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Reference

Method

To add a positive integer $b$ to an integer $a,$ move $b$ units to the right-hand side of $a$ on a number line. Consider $a=3$ and $b=7.$ *expand_more*
*expand_more*
Subtracting a positive integer $b$ from $a$ is similar. In this case, move $b$ units to the left-hand side of $a$ on a number line. Consider the subtraction of $b$ from $a$ using the same example values.

$a=3,b=7⇓3+7=? $

The process of adding $a$ and $b$ will be illustrated using these values. 1

Plot $a$ on a Number Line

Begin by graphing $a$ on a number line. In this case, the value of $a=3.$ Move $3$ units to the right side of $0$ to plot $3.$

2

Move $b$ Units to the Right-Hand Side of $a$

Starting from $a,$ move $b$ units to the right to add $b$ units to $a.$ For this example, move seven units to the right of $3$ to add $7$ to $3.$

The point is now at $10.$ This means that the sum of $3$ and $7$ is $10.$

$3+7=10 $

$a=3,b=7⇓3−7=? $

This process can be performed on the number line.
Now the point is at $-4.$ The result of subtracting $7$ from $3$ is $-4.$

$3−7=-4 $

This process applies to adding or subtracting any positive integer $b$ from a positive or negative integer $a.$ The result can be a negative integer, a positive integer, or $0.$Method

Adding a negative integer $-b$ to an integer $a$ requires changing the addition sign to a subtraction sign and changing $-b$ to its additive inverse, $b.$ To illustrate this, consider $a=4$ and $-b=-5.$
*expand_more*
*expand_more*
*expand_more*
Subtracting a negative integer $-b$ from an integer $a$ requires changing the subtraction sign to an addition sign and changing $-b$ to its additive inverse. To illustrate this, consider $a=-2$ and $-b=-6$

$a=4,-b=-5⇓4+(-5)=? $

Next, this process is shown with these pair of integers. 1

Change the Addition Sign to a Subtraction Sign and Change $-b$ to $b$

Change the addition sign to a subtraction sign and then change $-b$ to its opposite $b.$ In this example, $-b=-5$ and its opposite is $5.$

$4+(-5)⇔4−5 $

The addition of an integer and a negative integer is now turned into a subtraction of an integer and a positive integer. 2

Plot $a$ on a Number Line

The process now is similar to subtracting one positive integer from another. First, plot $a$ on a number line. The value of $a,$ in this case, is $4.$

3

Move $b$ Units to the Left-Hand Side of $a$

Now move $b$ units to the left-hand side of $a$ to subtract $b$ from $a.$ In this example, move $5$ units to the left of $4$ to subtract $5$ from $4.$

The point is now at $-1.$ This means that the subtraction of $5$ from $4$ is $-1.$ This is also the result of adding $-5$ to $4.$

$4+(-5)=-1 $

$a−(-b)⇔a+b-2−(-6)⇔-2+6 $

The result is the sum of an integer and a positive integer.
The point is now at $4.$ The result of subtracting $-6$ from $-2$ is $4.$

$-2−(-6)=4⇔-2+6=4 $

This process applies to adding or subtracting any netative integer $-b$ from a positive or negative integer $a.$ The result can be a negative integer, a positive integer, or $0.$Loading content