Operations with Integers

Hierarchy of the Operations

1. Carry out the operations in parentheses, brackets and braces.

2. Calculate the powers and roots.

3. Calculate the products and quotients.

4. Perform the additions and subtractions.

Example

14 − {7 + 4 · 3 - [(−2)2 · 2 − 6)]}+ (22 + 6 − 5 · 3) + 3 − (5 − 23 : 2) =

First, calculate the powers, products and quotients within the parentheses.

14 − [7 + 4 · 3 −(4 · 2 − 6)] + (4 + 6 − 5 · 3) + 3 − (5 − 8 : 2) =

Then, calculate the products and quotients within the parentheses.

14 − [7 +12 −(8 − 6)] + (4 + 6 − 15) + 3 − (5 − 4) =

Then, calcualte the sums and differences within the parentheses.

14 − (7 +12 −2) + (−5) + 3 − (1) =

14 − (17) + (−5) + 3 − (1) =

The removal of parentheses can be done under the following conditions:

If the parentheses is preceded by the + sign, the sign can be deleted to maintain the terms it contains.

If the parenthesis is preceded by the sign −, remove the brackets and change the sign to all the terms it contains.

14 − 17 − 5 + 3 − 1 = −6