Learn about Adding Integers

TenMarks teaches you how the addition of integers.

Learn about Adding Integers In this lesson, let’s learn how to add integers using a number line as well as using absolute values. Let’s do all the problems one by one. The first one wants us to solve 3 + (-3) and we should use the number line. So what I’ve done is I’ve drawn a basic number line. You can notice that there is the center point which is 0 and on the right of the 0 marker we’ve got the positive numbers plus 4 all the way to 8 and the negative side we’ve got the opposites of the negative numbers. So if we’re adding two numbers, first one is +3 so the way we do this is we start at 0 and we move if it’s positive, positive means we move to the right. This is problem one by the way. So we move three spots to the right. So we arrive here. So first we move +3 then we look at the next value. We’re still adding and we’re adding a negative number. If it’s a negative number we move left. So we start from where we left off and we move three spots to the left. If we move three spots to the left and that’s all the values we’re given we look at where are we. We’re turned back to the 0 spot. What that means is +3 + (-3), the end result is a 0. That’s what we need to remember. All we did was started at 0, always start at 0. If it’s positive value move to the right. If it’s a negative value, move to the left and measure where we ended up. Let’s try the second problem. We need to evaluate using absolute values, -6 + (-2). So let’s do problem two. What we’re trying to do in the first part of the problem is -6 and we’re going to add that to -2. The way we do problems involving absolute values or the absolute value method is we convert all these values to their absolute values. So what we do is we do two steps. Step one involves find the sum of the absolute value. So in this case the absolute value of -6 is 6. The absolute value of -2 is 2 so the sum is 8. So that is step one. Let’s take a little bit more space and look at step two where we need to determine the sign of the result. If the two numbers being added have the same sign then the result shares that sign. So in this case taking a little bit more space, the two values had negative and negative so the signs are the same which means the final result will have a negative sign as well and that’s the we were looking for. So -6 +-2 = -8. We use the absolute values to determine the value of the number and then look at the two signs to determine the sign. Now let’s try the second part which is if I scroll up it is -9 +5. The second part is -9 +5. In this case, the absolute value of -9 is 9. The absolute value of 5 is 5. So the absolute values that we were looking for, the absolute value of -9 = 9 and absolute value of +5 = 5 which meant we are looking at the two numbers 9 and 5. The key to remember is if the signs are opposite then we simply subtract. If the signs are opposite -9 and 5, you notice the signs are opposite. If it’s opposite we subtract so 9-5 gives us 4. That’s the value similar to how we got the value here which is 8 and the end result sign is the sign of the greater number. Here, the greater value is 9 so the sign will be that of 9 which is -4, -9+5, we look at the two absolute values. If the signs were opposite we subtract them, 9-5gives us 4 and the resulting sign is the sign of the larger of two values. Now let’s look at the third problem which says a scuba diver descends 25 feet. Descends means goes down 25 feet below the surface of the water. And then it climbs up 12 feet up. Then it swims 12 feet up towards the surface. First, it goes down 25 feet then goes up 12 feet. What’s the location of the diver? Let’s do this using a number line. What I've done is for this third problem is we are going to start with 0 and what are we told? We are told the first they went down 25 feet. If they are going down that means it’s -25 feet. Then they went up 12 feet which is +12 feet. The key is to remember the positive and the negative. It’s positive if you're going up, negative if you're going down. So let’s use a number line. We start with 0 and first since the diver went down 25, we move left 25 units. So we get to -25. From that point now we move right 12 units because the diver climbed up. Let’s see where we ended up? We ended up at -13. What that means is -15 +12 = -13. Since the sign is still negative that means the diver is now 13 feet below the surface and the reason that is the below the surface is the value is still negative. So the value is 13 feet below the surface.