Understanding the Meaning of Absolute Value

One important concept in algebra that we learn is the distance between two points on the number line. In particular, we study the distance of a point that corresponds to a number to the point that corresponds to 0. In the following figure, the point (or circle) on the left represents 0, while the point on the right represents 5. To simplify our language, we will use coordinates to refer to its corresponding point on the number line. For instance, we will use -8 to refer to the point that corresponds to -8.

Looking at the number line, it is easy to see that 5 is 5 units away from 0 and that -8 is 8 units away from 0. We can also see that 0 is 0 units away from 0. The distance of a number from 0 on the number line is called its absolute value. Hence, the absolute value of 5 is equal to 5, the absolute value of -8 is equal to 8, and the absolute value of 0 is equal to 0. » Read more

How to Add Integers Using the Number Line

There are several ways that we can visualize addition of integers. One way is to use the number line. If you can see the pattern in this method, it is easier to see the sign of the sum of two integers. To be able to use this method to add integers, first we should think of integers as movements on the number line. We can think of the positive integers as movement to the right and the negative integers as movement to the left.  » Read more

Making Connection Between Distance and Absolute Value

We have learned about the distance formula and we also have discussed how to get the distance between two points given their coordinates.  In this post, we are going to explore a simpler concept: getting the distance between two points on the number line.

Suppose we want to get the distance between two p0ints on the number line whose coordinates are integers, we can just do it by counting. In the figure below, the distance from 0 to 5 is 5, and the distance from 5 to 9 is 4.

image via nctm illuminations

It is also obvious that we can get the distance by subtraction: 5-0=5 and 9-5=4.  It is clear that if we let a be the larger integer, and b be the smaller, then the distance can between the two integers is a-b. It is also clear that this formula applies to non-integral coordinates.  » Read more

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