### Video Transcript

Consider the following figure. What sum does this diagram represent? And what is the distance between the first addend, negative three, and the sum?

When we look at this figure, to find the sum that it represents, we need to consider both the distance between points and the direction. We know that the distance between zero and negative three is three units. However, because we’re moving down from zero, we know that this is going to be negative. Our first addend should be negative three.

When we look at our second addend, we again see a distance of three units. However, again, we’re moving away from zero. We’re moving in the negative direction, making our second value negative three as well. This sum is then negative three plus negative three, for an end result of negative six.

What is the distance between the first addend, negative three, and the sum? Our first addend, negative three, is located here, and the sum of negative six is here. Visually, we’ve already said that this represents a distance of three units. Remember that we don’t represent distance with negative values. Because of that, we take the negative three that our second addend represents and we take its absolute value to show distance. We say that the distance between these values is the absolute value of negative three.

And that means as we talk about the distance between zero and negative three, we could say it’s the absolute value of negative three, which equals three, for both of these distances.