Addition and Subtraction of Integers

� One way of adding and subtracting integers is to use a number line.

� A vertical number line (like a ladder) may be used.

� As we move up the ladder, the integers increase and as we move down, the

integers decrease.

Example

Using a vertical number line, evaluate

(a) (–3) + 2

(b) (–2) + 5

(c) 1 – 3

(d) (–1) – 2

Solution

(a) (–3) + 2 = –1

The little man starts at (

2 steps to reach at –1.

1

Addition and Subtraction of Integers

One way of adding and subtracting integers is to use a number line.

A vertical number line (like a ladder) may be used.

As we move up the ladder, the integers increase and as we move down, the

Using a vertical number line, evaluate

The little man starts at (–3) and moves up

.

One way of adding and subtracting integers is to use a number line.

As we move up the ladder, the integers increase and as we move down, the

(b) (–2) + 5 = 3

The little man starts at (

5 steps to reach at 3.

(c) 1 – 3 = –2

The little man starts at 1 and moves

3 steps down to reach at (

(d) (–1) – 2 = –3

The little man starts at (

2 steps down to reach at (

2

The little man starts at (–2) and moves up

little man starts at 1 and moves

3 steps down to reach at (–2).

The little man starts at (–1) and moves

2 steps down to reach at (–3).

Addition and Subtraction of

( )a b a b+ − = −

( )a b a b− + = −

( ) ( ) ( )a b a b− + − = − +

( )a b a b− − = +

Example

Using a number line or otherwise, evaluate

(a) 4 ( 6)+ −

(b) 3 ( 4)− +

(c) ( 2) ( 3)− + −

(d) 4 ( 2)− −

Solution

(a) 4 ( 6) 4 6 2+ − = − = −

(b) 3 ( 4) 3 4 1− + = − = −

3

Addition and Subtraction of Integers

Using a number line or otherwise, evaluate

(c) ( 2) ( 3) (2 3) 5− + − = − + = −

(d) 4 ( 2) 4 2 6− − = + =

Imagine we need to evaluate the following.

( 24) ( 38)− + − or ( 125) 70− +

� As you must have noted a number line may not be convenient for operating

on large numbers.

� We will use a different method involving a positive column and a negative

column to make our task

4

( 2) ( 3) (2 3) 5− + − = − + = −

Imagine we need to evaluate the following.

( 125) 70− +

As you must have noted a number line may not be convenient for operating

We will use a different method involving a positive column and a negative

column to make our task easy.

As you must have noted a number line may not be convenient for operating

We will use a different method involving a positive column and a negative

Example

Evaluate

(a) ( 44) 56− +

(b) ( 112) ( 236)− + −

(c) ( 48) 164 139− + −

Note: In this method we are going to place all negative integers in the negative

column and all positive integers in the positive column.

Solution

(a) ( 44) 56 12− + =

Note:

(– 2) + 2 = 0

Similarly, (– 44) + 44 = 0.

Thus, 44 in the negative column cancels out with the 44 in the positive column.

We are left with 12 in the positive column

5

In this method we are going to place all negative integers in the negative

column and all positive integers in the positive column.

44) + 44 = 0.

Thus, 44 in the negative column cancels out with the 44 in the positive column.

We are left with 12 in the positive column.

In this method we are going to place all negative integers in the negative

Thus, 44 in the negative column cancels out with the 44 in the positive column.

(b) ( 112) ( 236) 348− + − = −

We add 112 and 236 and

the negative column.

(c) ( 48) 164 139 23− + − = −

We add 48 and 139 and we get 187

negative column.

We then write 187 as 164 + 23.

164 is common to both columns so we cancel

them out.

We are left with 23 in the negative column

Exercises for Practice

1. Using a number line, evaluate

(a) ( 4) 3− +

(b) ( 3) 7− +

(c) 2 5−

(d) ( 4) 1− −

6

( 112) ( 236) 348

and we get 348 in

( 48) 164 139 23− + − = −

We add 48 and 139 and we get 187 in the

187 as 164 + 23.

164 is common to both columns so we cancel

We are left with 23 in the negative column.

Practice

1. Using a number line, evaluate

7

2. Using a number line or otherwise, evaluate

(a) 3 ( 5)+ −

(b) 2 ( 3)− +

(c) ( 2) ( 4)− + −

(d) 5 ( 3)− −

3. Evaluate

(a) ( 39) 73− +

(b) ( 247) ( 158)− + −

(c) ( 54) 109 68− + −

Links:

https://www.mathgames.com/skill/7.65-add-and-subtract-integers

http://www.sheppardsoftware.com/mathgames/integers/FS_NumberLine_integer.htm

http://www.sheppardsoftware.com/mathgames/integers/FS_NumberLine_int_minus.htm