# How do you evaluate 4(8-(4*2))+1?

May 13, 2017

$4 \left(8 - \left(4 \times 2\right)\right) + 1 = 1$

#### Explanation:

In a calculation with different operations, they have to be done in a specific order, given by the acronym BODMAS, PEDMAS, or similar.

There are 2 terms. Each term must be simplified to a single answer which are added in the last step.

$\textcolor{g r e e n}{4 \left(8 - \left(4 \times 2\right)\right)} \textcolor{b l u e}{+ 1}$

Within each term, brackets must be done first, then the powers and roots, and then multiplication and division.

$\textcolor{g r e e n}{4 \left(8 - \left(4 \times 2\right)\right)} \textcolor{b l u e}{+ 1}$

There are 2 sets of brackets - start with the inner one.

4(8-color(red)((4xx2))color(blue)(+1)
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots .} \downarrow$
$= 4 \left(\textcolor{red}{8 - 8}\right) \textcolor{b l u e}{+ 1}$
$\textcolor{w h i t e}{\ldots \ldots l . .} \downarrow$
$= \textcolor{red}{4 \times 0} \textcolor{b l u e}{+ 1}$
$\textcolor{w h i t e}{\ldots \ldots .} \downarrow$
$= \text{ } \textcolor{red}{0} \textcolor{b l u e}{+ 1}$

$= 1$

Notice that there is nothing to be done with the last term $\left(+ 1\right)$.
It is just carried down with each line until the last step where it is added.