If you thought 8 ÷ 2(2+2) = ? was stupid and pointless, so did a lot of mathematicians.https://nyti.ms/2YKDk9f
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It works by definition. If there were no pre-defined order of operations, you would have throw parentheses everywhere to show the intended order of operations. What PEMDAS does is simplify the notation.
All this equation is take advantage of the fact that when you learn PEMDAS, you haven't learned about implied multiplication yet with the parentheses but no multiplication sign.
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So the first step in PEMDAS is eliminate the parentheses. That's adding 2+2, which gives 8 ÷ 2(4). It's not unreasonable that people think, oh, I need to multiply the 2 and 4 to get rid of the parentheses. When you learn PEMDAS, that's not part of what you learn.
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In addition, in algebra, you learn that stuff connected by implied multiplication are factors that stay together. But in algebra, you never use ÷. All of the equations are written as fractions, exactly to avoid this ambiguity.
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