### Addition of Integers:

In order to add two integers on a number line, we follow the following step wise procedure:

**PROCEDURE**

**STEP 1)** Draw a number line and mark integers on it.

**STEP 2)** Start from the point representing the first number on the number line.

**STEP 3)** Move as many units as the second number to the

i) ** right of the first number**, if the second number is

**.**

*positive*ii)

**, if the second number is**

*left of the first number***.**

*negative***STEP 4)**Obtain the number representing the point reached in the previous step. This number represents the required sum of the given integers.

**Example 1:** Add +7 and -4 on the number line.

**Solution:** On the number line we start from 0 and move 7 steps to the right to reach a point A. Now, starting from A, we move 4 steps to the left to reach a point B.

And, B represents the integer 3.

Therefore, 7 + (-4) = 3.

**Example 2:** Add +3 and -8 on the number line.

**Solution:** On the number line we start from 0 and move 3 steps to the right to reach a point A. Now, starting from A, we move 8 steps to the left to reach a point B.

B represents the integer -5.

Therefore, 3 + (-8) = -5.

**Example 3:** Add -2 and -4 on the number line.

**Solution:** On the number line we start from 0 and move 2 steps to the left to reach a point A. Now, starting from A, we move 4 steps to the left to reach a point B.

Clearly, B represents the integer -6.

Therefore, (-2) + (-4) = -6.

#### Rules for Addition of Integers:

**Rule 1)** To add two positive integers or two negative integers, we add their absolute values and assign the sign of the addends to the sum.

**Rule 2)** To add a positive and a negative integer, we determine the difference of their absolute values and assign the sign of addend having greater absolute value.

**Example 1:**

Add the following integers: 1259 and 3214

**Solution:**

We observe that both the integers are positive. By using the rule for addition of integers having the same sign, we have

1259 + 3214 = [|1259| + |3214|]

= [1259 + 3214]

= 4473

Therefore, 1259 + 3214 = 4473.

**Example 2:**

Add the following integers: -523 and 937

**Solution:**

The integers to be added are of the unlike signs, therefore to add them we find the difference of their absolute values and assign the sign of the addend having greater absolute value.

(-523) + 937 = [|937| – |-523|]

= [937 – 523] [Since, |937| = 937 and |-523| = 523]

= 414