Video: Finding Absolute Value

In this video we learn how to find the absolute value of a number, and to evaluate expressions involving the absolute values of terms, which means considering the order of operations.

05:35

Video Transcript

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 is 53.

Onto our next example.

The absolute value of 200 equals what?

The distance between 200 and zero on a number line, 200 units.

Example three, evaluate the following.

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 five.

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.

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