How to Multiply Integers

TenMarks teaches you all about multiplying integers.

How to Multiply Integers Let's talk about multiplying integers. We’re given three different problems, so it's going to be a relatively longer video but let's do them by one. So question 1A deals with, well let's try and multiply -3 with 4. The key thing to remember when we’re multiplying two integers that have different signs is; if both signs are positive or both signs are negative, then the end result is a positive. If any sign is a positive and a negative combination, if the signs are different, then the result is a negative. This is a key thing to remember. So in this case -3 x 4 will be 12, but will have a negative sign because the signs the different. That’s the first one. Let's look at 1B which is -2 x 5 x -9. Here as you can see, we’re multiplying three different terms, three different integers. The key is to multiply two of them first; easiest to do is left to right. So -2 x 5 is -10 because 2 x 5 is 10 and then negative and positive, different signs, so the end result is -10 x -9. Both signs are the same. If the signs the same, the result is positive and 10 x 9 is 90. So the ultimate answer here is 90. Let's look at the second problem now. The second problem and I'm going to change the color of my pen. The second problem says; evaluate the expression a x b + c when we are given a=-5, d=6, and c=-2. So all I have to do is substitute these values instead of a, b, and c. So first, we mm a x b. So that’s -5 x b is 6. I'm going to put them in parenthesis so we separate them up and then we add c which is -2. So let's multiply -5 x 6 first, will give us -30, signs are opposite. So the end result will be a negative and then we have to add to it -2. Adding -2 is the same as subtracting 2. So -30 + -2 will give us -32 and that’s the answer we were looking for, -32. Let's do the third problem which is a word problem. It says that a blue whale dives deep into the sea from the surface of the water at the rate of four feet per second. So the whale goes down four feet every second. Where will the whale be in relation to the surface after 10 seconds? So a key thing to remember is; four feet every second. We need to figure out where will the whale be after 10 seconds. That’s the problem. Since the whale is going below sea level, let's say that the distance moved in one second equals -4 feet. The reason it's negative four feet is because the whale is going below the surface. So it's going in the negative direction. So in one second, the whale will go negative four feet. Taking a little more extra space, the distance moved by the whale in 10 seconds will be -4 feet, that’s in one second times 10. -4 x 10 is -40 feet. So at the end of 10 seconds, the whale will move -40 feet or will move 40 feet but it will be at a distance of -40 feet from the surface. So the key things that we’ve got tor remember in this track is when we’re multiplying two integers, if the signs of the integers are different, the resulting integer is a negative and if the signs are the same, the result is a positive. In this case, 3 x 4 is 12 but it's a negative because one is a negative, one is a positive. If we’re multiplying three integers, we do them two by two. If we are looking at equation, we can substitute ab + c with the values and we treat them like we would treat anything else and we get the answer -32. In case of a word problem where the whale is descending or going down four feet every second; that means the distance moved in one second is -4 feet. This is the key part; -4 feet, because the whale is traveling under the sea and going away from the surface in the negative direction. The distance moved in 10 seconds is 10 times that which is 40 but the value is negative.