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The integers are natural numbers including zero and negatives of the non-zero natural numbers. The set of all integers is often denoted by $\mathbb{Z}$. Integers are subset of the real numbers, they are numbers that can be written without a fractional or decimal, and fall within the set { ......, -3, -2, -1, 0, 1, 2, 3, ....}.

For example, 41, 55, and -99 are integers; 1.4 and $\frac{2.3}{4}$ are not integers.

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## Types of Integers

There are two types of Integers:

1. Positive Integers:

Positive integers are whole numbers greater than zero. Example: 23, 29, 287, 768…etc.

2. Negative Integers:

Negative integers are the opposites of the whole numbers. Example: Negative integers of 19, 38, 458, 594 are -19, -38, -458, -594. Negative numbers indicated by the sign (-).

Zero is neither positive nor negative.

Rule 1: The sum of two positive integers is a positive integer.

Rule 2: The sum of two negative integers is a negative integer.

Rule 3: To add a positive and a negative integer, follow these steps

Step 1: Subtract the smaller number from the larger number.
Step 2: Put the sign of the integer with the greater value.

The properties are,

1. Identity property: 0 + c = c + 0 = c

Example: 41 + 0 = 0 + 41 = 41.

2. Community property: a + b = b + a

Example: 200 + 16 = 16 + 200 = 216.

3. Associative property: (a + b) + c = a + (b + c)

Example: (5 + 24) + 7 = 5 + (24 + 7) = 36.

4. Inverse property: c + (-c) = 0

Example: 7 + (-7) = 0.

### Solved Examples

Question 1: Solve 705 + 922
Solution:

7 0 5

+ 9 2 2
------------
1 6 2 7
------------

Question 2: Evaluate - 4694 - 5887 + 6559
Solution:

We can write given integers as - (4694 + 5887) + 6559

Step 1: Add 4694 and 5887

4694 + 5887 = 10581

=> - (4694 + 5887) = -10581

Step 2: Add -10581 to 6559

Since 10581 > 6559 and 10581 contained negative sign

So reduced the value of 6559 from 10581

- 10581 + 6559 = - 4022

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