Order of Operations

Order of Operations

GEMA

Why do we have Order of Operations?

When solving multi-step math problems, Order of Operations tells us what order to complete the steps in. If we didn't have the Order of Operations, we could get more than one answer for the same problem, which just doesn't make sense. The Order of Operations tells us what to do first, second, etc...

How can I remember the order?

You have probably learned PEMDAS in elementary school to help you remember the steps. In middle school, we use a different acronym that is a little more specific about what to do. We call this GEMA.

GEMA

• Grouping

• Exponents

• Multiplication & Division from left to right

• Addition & Subtraction from left to right

Grouping

• Parentheses ( )

• Brackets [ ]

• Fraction Bar

Exponents

• 4²

• 4 squared

• 5 cubed

• 3 to the 4th power

Multiplication/Division

• LEFT TO RIGHT AS THEY APPEAR

Addition/Subtraction

• LEFT TO RIGHT AS THEY APPEAR

Let's see what you can do!

Multiple Select

Which of the steps in GEMA require use of the left to right rule? (Hint: There is more than one answer.)

• Grouping

• Exponents

• Multiplication/Division

• Addition/Subtraction

Which of the steps in GEMA require use of the left to right rule?

Both MULTIPLICATION/DIVISION and ADDITION/SUBTRACTION are done from left to right as they appear. However, multiplication and division ALWAYS come before addition and subtraction.

Multiple Choice

Which operation would you do first to solve this problem?

 $\left(3\ +\ 3\right)\ \cdot\ 4\ \div\ 2$  

• Addition

• Multiplication

• Division

Which operation would you do first to solve this problem?  

 $\left(3\ +\ 3\right)\ \cdot\ 4\ \div\ 2$  

You would do ADDITION first, because it is in parentheses, which is part of Grouping.

Multiple Choice

Calculate the answer to this expression.

 $\left(3\ +\ 3\right)\ \cdot\ 4\ \div\ 2$  

• 12

• 2

• 6

• 9

 $\left(3\ +\ 3\right)\ \cdot\ 4\ \div\ 2$  
 $6\ \cdot\ 4\ \div\ 2$  
 $24\ \div\ 2$  
 $12$  

 $12\ is\ the\ answer!$ 

Multiple Choice

Which operation would you do first to solve this problem?

 $3\ +\ 3\ \cdot\ 4\ \div\ 2$  

• Addition

• Multiplication

• Division

Which operation would you do first to solve this problem?  

 $3\ +\ 3\ \cdot\ 4\ \div\ 2$  

You would do MULTIPLICATION first, because we multiply before adding, and in the expression, it comes before division from left to right.

Multiple Choice

Calculate the answer to this expression.

 $3\ +\ 3\ \cdot\ 4\ \div\ 2$  

• 12

• 9

• 8

• 18

 $3\ +\ 3\ \cdot\ 4\ \div\ 2$  
 $3\ +\ 12\ \div\ 2$  
 $3\ +\ 6$  
 $9$  

 $9\ is\ the\ answer!$ 

Multiple Choice

Which operation would you do first to solve this problem?

 $5\ \cdot\ \left(4\ +\ 6\right)\ -\ 3^2$  

• Addition

• Multiplication

• Subtraction

• Exponents

Which operation would you do first to solve this problem?  

 $5\ \cdot\ \left(4\ +\ 6\right)\ -\ 3^2$  

You would do ADDITION first, because it is GROUPED together by the parentheses, and we always do grouping first.

Multiple Choice

Calculate the answer to this expression.

 $5\ \cdot\ \left(4\ +\ 6\right)\ -\ 3^2$  

• 15

• 20

• 41

• 44

 $5\ \cdot\ \left(4\ +\ 6\right)\ -\ 3^2$  
 $5\ \cdot\ 10\ -\ 3^2$  
 $5\ \cdot\ 10\ -\ 9$  
 $50\ -\ 9$  
 $41$  

 $41\ is\ the\ answer!$ 

Try a few more for me. You've got this!

Multiple Choice

Calculate the answer to this expression.

 $\left(8\ +\ 5\right)\ \cdot\ 2$  

• 18

• 15

• 21

• 26

Multiple Choice

Calculate the answer to this expression.

 $56\ \div\ \left(2\ \cdot\ 4\right)$  

• 112

• 7

• 28

Multiple Choice

Calculate the answer to this expression.

 $80\ -\ \left(8\ +\ 4\right)$  

• 68

• 76

• 84

Poll

Stoplight Review: How are you feeling about Order of Operations?

• Green Light: Full speed ahead!

• Yellow Light: I'll get there with some practice.

• Red Light: Stop! What are we doing?