# Subtraction of Integers on Number line

In this post we will discuss how to subtract integers using number lines.
There are three possibilities of subtraction of integers
a. Both integers are positive
b. Both integers are negative
c. One integer is positive and other is negative

When both the integers are positive integers-

1.Subtract 5 – 2

Steps-

• Here 5 is positive integer then first we move 5 steps to the right from 0.
• Here 2 is also a positive integer but for subtraction we move 2 steps to the left of 5
• We reach at 3

Thus we get (5) – (2)= +3

2. Subtract 7 – 4

Steps-

• Here 7 is positive integer then first we move 7 steps to the right from 0.
• Here 4 is also a positive integer but for subtraction we move 4 steps to the left of 7
• We reach at 3

Thus we get (7) – (4)= +3

When one integer is positive and another is negative

1. Subtract (-5) and 2

• Here -5 is negative integer so we move 5 steps to the left of 0
• Now 2 is positive integer but for subtraction we move 2 steps left to the -5.
• We reach at -7
• Thus we get (-5)-(+2)=-5-2=-7

2. Subtract (-3) and 6

• Here -3 is negative integer so we move 3 steps to the left of 0
• Now 6 is positive integer but for subtraction we move 6 steps left to the -3
• We reach at -9
• Thus we get (-3)-(+6)= – 3 – 6= -7

When both integers are negative integers

1.Subtract -5 and -2

==> -5 – (-2)

Steps-

• Here -5 is negative integer so we move 5 steps to the left of 0
• In this case we have to take additive inverse of -2 as it is +2, Then it becomes (-5)+2
• Now after reaching at -5 we move 2 steps to the right of -5 (as 2 becomes positive integer)
• We reach at -3
• Thus we get (-5)-(-2)=-5+2=-3

2. Subtract -5 and -6

Steps-

• Here -5 is negative integer so we move 5 steps to the left of 0
• In this case we have to take additive inverse of -6 as it is +6, Then it becomes (-5)+6
• Now after reaching at -5 we move 6 steps to the right of -5 (as 6 becomes positive integer)
• We reach at +1
• Thus we get (-5)-(-6)=-5+6= 1

Let us take a special case

We have to subtract -3 from -3
Here (-3)-(-3)=(-3)+(additive inverse of -3 is +3) ==> (-3) + 3 = 0
It means when  we subtract two same digits on number line, we reach at point 0