How to Find Opposite and Absolute Values of Integers

TenMarks teaches you how to find opposites and absolute values using a number line.

How to Find Opposite and Absolute Values of Integers Here we will learn about opposite and absolute values and there are three questions. The first question asks us to find the opposite of -1/2 so first what is opposite? Let’s understand what opposite actually means. Well opposite is a number which is at the same distance from the 0 marker but in the opposite direction. So lets look at the question, it's asks us to find the opposite of -1/2, so this is my number line, this is my 0, so as you can see what I’ve done is I’ve marked -1/2 on this line. This is the distance between the 0 marker and the -1/2, so the opposite number is the exact distance but in the opposite direction right. So this went to the left, the opposite must be to the right, so I have to look at the exact distance on the right so if this was -1/2 this would be the same distance on the right which is +1/2 okay? So the answer here is the opposite of -1/2 is +1/2 okay? Fairly simple, now lets look at the second question which asks us—the second questions says evaluate the expressions within two vertical bars. The number -3 and the number -2 2/3 okay, so let’s actually scroll down a little bit and look at the second question in the first part. We need to determine what is the value of this, so what does these two vertical bars mean? Well this is actually a symbol for absolute value. An absolute value is the distance of the number from 0, so it's the value of the distance okay? So what does that mean? So in this particular case the marker says -3 rights so I start with 0 and then I have marked right above -3, what is the distance? The distance is actually 3 units, so the distance here is 3 units right? It's on the left side so it's -3 but the distance is actually 3 units okay? So the absolute value is actually 3, the absolute value is simply the distance. It doesn’t matter if it's to the left or to the right, the distance between 0 and this point is actually 3 units which is the absolute value okay? Now lets do the third problem that says evaluate the expression -2 2/3 so -2 and 2/3 within the two vertical bars. So what do we know? Let’s use the number line again right, so I need to evaluate the absolute value of -2 2/3 right. How do we do that? Well what I’ve done is I have started at the 0 point and I can basely break this down as this is the same as -2 right + the same us -2/3, so I just simply broke it down to two independent pieces right because negative of 2 2/3 is the same as -2 + -2/3 right? I’m putting in the absolute value bracket surround it. So what do I do, on the number line, first thing I start from 0 and I mark negative 2 which is right here, so that’s the first one right? Second one, I still have -2/3 so I start from this point and I -2/3 again, as you can see this was marker one, this was marker 2 this was marker 3. I broke down the marker between 2 and 3; I divided them into 3 equal pieces which is a third, a third and a third. So this becomes -2, this becomes -3 but this is 1/3 after -3, this is 2/3 after -3, this is an additional three thirds after -3 right? So additional 2/3 I move two more sub markers to the left which is what I did here, so this is my final marker which is -2 and 2/3. So all I’ve done so far is actually mark this value on the number line. Now what I need to do is compute the distance between 0 point and this final point right? What is the distance? This distance is what gives us the absolute value as denoted by this two vertical bars and this distance is 2 and 2/3 which means the absolute value of -2 2/3 is 2 and 2/3 okay? So what have we learned in this particular video? We’ve learned is the concept of an opposite and the way that you determine an opposite is you find on a number line the exact same value but on the opposite side of 0, so in this case the original value was -1/2 which means the opposite is +1/2 because the distance between -1/2 and 0 is exactly the same between 0 and 1/2 except +1/2 is on the right side, the opposite side. Second thing that we learned is the absolute value of a number is the distance of that number from 0 is the value of that distance. So in this case since the question asked us to find the absolute value of -3 well the distance between this marker and the 0 marker is actually 3 units. Now if the 3 units and the distance are 3 units and that’s the value, so the absolute value of -3 is actually +3 because it's 3 units. I just count. Same thing if I’m given a more complex thing like figuring out -2 2/3, what’s the absolute value, first I mark it by doing 2 and 2/3 and then I can compute the distance between this 2 points which is actually 2 and 2/3 which becomes the absolute value. Now one quick thing to remember is another easy way of determining the absolute value is just changing the negative sign to the positive sign that all we have to do. You just remove the negative sign and that’s all you do. So if you within that absolute value you see a negative sign, just remove and that gives you the absolute value.