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Question 776684: Please explain how 3+4[8(5*5-20)-41] equals -1
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! Algebra is a language.
You learned a few words related to arithmetic.
When you get into Algebra you want to use full number sentences.
All languages need some grammar and structure. You need to put your words in the conventional order if you want other people to understand you.
I didn't make the rules, they were made long before I was born.
Here are the order of operations rules.
1)  is for   . What's inside a set of brackets must be fully calculated before you start doing any oprations between what's inside those brackets and what's out side them.
2)  is for  , and you will not have to worry about those for a while, so ignore .
3)  and  stand for Multiplication and Division. They are done in order before any calculation not mentioned before.
4)  and  stand for Addition and Subtraction. They are done last (except for those inside parentheses, of course).
To remind students of order of operations, teachers use the acronym  that they say is short for
      or some other phrase.
3+4[8(5*5-20)-41] = 3+4[8(25-20)-41] because there is nothin we can do before we calculate the inside set of parentheses, and in 5*5-20 multiplication goes before subtraction
3+4[8(25-20)-41] = 3+4[8(5)-41] or    
is the next step because we still need to calculate 25-20 before we can do anything else. (The brackets around 5 were there to separate it from the 8 multiplying it, just because I could not type a middle dot or a times symbol).
3+4[8(5)-41] = 3+4[40-41] or, since we have only one set of parentheses,
3+4[8(5)-41] = 3+4(40-41) because now we can multiply 8 times 5 and that multiplication needs to be done before we can subtract 41.
3+4(40-41) = 3+4(-1) is next because we have to calculate the 40-41 inside the parentheses before we can do anything else.
3+4(-1) has multiplication and addition, and multiplication must be done before addition, so
3+4(-1) = 3 - 4 = -1
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