Deenreka wrote:Yoduh wrote:Deenreka wrote:10 - 5 + 2 would equal 7 no matter what order you do it in. If you add 5 + 2 to get 7 then subtract that from ten, you've added in a bracket, changing the problem to 10 - (5+2). As long as the numbers keep their signs attached, adding and subtracting can be down in any order, left to right (I.E. -5 + 2 = -3, 10 - 3 = 7).
a sign outside a bracket is applied to each number within, such as -(5x+7) = -5x-7. In the case of 10 - (5+2) it becomes 10 - 5 - 2, which performed left to right = 3. Which is also the answer you would expect from following BODMAS since you've introduced brackets, 10 - (7). So yes it does matter what order you perform DM/AS when there are no brackets to specify (a practice which should be avoided anyways).
Order wouldn't matter, because by adding 5 and 2 without keeping the negative sign attached to the five, you have added in brackets. Order doesn't matter when you keep signs attached. The mistake in adding 5 and 2, then subtracting that from 10 comes from separating the sign from the number. To put my argument into phrase, there is no subtraction, only addition of negative numbers (Also follows from this that there is no division, only multiplication of fractions). Therefore, BODMAS should be BOMA.
Yeah, what Deenreka said is correct. So to show the multiplication/division side of things, it works like this:
xorsyst wrote:10 ÷ 5 * 2 is 4, not 1, because D happens before M.
That is not why it equals 4. It equals 4 because the expression is actually shorthand for:
10 * (5^-1) * 2
10 * (1/5) * 2
Whenever there's a division sign, it's shorthand for "multiply by the reciprocal of the immediately following term".
A - B = A + (-1)B
This has sort of already been said but I wanted to put it in simple terms and it's been bugging me while I read this whole argument.