# What is [7+(10-:5-9)]-9?

$- 9$

#### Explanation:

We can use PEMDAS:

• $\textcolor{red}{P}$ - Parentheses (also known as Brackets)
• $\textcolor{b l u e}{E}$ - Exponents
• $\textcolor{g r e e n}{M}$ - Multiplication
• $\textcolor{g r e e n}{D}$ - Division (this has the same weight as M and so I gave it the same colour)
• $\textcolor{b r o w n}{A}$ - Addition
• $\textcolor{b r o w n}{S}$ - Subtraction - (again, same weight as A and so the same colour)

$\left[7 + \left(10 \div 5 - 9\right)\right] - 9$

We first look for $\textcolor{red}{P}$:

color(red)([7+(10-:5-9)]

Inside this bracket is another one:

$\textcolor{red}{10 \div 5 - 9}$

We have two operations here - division and subtraction. See that $\textcolor{g r e e n}{D}$ comes before $\textcolor{b r o w n}{S}$:

$\textcolor{g r e e n}{10 \div 5} \textcolor{b r o w n}{- 9}$

$\textcolor{g r e e n}{2} \textcolor{b r o w n}{- 9}$

$\textcolor{b r o w n}{- 7}$

Since we now know that $\left(10 \div 5 - 9\right) = - 7$, we can substitute that back into the original:

$\left[7 + \left(10 \div 5 - 9\right)\right] - 9 = \left[7 + \left(- 7\right)\right] - 9$

What we have left is addition and subtraction, and so we work from left to right:

$\left[7 + \left(- 7\right)\right] - 9 = \left[0\right] - 9 = - 9$