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Question 496223: 4 – 3[4 –2(6 – 3)] ÷ 2=
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! An acronym PEMDAS outlines the rules to be followed. (You can remember it by using the first letters of the statement "Please Excuse My Dear Aunt Sally".)
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The P stands for Parentheses. Do those first.
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Next do E for Exponents (there are none in this problem).
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Then, going left to right do the (M and D) Multiplications and Divisions as you come upon them.
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Finally, going from left to right do the (A and S) Additions and Subtractions as you come upon them.
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Now to your problem:
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4 – 3 ÷ 2
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Note that I added a couple of multiplication signs (*) that are normally understood and not written. This is just to make sure that you understand later that they need to be recognized. You don't need to put them in when you work problems such as these, but don't forget to do the understood and not written multiplications.
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First look for the most interior set of parentheses. That is the set (6 - 3). Within this set follow in order the remaining rules: exponents (none); multiplications & divisions (none); and finally additions and subtractions of 6 - 3. The result is that 6 - 3 equals 3, so you can replace the contents of those parentheses by 3. Your problem then becomes:
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4 – 3 ÷ 2
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Now you have another set of parentheses containing 4 - 2*3. You have to deal with this set of parentheses next. Again follow in order the remaining rules: exponents (none). Then in order reading 4 - 2*3 from left to right you have the multiplication ( and no divisions) of -2*3 which results in -6 and the contents of this set of parentheses then becomes 4 - 6. Finally, you do from left to right the additions (none) and subtractions to get that 4 - 6 = -2.
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So you can replace the contents of this set of parentheses by -2. When you do that the problem is then simplified to:
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4 - 3*-2 ÷ 2
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Now you have completed all the parentheses and there are no exponents. So all you have to consider is the multiplications and divisions followed next by the additions and subtractions.
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Reading this problem from left to right looking for multiplications and divisions you first come to the multiplication of -3 times -2. Do that multiplication to get +6 and put that into the problem. The problem is then:
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4 + 6 ÷ 2
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Now go back and read the problem looking from left to right for more multiplications and divisions. You have the division of 6 ÷ 2. Do that division and you get 3. So replace 6 ÷ 2 by 3 to get:
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4 + 3
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And now you are all done with parentheses, exponents, multiplications, and divisions. All you have left to do from left to right in order is additions and subtractions. All that is remaining is the addition of 4 + 3 and that results in 7.
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So the answer to your original problem is 7.
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Hope this helps to clarify a little bit the order of handling algebraic operations in problems such as these.
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