Adding Integers Explained How to Add Integers Math with Mr J

welcome to math with mr in this video i'm going to go through quick review of how to add integers and we're going to be working with both positive and negative 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 twelve plus negative seven we'll start this problem by taking look at the signs we have positive 12 and negative seven so we have different signs positive and 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 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 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 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 positive 5. so 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 sign 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 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 positive 12 and we are adding negative 7 by adding negative by adding that negative seven we are decreasing in value by seven from that twelve we can basically think of this as twelve minus seven or twelve take away seven that gives us our answer of five so twelve plus negative seven we are decreasing that twelve by value of seven so we get positive five so again we started at positive 12. always think about where you are starting and where you are going from that starting point so we are adding 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 look at the absolute value of negative 8 and negative 10. the absolute value of negative 8 is 8. 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 eight plus negative ten so again starting at negative 8 and we are adding negative 10 so that means we are decreasing in value by 10. that leaves us at negative 18. like mentioned earlier think about your starting point so the number you are starting with we have 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 so there you have it there's quick review of adding integers if you need more help or examples dropped links to other videos and examples down in the description hope that helped thanks so much for watching until next time peace