Addition of Integers

We will learn addition of integers using number line.

We know that counting forward means addition.


Addition of Two Positive Integers:

When we add positive integers, we move to the right on the number line.

For example to add +2 and +4 we move 4 steps to the right of +2. 

Addition on Number Line

Thus, +2 +4 = +6.

Addition of Two Negative Integers:

When we add two negative integers, we move to the left on the number line. 

For example to add -2 and -4 we move 4 steps to the left of -2. 

Integer Addition on Number Line

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


Addition of a Negative Integer and a Positive Integer:

When a negative integer is added to a positive integer we move to the left on the number line.

For example to add +2 + (-4), we move 4 steps to the left of +2. 

Adding Integers on Number Line

Thus, +2 + (-4) = -2.


Addition of a Positive Integer and a Negative Integer:

When a positive integer is added to a negative integer we move to the right on the number line.

For example to add (-6) + 3, we move 3 steps to the right of -6.

Addition of Integers

Thus, (-6) + 3 = -3.


We can add two integers having same sings by adding their absolute values and placing the common sign of two integers before it.


Solved Examples on Addition of Integers:

1. Find the value +18 + (+5)

Solution:

Absolute value of |+18| = 18

Absolute value of |+5| = 5

Sum of absolute values = 18 + 5

Since, both integers have common sign +, we place + sign in the answer.

Hence, +18 + (+5) = +23.

We can add two integers having opposite signs by finding difference of their absolute values and placing the sign of the integer with the greater absolute value before it.


2. Find the value -38 + (+28)

Solution:

Absolute value of |-38| = 38

Absolute value of |+28| = 28

Difference of absolute values = 38 – 28 = 10

Placing the sign of the integer with the greater absolute value = -10

Hence, -38 + (+28) = -10.

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