Learn About Opposite and Absolute Values of Integers This video lesson deals with opposite values and absolute values. We’re given four different problems. The first one, let’s do first, which is find the additive inverse of -1. So what we’re trying to do is figure out what’s the additive inverse. An additive inverse is also called the opposite. And the easiest way to do it is look at a number line because the additive inverse of the opposite is the same distance from zero as the original number by the new opposite direction. So I’m going to try and draw a number line and let’s say this is zero. So -1 is here, -2 is here and so on. And here we’ve got +1 and we’ve got +2 and so on. So if we look at the value that we’re given which is -1 that would be right here. So it’s right here. The distance between this and zero is one unit as we can see. So the additive inverse will be on the other side of zero and the same distance which is one unit, which will be right here. So, the additive inverse of -1 will be +1 or one. Now that we know how to do opposites, let’s try a few more. The second problem says, evaluate the expressions -9 so let’s do problem two, part A, which is absolute value of-9 plus absolute value of -7. So when we look at this, these brackets, when we look at a number between these two, we are looking to find the absolute value. And the absolute value is the distance from zero on a number line. It doesn’t matter which direction it’s at. So when we look at -9, the distance from zero is nine units because if we look at the number line above, the distance of any unit here, -2, -3, and -4 is four units, three units, two units from the number line. So the distance of -9 from zero is nine units plus distance of -7 from zero is seven units. So 9+7=16, relatively simple to do. Another trick we can remember is if we are trying to find the absolute value and it’s a negative number, we just convert it to a positive number. If it’s a positive number and it stays positive. Let’s use a couple of more examples. Let’s do B. It says -2 *9 we need to find the absolute value of. -2*9=-18, and the absolute value of -18 is +18. It’s relatively simple. The last problem is problem C, which is absolute value of 18 divide by absolute value of -3. So problem is C is absolute value of 18 divided by absolute value of -3. Like I said, absolute value of 18 which is a positive number is still 18 because the distance of 18 from zero on a number line is 18 units. If it’s a positive number, it stays positive. If it’s negative, it converts to positive, divided by a -3, which because we’re trying to figure out the absolute value, we’ll convert the positive three. So 18÷3=6. So quickly recapping what we’ve learned, we learned about absolute values and opposites. The opposite of a number like -1 is +1 because what we try and do is find the distance from the zero on a number line, and then find the exact opposite on the opposite side. When we are trying to do expression like we did here in these three, which involve absolute values, absolute value is the distance of this on a number line from zero. So -9 is nine units away from zero. Easier way to do it is a -9 converts to a +9, -3 converts to a +3 but a positive 18 stays 18. So absolute value does is converts a negative to a positive, and a positive stays the way it is. Once we know that, it’s easy to perform the expressions. 9+7=16, -2*9=-18, absolute of that is 18, and similarly 18÷(-3) will convert to 18÷3 because we’re taking the absolute values of both, and the answer is six.