# Which operation should be performed first according to the order of operations of 44-:2 + 9 - [120 - (5 + 10 *7)]?

Apr 8, 2016

First you have to multiply $10 \cdot 7$

#### Explanation:

When talking about order of operation the PEDMAS rule applies. According to this rule first you have to calculate everything which is in the most inner brackets.

In this expression you have 2 kinds of brackets, but it makes no difference how they look like because you only have to look at those which contain no other brackets, and they are $\left(5 + 10 \cdot 7\right)$

In those brackets you have 2 operations: addition and multiplication. According to PEDMAS rule you have to do multiplication first, then the addition, so you get:

$44 \div 2 + 9 - \left[120 - \left(5 + \textcolor{red}{10 \cdot 7}\right)\right] =$
$44 \div 2 + 9 - \left[120 - \left(\textcolor{red}{5 + 70}\right)\right] =$
$44 \div 2 + 9 - \left[\textcolor{red}{120 - 75}\right] =$
$\textcolor{red}{44 \div 2} + 9 - 45 =$
$\textcolor{red}{22 + 9} - 45 =$
$31 - 45 = - 14$

In every line the next operation is marked with the red color exept last line with only one operation (substraction $31 - 45$).

Jul 31, 2016

$- 14$

#### Explanation:

There is not actually only ONE operation which HAS to be done first!

There are three separate terms, so we can work in all three of them in the same line of working, because they are independent of each other.

In working with different operations in one calculation, it is important to count the number of TERMS first. Each term must simplify to a single value which are then added or subtracted in the LAST line.

Parentheses in a term need to be done first.
Work from most powerful to least powerful operations.
Calculations can be done within one term at each step.

color(magenta)(44div2)color(blue)(+9)color(green)( -[120-(5+color(red)(10xx7)])" " has 3 terms

color(magenta)(22)color(blue)(+9)color(green)( -[120-(5+color(red)70])

color(magenta)(22)color(blue)(+9)color(green)( -[120-color(red)((75))]

$\textcolor{m a \ge n t a}{22} \textcolor{b l u e}{+ 9} \textcolor{g r e e n}{- 45}$

=$- 14$