### People’s Expressions, on Mondays are Dire, Arduous and Stressful

Remember the ETAA mantra? Today we begin the most important item on the math section: Order of Operations, AKA PEMDAS. Of the 33 questions on the math section, 12 of them are PEMDAS. The 4 Numeric Sequence questions are the easy lay-ups, the PEMDAS questions are the bread and butter. By mastering both, you are over halfway to getting a perfect score on the math section. (And I promise you, the Linear Equations are cake once you see the tricks).

We are experts with Numeric Sequences now, but those math problems only measure your ability to add and subtract. Today, we will employ the full monty of numeric operations:

- Parenthesis
- Exponents
- Multiply/Divide
- Add/Subtract

Notice that there are only 4 (not 6) levels of math operations. Consider the following problem:

8 × 5 ÷ 2 × 5

What do you think the right answer is?

How about this one:

12 + 8 − 6 + 4

These two problems illustrate why there are only 4, not 6, levels to PEMDAS.

On the ETAA test, you will see crazy looking algebraic expressions, which will lead participants who didn’t prep for the test to think that they need to do some algebra. This leads to bulging veins in the temples and neck. NO!!! All you need to do is plug in the provided numbers for the associated letter (variable), and apply the rules of PEMDAS — simplify some crazy looking algebra down to a simple number, that most of the time will be an integer, no fraction or decimal.

The plugin process is what we will practice and drill, over and over again, during this course, because that’s the real skill you need to quickly come to the right answer. How much time do you have for each math question?

Let’s take a look at each level of PEMDAS:

#### Parenthesis

Whatever is inside a set of parenthesis break the usual PEMDAS rules. Simplify what is inside the parenthesis before you simplify anything outside. If you made a mistake with the problems above, it is because you applied parenthesis to the multiplications and additions.

#### Exponents

A “superscript” means that you are going to do something like multiplication, but different. Consider the following exponent:

## 4^{3}

This does not mean 4 × 3. It means to multiply four by itself, three times:

4 × 4 × 4 = 64

You won’t see many exponents greater than 3 or 4 on the test. You should try to memorize as many squares as you can to help speed up your finding the answer to a PEMDAS question (page 21 in the binder).

#### Multiply/Divide

Remember, you work *both* multiply *and* divide left to right. And like exponents, you will get to the answer faster if you memorized the Times Table (page 3 in the Binder) and the Truth Table (page 9).

#### Addition/Subtraction

The easiest level, right? Forget about it. Adding/subtracting is where most of the mistakes happen on ETAA PEMDAS questions. Why?

SIGNED NUMBERS

Remember, adding a negative is the same as takeaway. Subtracting a negative number is the same as adding. A lot of people forget that when taking the test.

Finally, the best way to speed up your ability to answer PEMDAS questions correctly is, …

PRACTICE, PRACTICE, PRACTICE.

Don’t forget about about the Takehome Materials. There are 4 sets of 60 PEMDAS problems (and the answers!) for you to solve whenever you have some time, preferably a few each day for the next month.

So let’s practice with page 72 in The Binder.

Try answering the other questions, and we’ll pick up with them on Wednesday. None of the answers have fractions/decimals.