On this page, we’ll explore the **Order of Operations**, a key math rule that ensures everyone arrives at the same answer when performing calculations.

The Order of Operations is** a set of rules that tells us the correct sequence** when performing calculations with multiple operations (mixtures of addition, subtraction, multiplication, division, etc.).

Following these rules ensures that everyone gets the same answer every time.

For example: $$2+3\times 4$$

, they will get this result.$${\color{red}2+3}\times 4={\color{red}5}\times 4=20$$(In this case, it__If one performs the operations from left to right____does not follow__the standard order of operations. Therefore,)__the answer is incorrect.__

- However,
, they will get a different result. $$2+{\color{red}3\times 4}=2+{\color{red}12}=14$$ (In this case, it__if one performs the multiplication first____follows__the standard order of operations. Therefore,)__the answer is correct.__

Since the two methods give different answers, "*the order of operations*" must be established to ensure everyone knows which steps to perform first. (The order of operations is, therefore, __simply a universal agreement__ that everyone follows.)

Remember **"P**lease** E**xcuse** M**y** D**ear** A**unt** S**ally** (PEMDAS)"**

**P**arentheses first**E**xponents (you'll learn these later)**M**ultiplication and**D**ivision (left to right)**A**ddition and**S**ubtraction (left to right)

$2\times (5+3)=2\times \underbrace{\color{red}(5+3)}_{①}=2\times {\color{red}8}=16$

${\color{red}(5+3)}$ is performed first because it is inside** **the **P**arentheses.

$2+3\times 4=2+\underbrace{\color{red}3\times 4}_{①}=2+{\color{red}12}=14$

${\color{red}3\times 4}$ is performed first because **M**ultiplication and **D**ivision (Step 3.) are done before **A**ddition and **S**ubtraction (Step 4.)

$(2+3)\times 4=\underbrace{\color{red}(2+3)}_{①}\times 4={\color{red}5}\times 4=20$

${\color{red}(2+3)}$ is performed first because the **P**arentheses (Step 1.) is done before **M**ultiplication and **D**ivision (Step 3.)

*Please compare this example with Example 2.*

$30\div 5\times 3=\underbrace{\color{red}30\div 5}_{①}\times 3={\color{red}6}\times 3=18$

${\color{red}30\div 5}$ is performed first because **M**ultiplication and **D**ivision (Step 3.) is done __from left to right__. If we do it differently, we will get the wrong answer, as shown below.

$30\div {\color{red}5\times 3}=30\div {\color{red}15}=2$ (**"Wrong"**)

$20\div 2+8\times 3=\underbrace{\color{red}20\div 2}_{①}+\underbrace{\color{red}8\times 3}_{①}=10+24=34$

Each **M**ultiplication and **D**ivision (Step 3.) __at these 2 places __are done before **A**ddition and **S**ubtraction (Step 4.)

$21-20\div 2+3=21-\underbrace{\color{red}20\div 2}_{①}+3=\underbrace{21-{\color{red}10}}_{②}+3=11+3=14$

**M**ultiplication and **D**ivision (Step 3.) is done before **A**ddition and **S**ubtraction (Step 4.) __from left to right__

$21-20\div (2+3)=21-20\div \underbrace{\color{red}(2+3)}_{①}=21-\underbrace{20\div {\color{red}5}}_{②}=21-4=17$

Compared to Example 6, $\color{red}(2+3)$ is performed first because it is inside the **P**arentheses.

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