[Music] welcome to math with mr j [Music] in this video i'm going to go through a review of how to add and subtract integers and we're going to be working with both positive and negative integers we'll start with adding integers now when it comes to these types of problems there are different ways to think through these we will go through two ways for each of our examples let's jump into number one where we have 12 plus negative 7. we'll start this problem by taking a look at the signs we have a positive 12 and a negative 7. so we have different signs a positive and a negative since we have different signs we are going to take the greater absolute value and subtract the lesser our answer will take the sign of the greater absolute value let's start by writing the absolute value of both 12 and negative 7 and remember absolute value is the distance a number is from 0. the absolute value of 12 is 12. the absolute value of negative 7 is 7. now we take the greater absolute value and subtract the lesser these are already in order so we can subtract if the larger absolute value comes second you can always switch the order to find the difference if need be let's subtract so 12 minus 7 is 5. now we need to determine if our answer is going to be positive or negative so we need to take a look at the larger absolute value which is this 12. so we take the sign of the larger absolute value from the original problem so the larger absolute value is 12 let's take a look at the 12 in the original problem and that 12 is positive that means our answer is going to be positive so our final answer a positive 5. so a quick recap here basically we forgot about any negatives because we were working with absolute values we then found the difference between the absolute values and the answer takes the sine of the greater absolute value from the original problem now let's think through this another way and this way is going to be more of a mental math approach just basically thinking about what's going on in this problem so let me rewrite 12 plus negative 7 here so our original problem so we are starting at a positive 12 and we are adding a negative seven by adding a negative by adding that negative seven we are decreasing in value by seven from that twelve we can basically think of this as 12 minus 7 or 12 take away 7 that gives us our answer of 5. so 12 plus negative 7 we are decreasing that 12 by a value of 7 so we get a positive 5. so again we started at a positive 12. always think about where you are starting and where you are going from that starting point so we are adding a negative 7 which is decreasing our 12 in value by 7 and we end up with 5. let's move on to number 2 where we have negative 8 plus negative 10. here we have two negatives so the same signs so we're going to add the absolute values and use the same sign so let's start by taking a look at the absolute value of negative 8 and negative 10. the absolute value of negative eight is eight plus the absolute value of negative ten which is ten now we add those absolute values because again we have the same signs eight plus ten is eighteen we use the same sign from the original problem which those are negatives there so our answer is negative final answer negative 18. now if we were to think through this we can think that we are starting at negative eight so let me rewrite here negative 8 plus negative 10. so again starting at negative 8 and we are adding a negative 10. so that means we are decreasing in value by 10. that leaves us at negative 18. like i mentioned earlier think about your starting point so the number you are starting with we have a negative 8 and then adding that negative 10 tells us we are decreasing in value and end up at negative 18 negative 18 is our final answer that's how we add integers let's move on to subtraction so here are our examples for subtracting integers let's jump into number one where we have five minus negative nine now when we subtract integers we're actually going to add the opposite so if you're able to add integers you're going to be able to subtract the opposite of subtraction is addition and then we take the opposite of the number we are subtracting so this gives us an equivalent problem and we are able to use this strategy so we have 5 and then let's add the opposite of negative 9. the opposite of negative 9 is positive 9 so 5 plus 9 that gives us 14 a positive 14 and that's our final answer now that answer may not make sense at first but let's think about how we end up with a positive 14 in this subtraction problem whenever we subtract a negative we actually increase in value i like to think of this in terms of money a negative represents a debt or an expense when it comes to money so that negative 9 would be a 9 debt or expense think of subtracting a negative like subtracting or taking away that debt or expense and getting that money back that is a good positive thing and increases the value of that problem so something to think about let's move on to number two where we have negative three minus twenty so let's add the opposite negative 3 plus the opposite of positive 20 is negative 20. so we have negative 3 plus negative 20. now adding that negative 20 we are decreasing in value by 20 so we're starting at negative 3 and then decreasing in value by 20. that's going to give us negative 23 and that's our final answer so there you have it there's how you add and subtract integers if you need any more help or examples i dropped links to more videos and examples down in the description i hope that helped thanks so much for watching until next time peace you