Pedmas

[bentleymrk]

Would these two examples produce the same result?

20 / 2 * (5+5)

and

20 / 2(5+5)

?

I believe the answer to both is 100. But others are questioning this. My understanding from PEDMAS is that we have to evaluate the parens first, but once they are cleared, division and multiplication have the same order, and we go left to right.

Thanks in advance.

 

[Ishuda]

Would these two examples produce the same result?

20 / 2 * (5+5)

and

20 / 2(5+5)

?

I believe the answer to both is 100. But others are questioning this. My understanding from PEDMAS is that we have to evaluate the parens first, but once they are cleared, division and multiplication have the same order, and we go left to right.

Thanks in advance.

Formally both lead to the same answer. How so some ever, it does occur fairly often that someone doesn't use the grouping symbols, that is they write
1/1+x
when what they (apparently) mean is
1/(1+x)
So sometimes it appears obvious that they meant them to be there from the rest of the discussion. In that case one might gently chide them about their misteak rather than make a large display about it. However, if it is not clear from context or some other reason or there appears to be any confusion about what is meant, it does seem to me that a question would be in order.

 

[stapel]

Would these two examples produce the same result?

20 / 2 * (5+5)

and

20 / 2(5+5)

?

In my experience, the answer is that "it depends who you ask", and opinion is generally evenly divided.

Had the first expression been written as follows:

. . . . .\(\displaystyle \dfrac{20}{2(5\, +\, 5)}\)

...then the meaning would have been obvious: divide the twenty on top by the 2(5 + 5) = 2(10) = 20 underneath, to get 1. However, when written horizontally, one can reasonably interpret the meaning as:

. . . . .\(\displaystyle 20\, \div\, 2\, \times\, (5\, +\, 5)\, =\, 20\, \div\, 2\, \times\, 10\)

Then, working from left to right, in accordance with the order of operations:

. . . . .\(\displaystyle (20\, \div\, 2)\, \times\, 10\, =\, 10\, \times\, 10\, =\, 100\)

Much the same can be said of the second expression. However, there are those who may interpret the first in accordance with the order of operations (getting 100), as displayed above, but interpret the second as being equivalent to the fractional form (getting 1). This is because many have absorbed the (utterly informal) rule that the 2, being multiplied against the parenthetical without any "times" symbol between, is somehow more "strongly" "attached" (by "juxtaposition") to the parenthetical. As a result, the expression must be viewed as containing implied grouping symbols: 20 / [2(5 + 5)]

I'm not saying which position is "right". As far as I know, this is the one case where notation causes confusion which has not, to my knowledge, yet been fixed with any universally-accepted convention. In a sense, there may not (currently) be a "right" answer. Sorry.