Question

How do you simplify `-8 - 81 / 9 times 2^2 + 7` using PEMDAS?

Answer 1

`-37` See explanation

Explanation:

We must solve the expression in the PEMDAS order. There isn't any parentheses, but there is an exponent: `2^2=4`

`-8-81/9*4+7`

Next is multiplication: `81/9*4=9*4=36`

`-8-36+7`

We've also taken care of the division. Next up is addition: `-36+7=-29`

`-8-29`

From here, it's simple subtraction: `-8-29=-37`

Answer 2

`-37`

Explanation:

Rather than just implementing PEDMAS blindly, first we need to realise that not all operations are equally strong.

The MOST powerful operations are powers and roots - they are done first. (These are the exponents)

Multiplication and division are the next strongest, while addition and subtraction are the LEAST important and are usually done LAST.

However if we want to change the normal order, we use parentheses to indicate this.

Count the number of TERMS first. Work with each term to get to a final answer.
In the last step all the answers are added or subtracted.

`color(magenta)(-8)color(blue)(-81/9*2^2)color(orange)(+7) " there are 3 terms"`

`color(magenta)(-8)color(blue)(-9*4)color(orange)(+7)`

`color(magenta)(-8)color(blue)(-36)color(orange)(+7)`

=`-37`