PEMDAS. “Please Excuse My Dear Aunt Sally”. This reflects the order of operations:

 

Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction.

 

Since multiplication and division are the same, as is addition and subtraction, this mnemonic can be simplified to

 

PEMAS: Please Excuse My Aunt Sally.

 

Multiplication and division. M said we start with the left. This is correct, but it must be stressed that the order does not matter. E.g.,

 

2 ÷ 3 · 1 / 2 = 2 · 1 / 2 ÷ 3.

 

This is why we start from the left.

 

Some calculators do not obey these rules. Errors can result. They should check:

2 + 3 * 4 should be 14, not 24.

 

The example was

 

-4 + 2(-2 + 5)2.

 

We get

 

-4 + 2 · 32.

 

We must write this without the parenthesis, to stress the rule that we first performed the operation on the inside of the parenthesis. That is, we do not write this as

 

-4 + 2 · (3)2.

 

Another example:

 

-4(-3)2+6(-3) – 5

 

Doing the parenthesis first:

 

-4 · 9 - 6 · 3 – 5

 

Note that when we finish doing the parenthesis we write the expression without the parenthesis.

 

Another example:

 

72 - 4(8 - 3) / 2.

 

One student distributed the 4 but not the 2. This is the same as

 

72 - 4 / 2(8 - 3).

 

If there are several ways to do a problem, the teacher should ask the class if anyone did it another way.