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The Water Cooler
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48÷2(9+3) =
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<blockquote data-quote="CHenry" data-source="post: 2039231" data-attributes="member: 6281"><p>Well Its been 25 years since I studies algebra in school and I rely on an HP calculator and computer now so I went and looked it up and I found this. It makes good sense as best I can remember from 25 years ago.</p><p></p><p>The answer is 288. Anyone who thinks the answer is 2 is doing their order of operations incorrectly. this is how i learned it:</p><p></p><p>1) Parenthesis</p><p>2) Exponents</p><p>3) Multiplication and Division (from left to right)</p><p>4) Addition and Subtraction (from left to right)</p><p></p><p>First you evaluate whats in the parenthesis</p><p>48÷2(9+3) = 48÷2(12)</p><p>Now you do multiplication and division from left to right. In this case, the division comes first since it is more to the left.</p><p>48÷2(12) = 24(12)</p><p>Now you multiply</p><p>24(12) = 288</p><p></p><p>"What are the order of operations anyway?"</p><p>They are a convention used in math to clarify ambiguous problems such as this one.</p><p></p><p>"Well it depends wheather you use PEMDAS or BEDMAS"</p><p>No it doesnt. Multiplication and division are treated with equal precedence regardless of acronym you choose to use. Multiplication and division are evaluated from left to right. Google "order of operations" or read any algebra textbook and it will say the same thing.</p><p></p><p>"But usually when theres a division sign, everything to the left is the numerator and everything to the right is the denomenator..."</p><p>No that is not true. There is no math property that says that everything on the right is naturally the denomenator.</p><p></p><p>"But some calculators say 2"</p><p>This is true. Not all calculators evaluate the order of operations correctly. In general, newer calculators/computer programs will get the order of operations correctly. For example, C++, Python, MATLAB, Maple, Wolframalpha, and my TI-89 all say 288 whereas many older calculators that dont do the order of operations correctly may say 2.</p><p></p><p>"But wait! The denomenator says 2(9+3), not 2*(9+3)"</p><p>The presence an "x" or "*" for multiplication (and similarly the presence of "/" or "÷" for division) makes no difference. Either way, it indicates the multiplication of 2 and (9+3), regardless of notation. The manner in which multiplication is notated has no impact on the order of operations. You still do multiplication and division from left to right</p><p></p><p>"but you can use the distributive property to determine that 2(9+3)=24, and 48/24=2!"</p><p>Mathmatically, the distributive property is exactly the same as multiplying 2 and (9+3). By doing it before the division of 48 and 2, you are violating the order of operations, and therefore you are wrong. The distributive property in no way takes precedence over normal multiplication (and in fact has no effect at all on the order of operations). That logic is faulty and the answer is 288.</p><p></p><p>"Ok, I understand that if you use BEDMAS you get 288, but what if I choose not to use BEDMAS?"</p><p>Then you are doing the problem wrong. BEDMAS is the math convention and there is no choice of wheather or not to use BEDMAS.</p><p></p><p>"Both answers are correct; it just depends on how you interpret/see the question!"</p><p>No you are also wrong. There is only one right answer and its 288. The idea that both answers are correct is also wrong. Like I said before, this problem is not ambiguous at all when you use the order of operations. Essentially, there is only one correct way of interpreting this problem.</p><p></p><p>"But we cant be sure if there are implied brackets around the denomenator like this 48÷(2(9+3)), therefore we can't be sure if the answer is 2 or 288!"</p><p>Yes, we can be sure that there are no implied brackets. The reason we know this is because the original problem was given like this: 48÷2(9+3). In math, you cannot imply brackets. The only brackets are the ones that are written in the equation.</p><p></p><p>I hope this clarifies things.</p></blockquote><p></p>
[QUOTE="CHenry, post: 2039231, member: 6281"] Well Its been 25 years since I studies algebra in school and I rely on an HP calculator and computer now so I went and looked it up and I found this. It makes good sense as best I can remember from 25 years ago. The answer is 288. Anyone who thinks the answer is 2 is doing their order of operations incorrectly. this is how i learned it: 1) Parenthesis 2) Exponents 3) Multiplication and Division (from left to right) 4) Addition and Subtraction (from left to right) First you evaluate whats in the parenthesis 48÷2(9+3) = 48÷2(12) Now you do multiplication and division from left to right. In this case, the division comes first since it is more to the left. 48÷2(12) = 24(12) Now you multiply 24(12) = 288 "What are the order of operations anyway?" They are a convention used in math to clarify ambiguous problems such as this one. "Well it depends wheather you use PEMDAS or BEDMAS" No it doesnt. Multiplication and division are treated with equal precedence regardless of acronym you choose to use. Multiplication and division are evaluated from left to right. Google "order of operations" or read any algebra textbook and it will say the same thing. "But usually when theres a division sign, everything to the left is the numerator and everything to the right is the denomenator..." No that is not true. There is no math property that says that everything on the right is naturally the denomenator. "But some calculators say 2" This is true. Not all calculators evaluate the order of operations correctly. In general, newer calculators/computer programs will get the order of operations correctly. For example, C++, Python, MATLAB, Maple, Wolframalpha, and my TI-89 all say 288 whereas many older calculators that dont do the order of operations correctly may say 2. "But wait! The denomenator says 2(9+3), not 2*(9+3)" The presence an "x" or "*" for multiplication (and similarly the presence of "/" or "÷" for division) makes no difference. Either way, it indicates the multiplication of 2 and (9+3), regardless of notation. The manner in which multiplication is notated has no impact on the order of operations. You still do multiplication and division from left to right "but you can use the distributive property to determine that 2(9+3)=24, and 48/24=2!" Mathmatically, the distributive property is exactly the same as multiplying 2 and (9+3). By doing it before the division of 48 and 2, you are violating the order of operations, and therefore you are wrong. The distributive property in no way takes precedence over normal multiplication (and in fact has no effect at all on the order of operations). That logic is faulty and the answer is 288. "Ok, I understand that if you use BEDMAS you get 288, but what if I choose not to use BEDMAS?" Then you are doing the problem wrong. BEDMAS is the math convention and there is no choice of wheather or not to use BEDMAS. "Both answers are correct; it just depends on how you interpret/see the question!" No you are also wrong. There is only one right answer and its 288. The idea that both answers are correct is also wrong. Like I said before, this problem is not ambiguous at all when you use the order of operations. Essentially, there is only one correct way of interpreting this problem. "But we cant be sure if there are implied brackets around the denomenator like this 48÷(2(9+3)), therefore we can't be sure if the answer is 2 or 288!" Yes, we can be sure that there are no implied brackets. The reason we know this is because the original problem was given like this: 48÷2(9+3). In math, you cannot imply brackets. The only brackets are the ones that are written in the equation. I hope this clarifies things. [/QUOTE]
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