# Simplify the following expression: 101-{[(110 -: 2)-: 11]xx(10+4xx2) +7}+ [8xx(20 -: 5-1)-3xx3] -: 5?

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.

$101 - \left\{\left[\left(110 \div 2\right) \div 11\right] \times \left(10 + 4 \times 2\right) + 7\right\} + \left[8 \times \left(20 \div 5 - 1\right) - 3 \times 3\right] \div 5$

Before we dive into this thing, let's look at the structure - there is $101$ - big brackets + smaller brackets$\div 5$. 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:

$\left\{\left[\left(110 \div 2\right) \div 11\right] \times \left(10 + 4 \times 2\right) + 7\right\}$

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:

$\left\{\left[55 \div 11\right] \times \left(10 + 8\right) + 7\right\}$

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

$\left\{5 \times 18 + 7\right\}$

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

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

$101 - 97 + \left[8 \times \left(20 \div 5 - 1\right) - 3 \times 3\right] \div 5$

Let's now work that second bracket:

$\left[8 \times \left(20 \div 5 - 1\right) - 3 \times 3\right]$

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:

$\left[8 \times \left(4 - 1\right) - 3 \times 3\right]$

and now the subtraction:

$\left[8 \times 3 - 3 \times 3\right]$

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

$\left[24 - 9\right] = 15$

Let's substitute that into the original:

$101 - 97 + 15 \div 5$

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

$101 - 97 + 3$

and now the subtraction and addition:

$4 + 3 = 7$

Jul 31, 2016

=$\textcolor{m a \ge n t a}{101} \textcolor{g r e e n}{+ 3} \textcolor{b l u e}{- 87}$

=$7$

#### 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:

$\textcolor{m a \ge n t a}{101} \textcolor{b l u e}{- \left\{\left[\left(110 \div 2\right) \div 11\right] \times \left(10 + 4 \times 2\right) + 7\right\}} \textcolor{g r e e n}{+ \left[8 \times \left(20 \div 5 - 1\right) - 3 \times 3\right] \div 5}$

Let's handle one at a time.
The first is easy. it is $\textcolor{m a \ge n t a}{101}$.

$\textcolor{b l u e}{- \left\{\left[\textcolor{red}{\left(110 \div 2\right)} \div 11\right] \times \left(10 + \textcolor{red}{4 \times 2}\right) + 7\right\}}$

$\text{parentheses first, but remember to do the multiplication }$
$\text{and division before addition and subtraction}$

$\textcolor{b l u e}{- \left\{\left[\textcolor{red}{55} \div 11\right] \times \left(10 + \textcolor{red}{8}\right) + 7\right\}}$

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

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

Now for the third term:

$\textcolor{g r e e n}{+ \left[8 \times \left(20 \div 5 - 1\right) - 3 \times 3\right] \div 5}$

$\textcolor{g r e e n}{+ \left[8 \times \textcolor{red}{\left(20 \div 5 - 1\right)} - \textcolor{\mathmr{and} a n \ge}{3 \times 3}\right] \div 5}$

$\textcolor{g r e e n}{+ \left[8 \times \textcolor{red}{\left(4 - 1\right)} - \textcolor{\mathmr{and} a n \ge}{9}\right] \div 5}$

$\textcolor{g r e e n}{+ \left[8 \times \textcolor{red}{3} - \textcolor{\mathmr{and} a n \ge}{9}\right] \div 5}$

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

$+ \textcolor{g r e e n}{15 \div 5} = \textcolor{g r e e n}{3}$

the whole expression simplifies to
$\textcolor{m a \ge n t a}{101} \textcolor{b l u e}{- 97} \textcolor{g r e e n}{+ 3}$

=$\textcolor{m a \ge n t a}{101} \textcolor{g r e e n}{+ 3} \textcolor{b l u e}{- 97}$

=$7$