All real numbers can be represented on a number line as shown below.
A number line can be used to model addition and subtraction of real numbers.
Addition :
To model addition of a positive number, move right. To model addition of a negative number, move left.
Subtraction :
To model subtraction of a positive number, move left. To model subtraction of a negative number, move right.
Add or subtract using a number line.
Example 1 :
-3 + 6
Solution :
On a number line, start at 0 and move left to -3.
To add 6, move right 6 units.
-3 + 6 = 3
Example 2 :
-2 - (-9)
Solution :
On a number line, start at 0 and move left to -2.
To subtract -9, move right 9 units.
-2 - (-9) = 7
The absolute value of a number is its distance from zero on a number line. The absolute value of 5 is 5.
|5| = 5
|-5| = 5
Adding Numbers with the Same Sign :
Add the absolute values and use the sign of the numbers.
4 + 7 11 |
-4 + (-9) -13 |
Adding Numbers with Different Signs :
Subtract the absolute values and use the sign of the number with the greater absolute value.
-7 + 12 5 |
5 + (-14) -9 |
Two numbers are opposites, if their sum is 0. A number and its opposite are additive inverses and are the same distance from the zero. They have the same absolute value.
For example, 5 and -5 are opposites, because
5 + (-5) = 0
Additive inverse of 5 is -5 and additive inverse of -5 is 5.
And also, 5 and -5 have the same absolute value.
|5| = 5
|-5| = 5
Words :
The sum of a real number and its opposite is 0.
Numbers :
7 + (-7) = (-7) + 7 = 0
Algebra :
For any real number y,
y + (-y) + (-y) + y = 0
Words :
To subtract a number, add its opposite. Then follow the rules for adding signed numbers.
Numbers :
2 - 6 = 2 + (-6) = -4
Algebra :
For two real numbers x and y,
x - y = x + (-y)
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