Welcome to Math with Mr. J. In this video, I'm going to go through a 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 a 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 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 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 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 7. By adding a negative, by adding that negative 7, we are decreasing in value by 7 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 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 8 is 8 plus the absolute value of negative 10, which is 10. Now we add those absolute values because again, we have the same signs. 8 plus 10 is 18. 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 8. 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 5 minus negative 9. 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 nine would be a nine dollar 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.
negative 3 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 23. 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 a negative times a positive. So we are working with different signs. Now when we're working with different signs, this tells us our product, the answer to a 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 28. And that's our final answer. To recap, different signs equal a negative product. So if we have a negative times a positive, that will equal a negative product. Or if we have a positive times a negative, that will equal a negative product. Let's move on to number two, where we have negative 10. times negative 6. 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 a positive 60. Our final answer, 60. So to recap, same signs. equals a positive product.
So negative times a negative. equals a positive product. And then a positive times a positive also equals a 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 8. For now, let's just think of this as 48 divided by 8 and what that quotient will be.
Remember, the quotient is the answer to a division problem. So 48 divided by 8 is 6. So let's write a 6 here. And now we need to determine if our quotient is positive or negative.
Well, we had a negative divided by a 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 8 equals. a positive 6. Now let me back up here and further explain same signs.
So same signs would be a negative divided by a negative like number 1. That equals a positive and then also a positive divided by a positive equals a positive. Let's move on to number two, where we have 36, a 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 a positive divided by a negative. So we have different signs. Different signs.
That is a negative quotient. So negative 9 there. 36 divided by negative 4 equals negative 9. So for different signs, that means a positive divided by a negative, like number 2. That equals a negative. And then a negative divided by a positive equals a negative. So there you have it.
There's how you add, subtract, multiply, and divide 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.