Really stupid order of operations question

Factual Questions
41

Just think of all subtraction as adding a negative number, and then add in any order you like.

1 - 2 + 3 - 5 - 3 + 8 =

1 + (-2) + 3 + (-5) + (-3) + 8 =

8 + 1 + 3 + (-2) + (-5) + (-3)

etc.

but I’m not sure where the confusing part is honestly

9+7+5-6-2+8-6
->
9+7 = 16, 16+5 =21, 21-6=15, 15-2=13, 13+8=21, 21-6=15

now backwards

-6+8=2, 2-2=0, 0-6=-6, -6+5=-1, -1+7=6, 6+9=15

adding in multiplication is easy, just multiply first, and then move on:

2+3*-7-62+3+8-6-7

3*-7=-21, 62= 12, 6-7=-42
sub in the results to the formula
2±21-12+3+8–42
apply any signs to one another (when you have a subtraction sign in front of a number that is multiplied by another number, you can choose whether to bring the negative sign with you into multiplication question and bring the result back as addition (of a possibly negative number) or do what I do and leave the negative sign behind and bring back the result as subtraction (alos, possibly of a negative number).
->
2-21-12+3+8+42
now we can add them in some random order,
-21+3 = -18
42-12=30
2+8=10
and then,
10+30=40
40-18=22

A really dumb way to do the problem, but you get the right answer.

More straightfoward way ->
2+3*-7-62+3+8-6-7 =
2+(-21)-(12)+3+8-(-42)
2-21=-19, -19-12=-31, -31+3=-28, -28+8=-20, -20+42=22

42

Oh, god, back in the day my TI-82 was grafted onto my body like some sort of futuristic shackle. Wonder what happened to that bastard?

43

I’ve heard of a method similar to what Darth Panda is getting at. If you treat each +/- term as being associated with its operator, then the method would be to group all terms of one kind together.

For example:

16 - 8 + 3

Group all the additive terms together and add them, and group and add all the subtractive terms. (And by group, I mean put in parentheses) :

(16 + 3) - (8) = 19 - 8 = 11

Or for one with more terms :

5 - 2 + 4 + 1 - 3

(5 + 4 + 1) - ( 2 + 3) = 10 - 5 = 5

You could also do this if you rearrange, and then perform your steps more similar to the mnemonic, i.e. :

Rearrange
5 + 4 + 1 - 2 - 3
Do additions:
=10 - 2 - 3
Then subtractions:
10 -2 -3 = 8 - 3 = 5

This grouping works even at higher levels, to avoid minus-sign distribution errors.

44

Zsophia, if you have trouble remembering to distribute the minus sign, you could also do (less elegantly):

4x-(2x-3)=0 Now add (2x-3) to both sides of the equation
4x = 2x-3 Now subtract 2x from each side of the equation
2x = -3
x = -3/2

45

Oh, you know, I bet that’s how they wanted me to do that.

46

Need any help with your homework tonight?

47

My 8th grade algebra teacher said, “My dear Aunt Sally is dead!” (At this point most of us had never heard of “my dear Aunt Sally” and were bit taken aback.) “And she’s buried in a gray box on page 17.”

The gray box on a page of our text described order of operations, pointing out that multiplication and division were of equal precedence and should be executed left to right. Same for addition and subtraction.

After they eat that, they shoot and leave. :wink: