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I have the following problem: $$100*\left\{24+100*[1001-4*(25*6+25*4)]\right\}$$

I'm very frustrated that I can't solve exercises like this. I have read about PEMDAS and followed the steps but somehow I am making a mistake because the result I get is not correct.(looked at answers in the book).

Can someone provide the steps in order to solve correctly this problem?

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Arturo + Zev: I think Morphism should be asked for his steps first, rather than us simply doing it for him in a matter of minutes. – GEdgar Jun 23 '12 at 19:57
@GEdgar: I would not say that I "did it for him"; I explained what steps he needs to take, but did not take them. – Arturo Magidin Jun 23 '12 at 20:08
up vote 1 down vote accepted

First, do the innermost products, $25*6$ and $25*4$. Then add them. Then multiply the result by $4$. Then subtract this from $1001$. Then multiply the answer by $100$. Then add $24$. Then multiply the result of that by $100$.


  1. You will need to multiply $100$ by the result of what is in curly brackets;

    • What is in curly brackets requires you to add $24$ to the result of multiplying $100$ by the answer you get from inside the square brackets;

      -What is inside the square brackets requires you to start with $1001$, and subtract the result of multiplying $4$ by the result of what you have inside the round parentheses.

      • To compute what is inside the round parentheses, you first do the products ($25$ times $6$ and $25$ times $4$), and add them.

Now "unfold" that to get the answer.

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I totally got it now! Thank you so much! – Morphism Cekl Jun 23 '12 at 19:53

$\newcommand{\myemph}[1]{{\color{red}{\bf #1}}}$ $$100*\left\{24+100*[1001-4*(\myemph{25*6}+\myemph{25*4})]\right\}$$ $$100*\left\{24+100*[1001-4*(\myemph{150+100})]\right\}$$ $$100*\left\{24+100*[1001-\myemph{4*(250)}]\right\}$$ $$100*\left\{24+100*[\myemph{1001-1000}]\right\}$$ $$100*\left\{24+\myemph{100*[1]}\right\}$$ $$100*\left\{\myemph{24+100}\right\}$$ $$\myemph{100*\left\{124\right\}}$$ $$\fbox{12400}$$

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