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48÷2(9+3) =


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2. We don't do Math from left to right, we do it by the Order of Operations from left to right. The O of O decrees that we add the 9 and the 3 within the parenthesis, multiply the result (12) by the 2, and then do the division.

 

Parenthesis/Brackets

Expontents

Multiplication

Division

Addition

Subtraction

 

nope, multiplication and division have the same precedence, you perform them from left to right. it's a common misconception that multiplication takes precedence over division and addition over subtraction, but they don't.

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As I recall, doing it left to right is just a convenience of most westerner's reading and writing left to right, with the one exception being DIVISION, and only then because it is generally expected to be written the way it would be said aloud. The order of operations was always paramount in how a math problem was solved. Multiplication has no precedence over division in the order of operations - they are at the same level of abstraction.

 

Others have sufficiently covered how to do the problem. Especially mim and TKA-001.

 

The answer is 288. Not really much opinion about it, as Lynk's Wolfram shows us.

 

@Prime: didn't do it on paper, did it WITH MY MIND o.O

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Others have sufficiently covered how to do the problem. Especially mim and TKA-001.[/Quote]
288

 

2

 

Now I'm really confused.

 

1288188810109626422.jpg

 

:xp:

The answer is 288. Not really much opinion about it, as Lynk's the mighty Sabre's Wolfram shows us.

 

Fixed ;)

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Similiar problem....

http://www.purplemath.com/modules/orderops2.htm

 

Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1.

16 ÷ 2[8 – 3(4 – 2)] + 1

= 16 ÷ 2[8 – 3(2)] + 1

= 16 ÷ 2[8 – 6] + 1

= 16 ÷ 2[2] + 1 (**)

= 16 ÷ 4 + 1

= 4 + 1

= 5

 

The confusing part in the above calculation is how "16 divided by 2[2] + 1" (in the line marked with the double-star) becomes "16 divided by 4 + 1", instead of "8 times by 2 + 1". That's because, even though multiplication and division are at the same level (so the left-to-right rule should apply), parentheses outrank division, so the first 2 goes with the [2],rather than with the "16 divided by". That is, multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Typesetting the entire problem in a graphing calculator verifies this hierarchy:

 

Note that different software will process this differently; even different models of Texas Instruments graphing calculators will process this differently. In cases of ambiguity, be very careful of your parentheses, and make your meaning clear. The general consensus among math people is that "multiplication by juxtaposition" (that is, multiplying by just putting things next to each other, rather than using the "×" sign) indicates that the juxtaposed values must be multiplied together before processing other operations. But not all software is programmed this way, and sometimes teachers view things differently.

 

So, looks like the answer to the OP is either 2 or 288.....depending on your teacher. :xp:

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But, that's wrong.

 

Based on what interpretation? That's the only one I've seen* where the O of O is addressed in that fashion (ie. w/ regard to 2() vs 2 * () ). I'd just tend to go with the intrerpretation of sloppy or ambiguous notation.

 

*mind you, it was by no means an exhaustive search (several O of O sites via googling). If you've got something more definitive, by all means share it. I don't have a dog in this race.

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Based off the implication that placing a number against a bracket makes it "stronger". I've not heard of implied multiplication taking president over other forms. If this was true, the answer to the first problem would be 2.

 

16 ÷ 2[8 – 3(4 – 2)] + 1

=> 16 ÷ 2[8 – 3(2)] + 1

=> 16 ÷ 2[8 – 6] + 1*

=> 16 ÷ 2[2] + 1

=> 8[2] + 1

=>17

 

* = or distribute here: (16/2*8 - 16/2*6) + 1 => 17

This method can also be used on the first problem:

24*9 + 24*3 => 288

 

 

 

Augh. Looking online it seems there's huge debates on this even in math and physics forums. God I hate maths. :migraine:

headasplode.jpg

My 89, 92 and MATLAB agree with me on both problems though. And they've never steered me wrong before. :raise: The biggest problem with all of these equations are that they are poorly written and would hopefully never be used in real life calculations for the reasons this thread has demonstrated.

 

Also, This.

 

Now, if you'll excuse me, I must be off to perform my post-math ritual of taking a baby apsrin and squishing blue play-dough between my hands until all is once again right in the world.

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Augh. Looking online it seems there's huge debates on this even in math and physics forums. God I hate maths. :migraine:

Also, This.

 

Now, if you'll excuse me, I must be off to perform my post-math ritual of taking a baby apsrin and squishing blue play-dough between my hands until all is once again right in the world.

 

"Augh" is about right. I noticed the same problem in many of those forums myself. The baby thing was kinda funny, though.

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I should've remembered, PEMDAS isn't really valid. It really should be PE(M&D)(A&S), but that would defeat the purpose of the mnemonic. Multiplication has the same priority as division.

 

The only thing that makes this math problem a matter of opinion is whether the sloppy notation allows implied multiplication. The solution is, of course, not using sloppy, ambiguous, notation.

 

My new answer: If the question itself isn't right, there can't be a right answer.

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What exactly was sloppy about it? Besides using an ÷ instead of /. I'm no math genius but it seemed pretty straightforward to me. Why use ()s if your just going to ignore them? Values side by side should be multiplied as in: E=MC² is the same as E=M*C².

 

Lol @Tommycat

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It's very ambiguous in it's delivery. Is it 48 over everything else or what?

 

For instance, if this had to compile for a microprocessor, I would most likely use the distributive property to rewrite it like this:

 

Where 48=a, 2=b, 9=c, and 3=d:

 

((a/b*c) + (a/b*d))

 

Unless you want it to be 2 *fist shake* and then it would just be a matter of doing this: (a÷(b(c+d)))

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It's very ambiguous in it's delivery. Is it 48 over everything else or what?

 

For instance, if this had to compile for a microprocessor, I would most likely use the distributive property to rewrite it like this:

 

Where 48=a, 2=b, 9=c, and 3=d:

 

((a/b*c) + (a/b*d))

 

Unless you want it to be 2 *fist shake* and then it would just be a matter of doing this: (a÷(b(c+d)))

 

The Rhett knoweth the truth and the Rhett sayeth the truth.

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