Simplifying with PEMDAS

Order of Operations

by Angela Cochran

​Order of Operations

​P arentheses

​E xponents

​M ultiplication

​D ivision

​A ddition

​S ubtraction

​or

​

​

​or

​What comes first?

​

​ P E (M D) (A S)

​

​

​

​

​Parentheses

​P E M D A S

The parentheses in the problem indicate multiplication. (There is not anything to simplify within the parentheses.)

​There are not any exponents.

​There is multiplication indicated by 3(7). This would be completed before the division because multiplication & division are as they appear from left to right.

​What is the next step?

​Almost done: 2 + 21 + 4

​The only operation remaining is ADDITION. The great thing about addition is you can add in any order and still get the same answer. You can add from left to right or you can MIX it up and add right to left or however you want.

​​2 + 21 + 4

​

​23 + 4

​27

​{

Multiple Choice

What does the E in PEMDAS stand for?

• Equals

• Equivalent

• Exponent

• Even

Multiple Choice

Solve: (2×10)+4

• 20

• 26

• 7

• 24

Multiple Choice

Solve: (3+12)-3²

• 4

• 6

• 2

• 7

Multiple Choice

12 - 4 x 2 = 

• 16
• 4
• 8
• 18

Multiple Choice

What would be my first step? 3 + 4 x 6 - 4 =

• Addition

• Multiplication

• Subtraction

• Division

Multiple Choice

Which operation would you do first?

(12 + 10) ÷ 10 x 14 - 6

• Division of 10 / 10

• Multiplication of

  10 x 14

• Addition of 12 + 10

• Subtraction of 14 - 6

Multiple Choice

(7 + 41) ÷ 2 – 15 =

• 19
• 9
• 25
• 3

​What about the negatives???

​When completing order of operation problems, you NEED to pay attention to the SIGN in front of EVERY number.

​In a simple problem like the following, you should do addition and subtraction together from left to right. (Addition doesn't not come before Subtraction, unless it appears first from left to right.)

5 - 3 + 2 ​

​However, if you choose to do the addition of 2 first, notice that the sign in front of 3 is negative. Therefore it is -3 + 2.

​5 - 3 + 2 OR 5 - 3 + 2

2 + 2 OR 5 - 1

​4 4

​{

​{

​Simplify: 6 - 3 x 9 - (8 - 6)³

​For order of operations in this problem, there are Parentheses, Exponents, Multiplication, and Subtraction

​

​Start inside the Parentheses: 6 - 3 x 9 - (8 - 6)³

​6 - 3 x 9 - (2)³

Next is Exponents: ​6 - 3 x 9 - 8

​Now Multiplication (watch the signs): 6 - 3 x 9 - 8

​ 6 - 27 - 8

​Now Subtract (left to right): -21 - 8

​ -29

Multiple Choice

9 - 3 + 4

• 10
• 2
• 16

Multiple Choice

3 x 8 - (9 - 7)³

• 16
• 18
• 0

Multiple Choice

35 ÷ 7 x 2 - 4

• 3.5
• -1.5
• 6

Multiple Choice

18 − 4 × 2

• 28
• 16
• 10
• 12

Multiple Choice

7[12 − (6 − 2) ÷ 4]

• 7
• 77
• 14
• 0

Multiple Choice

7 - 3(4 - 9) + 12 $$\div$$ (-2)

• -2

• -14

• 2

• 16

Fill in the Blank

$$\left(10\div\left(-5\right)-\left(-2\right)\right)\times\left(-3\right)^3$$  

What do we do when we have a fraction bar?

​( )

​( )

Multiple Choice

$$\frac{2\left(6\ +\ 8\right)\ +\ 22}{25\ \times3\ -\ 50}$$  

• 2

• $$\frac{42}{25}$$  

• $$-\frac{2}{47}$$  

• 3

Multiple Choice

$$\frac{\left(-2\right)\left(-5\right)^3}{\left(10\right)\left(-5\right)}$$  

• $$-\frac{4}{5}$$  

• -5

• 7

• -20

Multiple Choice

$$\frac{3\left(15-13\right)\ -\ 6}{4\times5}$$  

• $$\frac{13}{10}$$  

• 20

• 0

• 5

Multiple Choice

$$\frac{-5\left(3\right)\ -\ 4\left(7\right)}{7\ +\ 6\left(-1\right)}$$  

• -43

• 13

• -13

• $$-\frac{43}{13}$$  

Multiple Choice

$$\left(-2+6\right)^2\div2\ +\ 9\left(7-2\right)$$  

• $$\frac{16}{35}$$  

• 77

• $$\frac{64}{35}$$  

• 53