In this lesson, we'll be working on operations with real numbers, specifically with integers. We've got examples of integers listed here.They're positive and negative whole numbers, like negative 3, negative 2, negative 1, 0, 1,2,3 and so on in both directions. [NOISE] To add integers, if the integers have the same sign, you'll add and keep the sign. If the integers have different signs, you will subtract the absolute value and keep the sign of the number with the larger absolute value. Remember that absolute value always gives you a positive number. The absolute value of something like negative 3 is three. The absolute value of three is also three. Absolute value can be thought of as the distance a number is from zero. Let's look at Number 1. We get negative 3 plus negative 8. Those both have a negative in front of them, so they have the same sign. We're going to add three and eight together. That's the absolute value of those two numbers. 3 plus 8 is 11. We're going to keep the negative sign, so that'll be negative 11. Number 2, we have 18 plus 89. There's no negative signs in there. Both those numbers are positive. I'm going to just add 18 plus 89. Eight and nine is 17, 8 plus 1, plus 1 is 10. We get 107, added the numbers together and we kept the sign. Number 3, negative 23 plus 85. The 23 is negative, 85 is positive. They have different signs, so we need to subtract their absolute value. Right now we're not going to really worry about the signs, which is know that that tells us to subtract. The biggest absolute value on top 5 minus 3 is 2, 8 minus 2 is 6. I got 62. I'm going to look back at my numbers. Which is bigger 23, or 85? Eighty-five is the larger number. My answer is going to be positive 62 because 85 is bigger than the 23, and 95 is positive. Number 4, 8 plus negative 3. The eight is positive, the three is negative. They have different signs. Subtract the absolute value. 8 minus 3 is 5. Now I have to determine the sign. The sign is determined by the number with the larger absolute value. Eight is bigger than three, eight has the larger absolute value it is positive so my answer is positive 5. Number 5, negative 26 plus negative 18. Both numbers are negative, so I'm going to add the absolute value together, 26 and 18, 6 and 8 is 14, 2 and 1 and 1 is four. I get 44. The rule is if they have the same sign you add and you keep the sign, they're both negative, so my answer is negative. Number 6, 28 plus negative 32. Twenty-eight is positive, 32 is negative. I'm going to subtract those two numbers 32 minus 28 is 4. Now I need to think about what the sign is going to be on the four. Thirty-two has a larger absolute value than 28, 32 is negative, so my answer is negative 4. Let's do subtraction. Subtraction is like addition, except we're going to use the rule, keep change, change. We're going to keep the sign of the first number, change the subtraction to an addition, and then change the sign of the second number. An alternative approach to this is, is just to pool that subtraction sign into the number. For now I'm going to do keep change, change. On Number 1 we have 7 minus 5. We know, that's two, but let's use the rule and see how it works. We keep the sign on the seven. It's currently positive. There's no sign there, so we know it's positive. We're going to keep that. We're going to change the subtraction sign to an addition sign, and then change the sign on the five to negative. 7 plus negative 5 now use your addition rules. We've got a positive 7 and a negative 5. Those signs are different, so we subtract 7 minus 5 and get 2. Then we determine the sign by whichever one has the larger absolute value. Seven has the larger absolute value. It's positive, so my answer is two. Number 2, 5 minus 9. Keep the sign on the five, change the subtraction to an addition, and then change the sign of the nine to negative. Now they have different signs. The five is positive, the nine is negative. Subtract 9 minus 5 and get 4. Which one has the larger absolute value five or nine? Well, nine is larger. Nine is negative, so my answer is negative 4. Number 3, keep change, change, keep the sign on the negative 9, change the subtraction to an addition problem, and then change the sign on the second number to a positive. I get a negative 9 and a positive 13. They have different signs, so we subtract the absolute value. 13 minus 9 is 4,13 is the larger number, 13, bigger than 9. It is positive so my answer is positive 4. Number 4, I'm going to keep change, change, keep the sign on the 17, change the subtraction to an addition problem, and change the sign on the following number. Now we have 17 plus 26. We just need to add those together. They have the same signs. I'm going to add and keep the sign. The answer is positive 43. Number 5, negative 18 minus 5. We're doing keep change, change, keep the sign on the first one. Negative 18 stays. Change the subtraction to an addition problem and change the sign on the following number. We have negative 18 plus negative 5. They both have a minus sign. Add the absolute value of those two numbers 18 and 5 is 23 and we keep the sign that they both have. Then on Number 6 we have negative 23 minus 37. Keep the sign on the negative 23, change the subtraction to an addition, and change the sign on the 37 to negative. Now they're both negative, negative 23 and negative 37. We'll add the absolute value in 23 plus 37, 60. Both numbers are negative, so we're going to keep that sign.