Question

What rule can we use to evaluate an algebraic expression?
What is the GEMDAS rule?

Answer 1

it makes a rule for the priority of operations

usually, you make operations from left to right:
3+5+2 =

first, you do the first addition from the left
__3+5__ + 2
__8__ +2

then, the next one
8 + 2
__8+2__ = 10

do you understand so far ?

Answer 2

Yes.

Answer 3

in some cases, you have to apply operations that are further to the right FIRST
because they have a higher priority

example:
2 + 3 * 4 =

usually, you would begin by adding 2 and 3.
however, since there are DIFFERENT operations (multiplication and addition), there is a priority that overrides the one "left to right" (which is the weakest one).

Answer 4

you go through the GEMDAS priority list, and stop when you find an entry
that has an occurence in the expression

this is the list:
1. Grouping
2. Exponents
3. multiplication and/or division
4. addition and/or subtraction

we start by checking if there's any grouping (parentheses).
there isn't, so we move on.

are there any exponents? no, so this high priority does not occur in the expression

do we have 3. multiplication and/or division?
YES! we do have an occurence of a priority 3. term

Answer 5

so that means, we must first apply this operation, and when we have done that, we again go through the list!

2 + 3*4 =

the priority 3. was the multiplication, so we do that now:

2 + 12 =

ok, now we can again go through the list

Answer 6

Yah

Answer 7

actually the last time there's only one operation so it's clear there can't be any other operation that must be done before it

so the final result is 2 + 12 = 14

if we had not done GEMDAS rule, then we would have gotten:
2 + 3 * 4 =
5 * 4 = 20 , which is a different value and is WRONG

Answer 8

Ok. How about if the exponent and parenthesis appear simultaneously which one should be first to perform?

Answer 9

good question!

in that case, we also run through the GEMDAS list:

1. Grouping
2. Exponents
3. multiplication and/or division
4. addition and/or subtraction

because 1. Grouping comes earlier, and we stop whenever we find
an entry in the list that we have in the expression:

that means we would do the parentheses FIRST, and then after doing them
we run through the list again.
(the second time, exponents will win any addition or subtraction)

Answer 10

as long as there is still one parentheses left, we do them before
any exponent

Answer 11

Ok. Thank You so much :)