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fftopic:
inb4 you get 50 PM's
48÷2(9+3) = ????
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inb4 you get 50 PM's
"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 second page gives this example: "Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1" After the solution, it talks about the situation that is the focus of the argument in this thread (pertinent part in bold):
"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."
"A coefficient preceding a parenthetical operation implies that the operation be first performed as a distributive calculation. 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."
It's the same reason we had to add a whole bunch of parentheses to get the correct when answer when we did our calculus homework. Most calculators don't include distribution properties, etc. If I type -9^2 (negative nine squared) into a calculator, it gives me -81, which most of us would know that if we squared -9, it's actually 81.
The way I read this is that the 2(9+3) is all attached (with or without parentheses around the entire equation) because of the fact that multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Again, I'd have no problem agreeing with the 288 answer if there was a * or x symbol (regular multiplication) in between the 2 and parentheses. We process the (2*9+2*3) first. This gives us 24. Then we take our 48 and divide the 24 to give us 2.
Also, if we try to solve algebraically,
When we solve for 2,
48/a(9+3) = 2
48/(9a+3a) = 2
48/12a = 2
48 = 24a
a=2
"The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble."
"The second page gives this example: "Simplify 16 ÷ 2[8 – 3(4 – 2)] + 1" After the solution, it talks about the situation that is the focus of the argument in this thread (pertinent part in bold):
"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."
"A coefficient preceding a parenthetical operation implies that the operation be first performed as a distributive calculation. 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."
It's the same reason we had to add a whole bunch of parentheses to get the correct when answer when we did our calculus homework. Most calculators don't include distribution properties, etc. If I type -9^2 (negative nine squared) into a calculator, it gives me -81, which most of us would know that if we squared -9, it's actually 81.
The way I read this is that the 2(9+3) is all attached (with or without parentheses around the entire equation) because of the fact that multiplication that is indicated by placement against parentheses (or brackets, etc) is "stronger" than "regular" multiplication. Again, I'd have no problem agreeing with the 288 answer if there was a * or x symbol (regular multiplication) in between the 2 and parentheses. We process the (2*9+2*3) first. This gives us 24. Then we take our 48 and divide the 24 to give us 2.
Also, if we try to solve algebraically,
When we solve for 2,
48/a(9+3) = 2
48/(9a+3a) = 2
48/12a = 2
48 = 24a
a=2
"The main lesson to learn is not which rule to follow, but how to avoid ambiguity in what you write yourself. Don't give other people this kind of trouble."
End of maths as you knew it
(1) Multiplication and division are same (8/2 = 8 * 1/2 )
(2) Addition and subtraction are same (8 - 2 = 8 + -2)
(3) Multiplication is the same as addition (2 * 4 = 2 + 2 + 2 + 2).
......
......
So, multiplication, division, subtraction and addition are all the same.
(1) Multiplication and division are same (8/2 = 8 * 1/2 )
(2) Addition and subtraction are same (8 - 2 = 8 + -2)
(3) Multiplication is the same as addition (2 * 4 = 2 + 2 + 2 + 2).
......
......
So, multiplication, division, subtraction and addition are all the same.
If your answer is 2 you need to read this very basic rules of Math and Beginners guide to Pure Math first
Remember what I said on page 1 about this being a poorly written question? THAT's why people are so polarized. Nobody who answered 2 is dumb. Nobody who answered 288 is dumb.
Let me clear up a misconception that people on both sides have been throwing out--that all expressions have correct answers. Consider this:
2+*5^)6
This is a much more extreme example; it clearly cannot be simplified, as symbols don't line up with each other or other numbers. What I stated before was not that math is open to interpretation, but that poorly written math is. 48÷2(9+3) is poorly written. The problem is not the "incorrect" answers people have given, but the unclear question.
Anyone who's even glanced through this thread has seen a dozen interpretations and rules thrown out. That should never happen. This would never stand in a thesis or paper. Mathematicians have a duty not only to solve problems correctly, but also, and probably more importantly, to express them correctly.
Let me clear up a misconception that people on both sides have been throwing out--that all expressions have correct answers. Consider this:
2+*5^)6
This is a much more extreme example; it clearly cannot be simplified, as symbols don't line up with each other or other numbers. What I stated before was not that math is open to interpretation, but that poorly written math is. 48÷2(9+3) is poorly written. The problem is not the "incorrect" answers people have given, but the unclear question.
Anyone who's even glanced through this thread has seen a dozen interpretations and rules thrown out. That should never happen. This would never stand in a thesis or paper. Mathematicians have a duty not only to solve problems correctly, but also, and probably more importantly, to express them correctly.
it is?
doesn't seem so to me...
2+*5^)6
is not even an expression...
you can not raise to ) nor can you add a multiplication symbol
After seeing the poll results and replies I see a highly profitable potential business:
Write a crappy eBook copy pasting BODMAS rule and a few other basics, name it "Mathematics for Affiliate Marketeers" and sell it on WaFo, PROFIT
Write a crappy eBook copy pasting BODMAS rule and a few other basics, name it "Mathematics for Affiliate Marketeers" and sell it on WaFo, PROFIT