I need help trying to understand how to do pemdas

Question

I am working on algebra one and need help with the order of operations. Know the order can get started but third step is where I get lost

Answer 1

PEMDAS stands for Parenthesis, Exponents, Multiply/Divide, and Addition/Subtract...IN THAT ORDER.  It's very important you follow this "order of operations". 

Start by solving the problems/values in parenthesis.  If there are exponents, you must evaluate/solve those first.  For example, (2 x 8²) + 4 gives you a different answer than (2 x 8)² + 4.  In both equations, I solve for everything in parenthesis first.  This means I completely ignore the "+4"...at least for now.  Here's how both look:

(2 x 8²) + 4 = (2 x 64) + 4 = 128 + 4 = 132.  Notice how I started and solved everything in parenthesis first....essentially only focusing on 2 x 8² to start.  WITHIN the parenthesis, there's an exponent; so I must solve 8² before multplying.  Once you solve for all exponents, you move to the other operations...all WITHIN that parenthesis.  So even if I had (2 + 8) x 4, you still must solve the parenthesis first.  (The answer is 40, not 34)

For the second equation above, I again solve everything WITHIN parenthesis first: (2 x 8)² + 4 = 16² + 4 = 256 + 4 = 260.

 

THEN you move to multiply or division.  Notice how I group multiply and division together...these operations can be solved in any order, but the rule of thumb is typically work left-to-right...just like reading a book.  For example, for the equation 2 x 8 / 4, you can either

(1) multiply first: 2 x 8 / 4 = 16/ 4 = 4, or

(2) divide first: 2 x 8 / 4 = 2 x 2 = 4,

because they both equal 4.  The importance is that you solve all multiplication and division BEFORE moving to addition and subtraction.

Similarly, you can complete addition and subtraction in either order.  But it MUST be the LAST step.  Let's take the example above again.  If my equation were 2 x 8 + 4, there's a DIFFERENCE if I multiply or add first:

(1) If you multiply first: 2 x 8 + 4 = 16 + 4 = 20

(2) If you add first: 2 x 8 + 4 = 2 x 12 = 24.

So you get two different answers.  HOWEVER, according to PEMDAS (i.e. order of operations), you MUST multiply first.  Therefore, only the first one is correct (i.e. 20)--NOT the second one (i.e. NOT 24).

Again, you can simply work left-to-right when only addition or subtraction is left.  So if the equation were 2 + 8 - 4, it won't matter if I add or subtract first, the answer is always 6.

Answer 2

PEMDAS

P= Parentheses

E= Exponents

MD = Multiply/Divide from left to right

AS = Add/Subtract from left to right

So if you have parentheses you must eliminate parentheses first. 8+4(5) - (6+10 /2) +44