How to Add Subtract Multiply and Divide Integers A Review of Integers Math with Mr J

welcome to math with mr in this video i'm going to go through review of how to add subtract multiply and divide integers and we're going to be working with both positive and negative integers we'll start with adding integers and when it comes to adding integers there are couple of different ways to think through these so i'll show you two ways to go through each of our examples here let's jump into number one where we have 12 plus negative 7. we'll start this problem by taking look at the signs we have positive 12 and negative 7. 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 zero the absolute value of twelve is twelve the absolute value of negative seven is seven 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 seven by adding negative by adding that negative seven we are decreasing in value by seven from that 12. 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 value of seven so we get positive five so again we started at positive twelve 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 eight and negative ten 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 eight plus negative ten so again starting at negative eight and we are adding negative ten 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 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 nine the opposite of negative nine is positive nine so five plus nine that gives us 14 positive fourteen 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 positive 14 in this subtraction problem whenever we subtract negative we actually increase in value like to think of this in terms of money negative represents debt or an expense when it comes to money so that negative nine would be nine dollar debt or expense think of subtracting negative like subtracting or taking away that debt or expense and getting that money back that is 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 20 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 and that's our final answer that's how we subtract integers let's move on to multiplication here are our examples for multiplying integers let's jump into number one where we have negative seven times positive four we have negative times positive so we are working with different signs now when we're working with different signs this tells us our product the answer to multiplication problem will be negative so negative 7 times 4 well 7 times 4 is 28 and then we know this product is negative because we are working with different signs so this is negative and that's our final answer to recap different signs equal negative product so if we have negative times positive that will equal negative product or if we have positive times negative that will equal negative product let's move on to number two where we have negative 10 times negative six so we have the same signs there we have two negative numbers so our product will be positive so let's think 10 times 6 is 60 and we have the same signs there so this is going to be positive 60. our final answer 60. so to recap same signs equals positive product so negative times negative equals positive product and then positive times positive also equals positive product that's how we multiply integers let's move on to division so here are our examples for dividing integers and you'll notice that our rules are the same for dividing integers as they were for multiplying integers as far as working with those positives and negatives and if we're working with the same signs or different signs let's jump into number one where we have negative 48 divided by negative eight for now let's just think of this as 48 divided by eight and what that quotient will be remember the quotient is the answer to division problem so 48 divided by 8 is 6. so let's write 6 here and now we need to determine if our quotient is positive or negative well we had negative divided by negative so anytime we have the same signs in our original problem our quotient is positive so same signs positive quotient so negative 48 divided by negative eight equals positive 6. now let me back up here and further explain same signs so same signs would be negative divided by negative like number one that equals positive and then also positive divided by positive equals positive let's move on to number two where we have 36 positive 36 divided by negative 4. so let's think of this as 36 divided by 4 which is 9. now we need to determine if that quotient is positive or negative well we have positive divided by negative so we have different signs different signs that is negative quotient so negative 9 there 36 divided by negative equals negative nine so for different signs that means positive divided by negative like number two that equals negative and then negative divided by positive equals negative so there you have it there's how you add subtract multiply and divide integers if you need any more help or examples dropped links to more videos and examples down in the description hope that helped thanks so much for watching until next time peace you