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

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

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Answer 1 · 2016-05-27T12:27:30

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

Explanation:

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

First we'll start with the original:

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

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

${[(110 \div 2) \div 11] \times (10 + 4 \times 2) + 7}$ ${[(110-:2)-:11]xx(10+4xx2)+7}$

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:

${[55 \div 11] \times (10 + 8) + 7}$ ${[55-:11]xx(10+8)+7}$

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

${5 \times 18 + 7}$ ${5xx18+7}$

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

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

$101 - 97 + [8 \times (20 \div 5 - 1) - 3 \times 3] \div 5$ $101-97+[8xx(20-:5-1)-3xx3]-:5$

Let's now work that second bracket:

$[8 \times (20 \div 5 - 1) - 3 \times 3]$ $[8xx(20-:5-1)-3xx3]$

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:

$[8 \times (4 - 1) - 3 \times 3]$ $[8xx(4-1)-3xx3]$

and now the subtraction:

$[8 \times 3 - 3 \times 3]$ $[8xx3-3xx3]$

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

$[24 - 9] = 15$ $[24-9]=15$

Let's substitute that into the original:

$101 - 97 + 15 \div 5$ $101-97+15-:5$

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

$101 - 97 + 3$ $101-97+3$

and now the subtraction and addition:

$4 + 3 = 7$ $4+3=7$

Answer 2 · 2016-07-31T21:41:01

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

= $7$ $7$

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:

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

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

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

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

$- {[55 \div 11] \times (10 + 8) + 7}$ $color(blue)(-{[color(red)(55)-:11]xx(10+color(red)(8))+7})$

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

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

Now for the third term:

$+ [8 \times (20 \div 5 - 1) - 3 \times 3] \div 5$ $color(green)(+[8xx(20-:5-1)-3xx3]-:5)$

$+ [8 \times (20 \div 5 - 1) - 3 \times 3] \div 5$ $color(green)(+[8xxcolor(red)((20-:5-1))-color(orange)(3xx3)]-:5)$

$+ [8 \times (4 - 1) - 9] \div 5$ $color(green)(+[8xxcolor(red)((4-1))-color(orange)(9)]-:5)$

$+ [8 \times 3 - 9] \div 5$ $color(green)(+[8xxcolor(red)(3)-color(orange)(9)]-:5)$

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

$+ 15 \div 5 = 3$ $+color(green)(15-:5) = color(green)3$

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

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

= $7$ $7$

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

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Explanation:

Explanation:

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Simplify the following expression: 101−{[(110÷2)÷11]×(10+4×2)+7}+[8×(20÷5−1)−3×3]÷5101-{[(110 -: 2)-: 11]xx(10+4xx2) +7}+ [8xx(20 -: 5-1)-3xx3] -: 5?

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Explanation:

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