When we add two negative integers, we always get _____

(i) The numbers $\dots ., –4, –3, –2, –1, 0, 1, 2, 3, 4, \dots .$ etc. are Integers.

(ii) $1, 2, 3, \dots .$ are positive Integers and $–1, –2, –3, \dots .$ are negative Integers.

(iii) $0$ is an Integer which is neither positive nor negative.

(iv) On an Integer number line, all numbers to the right of $0$ are positive Integers and all numbers to the left of $0$ are negative Integers.

(v) $0$ is less than every positive Integer and greater than every negative Integer.

(vi) Every positive Integer is greater than every negative Integer.

(vii) Two Integers that are at the same distance from $0$, but on opposite sides of it are called opposite numbers.

(viii) The greater the number, the lesser is its opposite.

(ix) The sum of an Integer and its opposite is zero.

2. Absolute Value:

The Absolute Value of an Integer is the numerical value of the Integer without regard to its sign. The absolute value of an Integer $a$ is denoted by $\left|a\right|$ and is given by: $\left|a\right|=\left|-a\right|=a$

3. Addition and Subtraction of Integers:

(i) The sum of two Integers of the same sign is an Integer of the same sign then absolute value of the sum is equal to the sum of the absolute values of the given Integers.

(ii) The sum of two Integers of opposite signs is an Integer whose absolute value is the difference of the absolute values of addend and whose sign is the sign of the addend having greater absolute value.

(iii) To subtract an Integer $b$ from another Integer $a$, we change the sign of $b$ and add it to $a$. Thus, $a-b=a+(-b)$

4. Properties of Integers:

(i) If $a$ and $b$ are two Integers, then $(a-b)$ is also an Integer.

(ii) $–a$ and $a$ are negative or Additive Inverses of each other.