)\right)-2$

For this example we evaluate the inner brackets first, then the remaining brackets, and finally subtraction from left to right: $$\begin{align*}60-\left(3+{\color{red}{(70\div 10)}}\right)-2&= 60-{\color{blue}{(3+{\color{red}{7}})}}-2\\ &=60-{\color{blue}{10}}-2\\ &=48 \end{align*}$$

Think you understand these examples? Try these questions to test your understanding.