Rules for Addition and Subtraction of Integers
Integers are a variety of numbers. They range from positive numbers to negative numbers and also includes the number zero. Integers are anything other than fractions. The rules applicable for addition and subtraction are same for both natural numbers as well as integers because natural numbers are nothing but integers itself. Before we move forwards and learn the rules for addition and subtraction, let’s understand the positive and negative rules that are applied during addition and subtraction operations.
Positive and Negative Rules
When two integers have the same sign or different signs, the product will have either a negative or positive sign. To understand it better, follow the table shown below.
|
Signs |
Result |
|
( + ) x ( + ) = ( + ) |
Positive x Positive = Positive |
|
( + ) x ( – ) = ( – ) |
Positive x Negative = Negative |
|
( – ) x ( + ) = ( – ) |
Negative x Positive = Negative |
|
( – ) x ( – ) = ( + ) |
Negative x Negative = Positive |
Rules
-
When a positive integer is multiplied by a positive integer the result is going to be positive.
-
When a negative integer is multiplied by a positive integer the result is going to be negative.
-
When a positive integer is multiplied by a negative integer the result is going to be positive.
-
When a negative integer is multiplied by a negative integer the result is going to be positive.
-
When there is no symbol present before the integer, it is considered to be positive.
Addition of Integers
There are three possibilities when the addition operation is applied between two integers:
-
The addition operation is applied between two positive integers.
-
The addition operation is applied between negative positive integers.
-
The addition operation is applied between one positive integer and one negative integer.
Addition Rules for Integers
|
Types of Numbers |
Operation Applied |
Final Result |
Example |
|
( + ) + ( + ) |
Add |
Positive ( + ) |
1449 + 1854 = 3303 |
|
( – ) + ( – ) |
Add |
Negative ( – ) |
(- 1449 ) + ( – 1854 ) = – 3303 |
|
( – ) + ( + ) |
Subtract |
Positive ( + ) |
( – 1449 ) + ( 1854 ) = 405 |
|
( + ) + ( – ) |
Subtract |
Negative ( – ) |
( 1449 ) + ( – 1854 ) = -405 |
Subtraction of Integers
There are three possibilities when the subtraction operation is applied between two integers:
-
The subtraction operation is applied between two positive integers.
-
The subtraction operation is applied between negative positive integers.
-
The subtraction operation is applied between one positive integer and one negative integer.
To Easily Solve Difference Problems, Follow the Steps Given Below:
Step 1: Convert the given negative sign to a positive sign.
Step 2: After converting the negative sign, find the inverse of the upcoming number.
For example: find the difference between ( – 7654 ) and ( – 9342 )
Step 1: Convert the given negative sign to a positive sign ( – 7654 ) – ( – 9342 )
⇒ ( – 7654 ) + ( 9342 )
Step 2: After converting the negative sign, find the inverse of the upcoming number.
⇒ ( – 7654 ) + ( – 9342 ) ( opposite of 9 is – 9 )
⇒ ( – 7654 ) + ( – 9342 ) = -16,996 [ Perform addition operation ]
Solved Problems
1. Evaluate the following: a ) 10 + 14, b) ( – 6 ) – ( 12 ), c) ( + 31 ) + ( – 21 )
Solution:
a ) 10 + 14 = 24 ( apply addition operation )
b ) ( – 6 ) – ( 12 ) = – 18 ( addition is performed two negatives numbers )
c) ( + 3 ) + ( – 2 ) = 10
Step 1: Convert the given negative sign to a positive sign ( + 31 ) + ( – 21 )
⇒ ( + 31 ) – ( + 21 )
Step 2: After converting the negative sign, find the inverse of the upcoming number.
⇒ ( + 31 ) + ( – 21 ) ( opposite of 9 is – 9 )
⇒ ( + 31 ) + ( – 21 ) = 10 [ Perform addition operation ]