What is the absolute value? And how do we find it? Absolute value of a number is the
distance between that number and zero on a number line. Let me show you what I mean. The distance between zero and four
on the number line shown here is four units. The distance between negative four
and zero on this number line is also four units. So we say the absolute value of
four is four. The straight lines on either side
of the four is the symbol for the absolute value. The absolute value of negative four
is four. When we talk about absolute value,
we’re talking about distance. We’re talking about how far a
number is from zero on a number line. And distance is represented by
positive integers. Let’s look at two examples.
Example one, what is the absolute
value of negative 53?
Remember, we’re trying to answer
the question, how far is a negative 53 from zero? The answer is 53 units. The absolute value of negative 53
Onto our next example.
The absolute value of 200 equals
The distance between 200 and zero
on a number line, 200 units.
Example three, evaluate the
Before we move forward, I wanted to
take a second and note that anytime you see the absolute value bars around
something, you read it like this, the absolute value of whatever is inside the
absolute value bars. In this case, we say the absolute
value of negative three. Reading this would sound like the
absolute value of negative three plus three minus the absolute value of negative
seven. We’re going to use order of
operations to solve this problem. Solving for absolute value occurs
in the step for parentheses or grouping. For us, that means we’re going to
need to solve the absolute value of negative three and the absolute value of
negative seven before we can do anything else.
The absolute value of negative
three or the distance from negative three to zero on a number line is three. The absolute value of negative
seven or the distance from negative seven to zero on a number line is seven. At this point, we need to copy down
the rest of the equation exactly how it was written. We finished all of our
grouping. There are no exponents in this
problem. There is no multiplication or
division; we’re free to add or subtract from left to right. Three plus three is six. Bring down the rest of the
equation; six minus seven is negative one.
Here’s another example.
Calculate the following: negative
absolute value of negative nine times the negative of the absolute value of negative
This problem might sound a little
bit more complicated than the last one, but we’ll follow the same steps. Order of operation tells us that we
would do the parentheses — the grouping first. Remember that finding the absolute
value falls in this step. So we need to start here. The absolute value of negative
nine, the distance between negative nine and zero, is nine. The absolute value of negative five
is five. The next step is just to copy down
the problem exactly how it was written in the first line. Be careful that you copy down the
problem exactly how it was in the first line, with the exception of adding in the
absolute values that you’ve already solved for. There’s no more parentheses or
grouping; there are no exponents in this problem. We can multiply and divide from
left to right. In this case, we’ll only be
multiplying: negative nine times negative five equals positive 45.
Let’s review the keys to absolute
value. The absolute value of a number is
the distance from that number to zero. When solving equations that have
absolute value in them, absolute value is calculated in the first step — the
parentheses step of the order of operations. These are the keys that you need to
work with absolute value.