View Poll Results: 48÷2(9+3) = ????
2
29
80.56%
288
7
19.44%
Voters: 36. You may not vote on this poll
48÷2(9+3) = ????
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Did more looking. Even dug up another calculator. That one give 2 as the answer, and after playing with the formula this is what I find.
48/2(9+3)=288 on many, and 2 on some
48/2*(9+3)=288 on all
48/2/(9+3)=2 on all
So I have located the problem. As I said from the start, it'* a bad notation. It is my understanding that in the absence of a command multiply is used. By doing this, the formula becomes 48/2*(9+3)=288.
48/2(9+3)=288 on many, and 2 on some
48/2*(9+3)=288 on all
48/2/(9+3)=2 on all
So I have located the problem. As I said from the start, it'* a bad notation. It is my understanding that in the absence of a command multiply is used. By doing this, the formula becomes 48/2*(9+3)=288.
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The rules of math are not concrete and the answers depend on what "school of thought" and which of, unfortunately there are many, varied perceptions of equation structure. But for 99% percent of us, the only correct math that concerns us, is that which the Bank uses when we get our statements. The rest either have to much time on their hands, or have a balance that doesn't require caring about(high/low).........I've never known a rich mathematician.
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I think the answer is clearly 288. For those getting 2, the formula would have to be:
48/(2(9+3))=2
Whereas, 48/2(9+3)=288. Doesn't matter if the "*" is there or not.
But that is not my purpose for posting. I wanted to share one of the most useful sites for solving equations and the like. Go to: http://www.wolframalpha.com/ .
This is a very cool site.
48/(2(9+3))=2
Whereas, 48/2(9+3)=288. Doesn't matter if the "*" is there or not.
But that is not my purpose for posting. I wanted to share one of the most useful sites for solving equations and the like. Go to: http://www.wolframalpha.com/ .
This is a very cool site.
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So color me an *******.
I sent my college algebra professor this question and the answer I got back: 2.
She said the reason why is because in 48/2(9+3), 2 is the coefficient of the (9+3) which means it has to be distributed. That makes the problem 48/24=2.
I also asked her about a source that I found here: http://www.purplemath.com/modules/orderops2.htm
I'm still waiting for her reply on this part of things.
I sent my college algebra professor this question and the answer I got back: 2.
She said the reason why is because in 48/2(9+3), 2 is the coefficient of the (9+3) which means it has to be distributed. That makes the problem 48/24=2.
I also asked her about a source that I found here: http://www.purplemath.com/modules/orderops2.htm
This next example displays an issue that almost never arises but, when it does, there seems to be no end to the arguing.
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'* 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. If in doubt, ask!
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'* 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. If in doubt, ask!
I'm still waiting for her reply on this part of things.