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# Confusion??

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Could someone please setting an argument surrounding the following:-

Does....... 48÷2(9+3) = 2 or does it equal 288 and why.

Using BODMAS or BIDMAS one gets 2 because the brackets are sorted out first thus 48÷2(12) = 48÷24 = 2

However on my Texas TI-83 I get 288 viz. 48÷2(9+3) = 24*(9+3) = 24*12= 288

Thanks.

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There isn't a "right" or "wrong" here -- it depends on convention. The problem is that you've got an ambiguity in the expression as typed.

Is it: (48/2)*(9+3) or is it 48/(2*(9+3)) ? I.e is the 48 to be divided by the (9+3) term or multiplied? This ambiguity needs to be answered.

Most conventions do everything in the brackets first. Then do exponentiation, then division and multiplication, then addition and subtraction, each from left to right. But that is just a convention, it isn't the "right" or only way to do it. There have been many conventions used over the years -- with the biggest one being to use brackets to remove as much ambiguity as possible.

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There isn't a "right" or "wrong" here -- it depends on convention. The problem is that you've got an ambiguity in the expression as typed.

Is it: (48/2)*(9+3) or is it 48/(2*(9+3)) ? I.e is the 48 to be divided by the (9+3) term or multiplied? This ambiguity needs to be answered.

Most conventions do everything in the brackets first. Then do exponentiation, then division and multiplication, then addition and subtraction, each from left to right. But that is just a convention, it isn't the "right" or only way to do it. There have been many conventions used over the years -- with the biggest one being to use brackets to remove as much ambiguity as possible.

I'm afraid I cannot address the ambiguity as the question was posed as above i.e. what does 48÷2(9+3) =??

So presumably in this case there isn't a single answer.

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Seems to me that the TI-83's approach is fairly logical:

$48 \div 2(9+3) = 48 \div 2 \times (9+3) = 48 \div 2 \times 12 = 24 \times 12 = 288$

[imath]2(2+3)[/imath] is just implied multiplication. Multiplication and division are of the same precedence, so the division on the left comes first.

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But ask yourself

3÷(1+2) = ?

If we use the pattern mentioned above , it will be just like 3÷1x(1+2) = 3 x 3 = 9 which is completely nonsense

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