The absolute value of a number is its distance from zero when viewed on a number line.
Distances are never negative. Therefore, the absolute value of a number is always positive or zero.
Let's consider the number and its position on a number line, shown below.
The distance between and zero equals because is five steps away from zero.
Therefore, the absolute value of equals We write this as follows:
There is a fast way to find the absolute value of a number:
The absolute value of a positive number is equal to itself. For example,
To find the absolute value of a negative number, we drop the negative sign. For instance,
What is the value of
The absolute value of a positive number equals the number:
The absolute value of a number gives the distance between the number and zero on a number line.
$\mid 3\! \mid = $
|
a
|
$6$ |
|
b
|
$3$ |
|
c
|
$-6$ |
|
d
|
$1$ |
|
e
|
$-3$ |
$\Bigg| \dfrac{16}3\Bigg| = $
|
a
|
$\dfrac{16}3$ |
|
b
|
$5$ |
|
c
|
$6$ |
|
d
|
$-\dfrac{16}3$ |
|
e
|
$-5$ |
$|\,7.4\,| = $
|
a
|
$7.4$ |
|
b
|
$7$ |
|
c
|
$-8$ |
|
d
|
$-7.4$ |
|
e
|
$8$ |
Find
To find the absolute value of we simply drop the negative sign:
The absolute value of a number gives the distance between the number and zero on a number line.
$\mid-6\!\mid = $
|
a
|
$3$ |
|
b
|
$-3$ |
|
c
|
$6$ |
|
d
|
$4$ |
|
e
|
$-6$ |
$\left| -\dfrac{5}{2} \right| = $
|
a
|
$\dfrac52$ |
|
b
|
$-\dfrac52$ |
|
c
|
$-2$ |
|
d
|
$2$ |
|
e
|
$-3$ |
$\mid-4.7\!\mid = $
|
a
|
$-5$ |
|
b
|
$-4$ |
|
c
|
$-4.7$ |
|
d
|
$5$ |
|
e
|
$4.7$ |
The point shown below represents a number on a number line. The absolute value of this number is What is the number?
The number is negative because it is to the left of zero.
The absolute value of the number is so the distance between that number and zero on a number line is
The negative number at a distance of from zero is so the number is
The point shown above represents a number on a number line. The absolute value of this number is $5.$ What is the number?
|
a
|
$-3$ |
|
b
|
$5$ |
|
c
|
$3$ |
|
d
|
$-5$ |
|
e
|
$6$ |
The point shown above represents a number on a number line. The absolute value of this number is $3.$ What is the number?
|
a
|
$3$ |
|
b
|
$2$ |
|
c
|
$4$ |
|
d
|
$-2$ |
|
e
|
$-3$ |
