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Study Guide

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The order in which we complete a mathematical equation or expression is super important. Doing the steps of a problem out of order can lead to a totally different answer, even if we do the calculations correctly. So, for everyone to get the same answer, the **order of operations** was developed. We'll be using these almost every day of our mathematical careers from now on.

All equations and expressions must be completed in the following order. There's even a handy acronym to help us remember it.

**P**arentheses: simplify everything inside the parentheses.

**E**xponents: simplify any exponents (see Powers and Roots.)

**M**ultiplication &**D**ivision: multiply and divide from left to right.

**A**ddition &**S**ubtraction: add and subtract from left to right.

PEMDAS will be our friend for life. If we have trouble remembering our new BFF's name, we can try out this memory trick:

"**P**lease **E**xcuse **M**y **D**ear **A**unt **S**ally"

**Look Out**: even though M comes before D, multiplication and division are equals; we'll need to complete these operations from left to right. The same is true for addition and subtraction. Think of them as equal partners.

Let's try simplifying 4(3 + 7)^{2} – 25(100 ÷ 5) ÷ 50. Where do we start?

According to our new buddy PEMDAS, we simplify all the stuff inside the parentheses (P) first.

4**(3 + 7)**^{2} – 25**(100 ÷ 5)** ÷ 50 =

4(10)^{2} – 25(20) ÷ 50

Nice. Next up is the E in PEMDAS, which stands for exponents. There's an exponent of 2 on that 10, so our next step is to find (10)^{2}.

4**(10) ^{2}** – 25(20) ÷ 50 =

4(100) – 25(20) ÷ 50

So far, so good. Our next letters are M and D, so now we rock multiplication and division. Remember, these two letters are equal partners, so we do all our multiplying and dividing from left to right.

**4(100)** – 25(20) ÷ 50 =

400 – **25(20)** ÷ 50 =

400 – **500 ÷ 50** =

400 – 10

Our very last letters in PEMDAS are A (addition) and S (subtraction), which we also do from left to right. There isn't any addition here, so we finish up by subtracting 10 from 400.

400 – 10 = 390

We're done!

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