document.write( "Question 776684: Please explain how 3+4[8(5*5-20)-41] equals -1 \n" ); document.write( "

Algebra.Com's Answer #473673 by KMST(5328) $\"\"$ $\"About$

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Algebra is a language.
\n" ); document.write( "You learned a few words related to arithmetic.
\n" ); document.write( "When you get into Algebra you want to use full number sentences.
\n" ); document.write( "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.
\n" ); document.write( "I didn't make the rules, they were made long before I was born.\r
\n" ); document.write( "\n" ); document.write( "Here are the order of operations rules.
\n" ); document.write( "1) $\"highlight%28P%29\"$ is for $\"P\"$ $\"arentheses\"$ . 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.
\n" ); document.write( "2) $\"highlight%28E%29\"$ is for $\"exponents\"$ , and you will not have to worry about those for a while, so ignore $\"highlight%28E%29\"$ .
\n" ); document.write( "3) $\"highlight%28M%29\"$ and $\"highlight%28D%29\"$ stand for Multiplication and Division. They are done in order before any calculation not mentioned before.
\n" ); document.write( "4) $\"highlight%28A%29\"$ and $\"highlight%28S%29\"$ stand for Addition and Subtraction. They are done last (except for those inside parentheses, of course).
\n" ); document.write( "To remind students of order of operations, teachers use the acronym $\"PEMDAS\"$ that they say is short for
\n" ); document.write( " $\"highlight%28P%29\"$ $\"lease\"$ $\"highlight%28E%29\"$ $\"xcuse\"$ $\"highlight%28M%29\"$ $\"y\"$ $\"highlight%28D%29\"$ $\"ear\"$ $\"highlight%28A%29\"$ $\"unt\"$ $\"highlight%28S%29\"$ $\"ally\"$ or some other phrase.
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\n" ); document.write( "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
\n" ); document.write( "3+4[8(25-20)-41] = 3+4[8(5)-41] or $\"3%2B4\"$ $\"%22%5B%22\"$ $\"8%2825-20%29-41\"$ $\"%22%5D%22+=+3%2B4%288%2A5-41%29\"$
\n" ); document.write( "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).
\n" ); document.write( "3+4[8(5)-41] = 3+4[40-41] or, since we have only one set of parentheses,
\n" ); document.write( "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.
\n" ); document.write( "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.
\n" ); document.write( "3+4(-1) has multiplication and addition, and multiplication must be done before addition, so
\n" ); document.write( "3+4(-1) = 3 - 4 = -1 \n" ); document.write( "

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