Order of Operations

While doing math operations, such as multiplication and addition, you have to do them in a certain order. 

*PEMDAS*

--Parenthesis--

--Exponents--

--Multiplication--

--Division--

--Addition--

--Subtraction--

There is an easy way to remember the order. Say the sentence "Please Excuse My Dear Aunt Sally". The P stands for parentheses( ), the E means exponents ^ or xy (this includes roots), the M means multiplication *, the D means division /, the A means addition +, and finally the S means subtraction -. 

*If a certain problem doesn't contain one of the above mathematical operations, simply skip the operation and move on to the next one.

    Example: If you are doing a problem that doesn't have any parenthesis, skip over that step, and go to the next one (which would be exponents).

  Example 2: In a math problem like this one, 4+5*3, you would multiply 5 by 3 and then add the 4 for a total of 19.

* Also Multiplication/Division and Addition/Subtraction come in pairs. So if you get 4-5+6, you don't have to add 5+6 before you subtract 4. You can just go left to right, unless one of the other operations inhibits you to do so.

    Example 1: If you have 4-(5+6), you have to add the 5 and 6 before you subtract the 4,

                         but if you have 4-5+6, you would take 4-5=-1, and then take -1+6

    Example 2: If you have 12/4*3, you would take 12/4=3, and then multiply that by 3, so 3*3=9

                        but if you had 12/(3*4), you would have to take the 3*4 first=12, and then divide that by 12 which gets you 12/12=1

This can be difficult if you have many operations to do.

To solve (3*2)-42+(1+2*5)

First do what is in the parentheses 3*2 is 6 and 2*5+1 is 11.

                           (6) -42 + (11)

Now you don't need the () and your equation looks like this, 6-42+11.

Next do the exponent. 4 to the 2nd is 16.

                                    42 =16

Now you have 6-16+11.

                             6-16+11=1                  Answer is 1

• Simplify 4 – 3[4 –2(6 – 3)] ÷ 2.

  • I will simplify from the inside out: first the parentheses, then the square brackets, being careful to remember that the "minus" sign on the 3 in front of the brackets goes with the 3. Only once the grouping parts are done will I do the division, followed by adding in the 4.

    • 4 – 3[4 –2(6 – 3)] ÷ 2

    •     = 4 – 3[4 – 2(3)] ÷ 2

    •     = 4 – 3[4 – 6] ÷ 2

    •     = 4 – 3[–2] ÷ 2

    •     = 4 + 6 ÷ 2

    •     = 4 + 3

    •     = 7