Addition and Subtr One way of adding A vertical number l As we move up the integers decrease. Example Using a vertical number li (a) (–3) + 2 (b) (–2) + 5 (c) 1 – 3 (d) (–1) – 2 Solution (a) (–3) + 2 = –1 The little man starts a 2 steps to reach at –1. 1 raction of Integers and subtracting integers is to use a num line (like a ladder) may be used. e ladder, the integers increase and as w ine, evaluate at (–3) and moves up . mber line. we move down, the
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Addition and Subtraction of Integers Example · Addition and Subtraction of Integers One way of adding and subtracting integers is to use a number line. A vertical number line (like
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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− + = − = −
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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
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( 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
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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.