PEMDAS Examples

PEMDAS is an abbreviation that is often used to help students in mathematics remember the order of operations. In other words, it helps them remember which mathematical operation to perform and in which order.

When we first learn math, equations only have one operation. We either add, subtract, multiply, or divide.

Examples: 2 + 3 = 5   9 - 2 = 7   10 x 3 = 30    81/9 = 9

However, as math becomes more complicated, the equations have multiple steps. For example, how would you solve this equation?

3+8(4-2)-7

PEMDAS helps you remember how to solve the equation.

P = parentheses; you should solve anything inside of parentheses first.
E = exponents; if there are an exponents in the equation, you should solve those second.
M = Multiply
D = Divide
A = Add
S = Subtract

PEMDAS helps you to remember to take care of parentheses and then exponents first. After that, you perform the four operations. It is important to note, though, that you do not have to do all multiplication first and then division. Nor do you have to do all addition first and then subtraction. You should move across the equation from left to right, performing all multiplication and division. Then, go back across from left to right, performing all addition and subtraction.

So, to solve our equation, these are the steps we would take:

3+8(4-2)-7

Parentheses First = 3+8(2)-7
Exponents-none
Multiply/Divide   3+16-7
Add/Subtract   19-7 = 12

Note, there are various symbols that are commonly used for multiplying and dividing.

Multiply Symbols: x, . , or if a number is next to a parentheses, it means to multiply that number by what is in the parentheses.

Divide Symbols: / or fraction bar, ÷

Examples of PEMDAS

1. 10+4(9+8)+12/3-4
a. Parentheses   10+4(17)+12/3-4
b. Exponents-none
c. Multiply/Divide   10+68+4-4
d. Add/Subtract   78+0 = 78

2. 3²-(9-5)+7x3-8÷2
a. Parentheses   3²-(4)+7x3-8÷2
b. Exponents   6-4+7x3-8÷2
c. Multiply/Divide   6-4+21-4
d. Add/Subtract   2+17=19

3. 14-10²(3x8-2+1)+(15÷5-2)
a. Parentheses (follow the order of operations within the parentheses as well. 14-10²(24-2+1)+(3-2)

14-10²(21)+1