6th Grade - Order of Operations with Integers

Introduction to Order of Operations

• When solving a math expression, you use the order of operations as a rule to perform the sequence of steps to solve a math equation. Use these steps to solve equations from left to right. 

The best way to remember the sequence of the order of operations is to memorize PEMDAS or a phrase that helps remember the acronym, such as: 

"P-please E-excuse M-my D-dear A-aunt S-Sasha"

Each letter in this phrase stands for the operation you use in sequence to solve the equation:

P- "Parentheses" Perform the operation in the parentheses "()" first.

E- "Exponents" Next, solve the exponents. If the problem has a number with exponents, simplify the exponents.

M & D - "Multiplication and Division" should be solved after exponents. Solve multiplication and/or division in the problem from left to right, whichever comes first. 

A & S - "Addition and Subtraction" should be solved last. Solve addition and/or subtraction in the problem from left to right, whichever comes first.

Examples

Example 1:  9(3 + 4) + 9 $÷$ 3

Solution: Follow PEMDAS to solve the given operation.

First: Solve the operation within the parentheses: (3 + 4) = 7

= 9 (7) + 9 $÷$ 3

Next: Multiply 9 (7) = 63

= 63 + 9 $÷$ 3

Then, Divide: 9 $÷$ 3 = 3

= 63 + 3

Finally, Add: 63 + 3

= 66

 

Eaxmple 2:  $4^3$+ 6 (2 $÷$ 2)

Solution: Follow PEMDAS to solve the given operation.

First, Solve the operation within the parentheses: $\left(2 ÷ 2\right) = 1$.

$4^3+ 6 \left(1\right)$

Second, Simplify the exponent: $4^3 = 4 \times 4 \times 4 = 64$.

$64 + 6\left(1\right)$

Next, Multiply: 6(1) = 6

64 + 6

Finally, Add: 64 + 6

= 70 

 

Example 3: $6^2$ + 7( 4 x 1) - 7 $÷$7

First, Solve the operation within the parentheses $\left(4 \times 1\right) = 4$.

$6^2 + 7 \left(4\right) -7÷7$

Second, Simplify the exponents $6^2 = 6 \times 6 = 36$

$36 + 7\left(4\right) -7÷7$

Third, Multiply 7 x 4 = 28 

$36 + 28 -7÷7$

Next, Divide: $7÷7 = 1$

$36 + 28 - 1$

Then, Add: $36 + 28 = 64$

$64 - 1$

Finally: Subtract: $64 - 1$

= 63

Order of operations cheat sheet

• Follow PEMDAS for solving equations.
• Always work from left to right while solving equations.