48/2(9+3)
From MathWorld:
1. Parenthesization,
2. Factorial,
3. Exponentiation,
4. Multiplication and division,
5. Addition and subtraction.
For more complex operations, the order of operations depends on the system.
At the same level (e.g., multiplication and division), operations are executed left-to-right.
written on paper it would show as:
48
------
2(9+3)
therefore it should have been entered into the calculators as
48/(2(9+3))
doing it this way will result with the same exact answer every time on all of the above calculators
48
------
2(9+3)
therefore it should have been entered into the calculators as
48/(2(9+3))
doing it this way will result with the same exact answer every time on all of the above calculators
Okay, using that form then you are simply dividing 48 by 2(9+3). While a number in front of a parentheses tells you to multiply, it also represents itself as a factor describing the parenthetical statement.
The problem is many are looking at / as a fraction symbol, rather than division. That implies that either (48/2) is a fraction or (48/(2(9+3)) is a fraction. But a / is a division symbol on the computer, it must have ( ) to be a fraction.
48 DIVIDED by 2(9+3)
2 is a statement about 9+3.
No, not Multiplication, THEN Division.
From MathWorld:
1. Parenthesization,
2. Factorial,
3. Exponentiation,
4. Multiplication and division,
5. Addition and subtraction.
For more complex operations, the order of operations depends on the system.
At the same level (e.g., multiplication and division), operations are executed left-to-right.
The problem is many are looking at / as a fraction symbol, rather than division. That implies that either (48/2) is a fraction or (48/(2(9+3)) is a fraction. But a / is a division symbol on the computer, it must have ( ) to be a fraction.
48 DIVIDED by 2(9+3)
2 is a statement about 9+3.
Originally Posted by Ted H' timestamp='1302582470' post='20455932
. . . Safely follow the old order of operations: Parentheses, Multiplication, THEN division. That means 9+3=12, 12*2 is 24, 48 divided by (/) 24 is 2.
From MathWorld:
1. Parenthesization,
2. Factorial,
3. Exponentiation,
4. Multiplication and division,
5. Addition and subtraction.
For more complex operations, the order of operations depends on the system.
At the same level (e.g., multiplication and division), operations are executed left-to-right.
48 DIVIDED BY 2 TIMES (9+3)
becomes:
48 DIVIDED BY 2 TIMES 12
and doing the equivalent-order operations left-to-right:
24 TIMES 12
=
288
I screwed it up the first time I did it because I was reading the parenthesis as an operator, rather than just a grouping notation... so I was doing the 'implied' multiplication operation at the parentheses' priority.
becomes:
48 DIVIDED BY 2 TIMES 12
and doing the equivalent-order operations left-to-right:
24 TIMES 12
=
288
I screwed it up the first time I did it because I was reading the parenthesis as an operator, rather than just a grouping notation... so I was doing the 'implied' multiplication operation at the parentheses' priority.
As written, if the / is used to signify explicit division of 48 by 2 without consideration to anything else, that would indicate that they should also have a * in there to explicitly denote multiplication between 2 and (9+3). There is no such multiplication sign. I understand that there is an understood convention regarding placing a number directly against an expression bounded by parentheses to imply multiplication. However, there is also a common practice of "mushing" numbers together like this to indicate that they are to be considered as a single expression (ie, you must treat them as bounded by parentheses).
If they wanted the answer to be 288 and followed a consistent convention, it should read 48/2*(9+3). This, to me, would equal 288.
However, without the *, I deemed this to indicate that the 2(9+3) were to be taken as a "single" expression in the denominator even though no parentheses are shown. Thus, to me, the answer is 2.
Technically, 288 is the correct answer. In real world practice, if I was writing this expression, 2 would be my intended answer.
If they wanted the answer to be 288 and followed a consistent convention, it should read 48/2*(9+3). This, to me, would equal 288.
However, without the *, I deemed this to indicate that the 2(9+3) were to be taken as a "single" expression in the denominator even though no parentheses are shown. Thus, to me, the answer is 2.
Technically, 288 is the correct answer. In real world practice, if I was writing this expression, 2 would be my intended answer.

And it should be, ". . . if I were writing this expression . . . ."
That, however, is another matter entirely.



That's how I was taught.







