Question

Simplify the following expression: `101-{[(110 -: 2)-: 11]xx(10+4xx2) +7}+ [8xx(20 -: 5-1)-3xx3] -: 5`?

Answer 1

Take your time and methodically go through each bracket and you'll eventually get to `7`

Explanation:

Wow... that's one big equation. Let's take this step by step.

First we'll start with the original:

`101-{[(110-:2)-:11]xx(10+4xx2)+7}+[8xx(20-:5-1)-3xx3]-:5`

Before we dive into this thing, let's look at the structure - there is `101` - big brackets + smaller brackets`-:5`. PEDMAS has us work things in brackets (Parentheses) first and since the big brackets and the smaller brackets are separated by the `+`, we can work them separately. I'm going to simplify the big brackets first:

`{[(110-:2)-:11]xx(10+4xx2)+7}`

There are brackets (and brackets within brackets) in this, so I'm going to work those first. There are 2 sets here and I'll work them side by side. In this first step, let's do the division and in the second set we have both addition and multiplication - so we'll do the multiplication first:

`{[55-:11]xx(10+8)+7}`

I can now do the next division in the first bracket and do the addition in the second:

`{5xx18+7}`

We'll finish this up with the multiplication first, then the addition:

`90+7=97` which I'll substitute back into our original:

`101-97+[8xx(20-:5-1)-3xx3]-:5`

Let's now work that second bracket:

`[8xx(20-:5-1)-3xx3]`

There's a bracket in here that we need to work first. Within that bracket there is both division and subtraction - we'll divide first:

`[8xx(4-1)-3xx3]`

and now the subtraction:

`[8xx3-3xx3]`

We now have 2 multiplications and a subtraction, so we'll do the multiplications first:

`[24-9]=15`

Let's substitute that into the original:

`101-97+15-:5`

Almost there! We have subtraction, addition, and division. We'll do the division first:

`101-97+3`

and now the subtraction and addition:

`4+3=7`

Answer 2

=`color(magenta)(101)color(green)(+3)color(blue)(-87)`

=`7`

Explanation:

Count the number of terms and work through each one carefully.
Each term must give a number answer.

There are only 3 terms in this expression:

`color(magenta)(101)color(blue)(-{[(110-:2)-:11]xx(10+4xx2)+7})color(green)(+[8xx(20-:5-1)-3xx3]-:5)`

Let's handle one at a time.
The first is easy. it is `color(magenta)(101)`.

`color(blue)(-{[color(red)((110-:2))-:11]xx(10+color(red)(4xx2))+7})`

`"parentheses first, but remember to do the multiplication "`
`"and division before addition and subtraction"`

`color(blue)(-{[color(red)(55)-:11]xx(10+color(red)(8))+7})`

`color(blue)(-{[color(red)(5]xx(color(red)(18))+7})`

`color(blue)(-[color(red)(90+7)] = -97`

Now for the third term:

`color(green)(+[8xx(20-:5-1)-3xx3]-:5)`

`color(green)(+[8xxcolor(red)((20-:5-1))-color(orange)(3xx3)]-:5)`

`color(green)(+[8xxcolor(red)((4-1))-color(orange)(9)]-:5)`

`color(green)(+[8xxcolor(red)(3)-color(orange)(9)]-:5)`

`+[color(red)(24)-color(orange)(9)]-:5)`

`+color(green)(15-:5) = color(green)3`

the whole expression simplifies to
`color(magenta)(101)color(blue)(-97)color(green)(+3)`

=`color(magenta)(101)color(green)(+3)color(blue)(-97)`

=`7`