Order of operations with integers

When simplifying an expression that has more than one operation symbol, there is a special order you must follow.

  1. Parentheses
  2. Exponents
  3. Multiplication and Division (from left to right)
  4. Addition and Subtraction (from left to right)

Be careful in steps 3 and 4! Multiplication does not always come before division, nor does addition always come before subtraction!  For example, in $$8-3\cdot~(-4)\div~2+4$$ you would multiply before dividing because it is to the left of the division. Similarly, you would subtract before adding because it is to the left of the addition. 

Example 1: $8-3\cdot~(-4)\div~2+4$

8 - 3 • (-4) ÷ 2 + 4

      \ /

8 - (-12) ÷ 2 + 4

        \ /

   8 - (-6) + 4

     \ /

      14 +4

       \ /

        18

 Example 2: $-20\div~(3+7)\cdot~2$

 -20 ÷ (3 + 7) • 2
\ /
-20 ÷ 10 • 2
\ /
-2 • 2
\ /
-4

 

 

 

 

Self-Check


Question 1

Simplify.

$9-(-8)•3=$

[show answer]


Question 2

Simplify.

$(-8)-8(8-4)=$

[show answer]


Question 3

Simplify.

$\large\frac{9-(-3)+(-9)}{(-5)+(+2)}$

[show answer]