# The Order of Operations with Brackets

How would one go about answering something like

-8-(-2)[4-(-5)]?


The problem here really isn't very complicated once one is used to getting down the right direction and order. Which would I do first and how would I go about moving on and finding the answer?

## 2 Answers

With your example

\begin{align} -8-(-2)[4-(-5)] &= -8-(-2)[4+5]&\text{resolve innermost parentheses}\\ &=-8-(-2)\cdot 9&\text{perform addition to get rid of brackets}\\ &=-8-(-18)&\text{multiplication preceeds add/sub}\\ &=-8+18&\text{as in first step}\\ &=10.&\text{done. Or first note that this is 18-8.}\end{align}

• Thank you very much, Hagen! – Mike Wentworth Jan 30 '14 at 17:46

Never forget the order of operations:

1. Parentheses

2. Exponents

3. Multiplication / Division

4. Addition / Subtraction

In practice, this works out as such:

\begin{align} -8-(-2)(4-(-5)) &= -8-(-2)(4-(-5))\\ &= -8-(-2)(4+5)\\ &= -8-(-2)(9)\\ &= -8-(-18)\\ &= -8+18\\ &= 10 \end{align} Remember that the first step is always to evaluate what's inside the parentheses. The expressions surrounded by the most parentheses take precedence.