WEBVTT mathematics/basic-math/pyo
00:00:00.000 --> 00:00:06.900
Welcome back to Educator.com; this lesson is on adding integers.
00:00:06.900 --> 00:00:12.000
To use a number line, we can add integers using a number line here.
00:00:12.000 --> 00:00:14.400
What we are going to do is start with the first number.
00:00:14.400 --> 00:00:23.100
If I give you a problem, 4 plus -2.
00:00:23.100 --> 00:00:25.700
I am going to start off at this number right here, 4.
00:00:25.700 --> 00:00:28.500
Let me just write out the numbers on this number line.
00:00:28.500 --> 00:00:37.100
Here is 0, 1, 2, 3, 4; I can just do a few more on this side.
00:00:37.100 --> 00:00:45.600
Here are my negatives; this is -4.
00:00:45.600 --> 00:00:51.000
I start at this first number 4; 4 is right here.
00:00:51.000 --> 00:01:01.400
I am going to start right here and then use the second number to move spaces.
00:01:01.400 --> 00:01:04.600
This number right here is how many spaces I am going to move.
00:01:04.600 --> 00:01:12.800
If it is positive, I am going to move to the right because this is the positive direction.
00:01:12.800 --> 00:01:18.000
If it is negative, I am going to move to the left because left is always negative.
00:01:18.000 --> 00:01:24.900
Since I have a negative number, -2, I am going to be moving to the left two spaces.
00:01:24.900 --> 00:01:32.300
The negative and the positive is to just see which direction you are going to go, to the right or to the left.
00:01:32.300 --> 00:01:35.100
I am going to move this many number of spaces.
00:01:35.100 --> 00:01:39.400
We are starting at 4, moving to the left two spaces.
00:01:39.400 --> 00:01:44.400
I am going to go 1, 2; his is where I land.
00:01:44.400 --> 00:01:50.800
This number right here is 2; my answer is 2.
00:01:50.800 --> 00:02:02.200
Let's do another example; if I have let's say 5 plus -8.
00:02:02.200 --> 00:02:08.900
Again I am going to start off at 5; here is 5 right here; I start right here.
00:02:08.900 --> 00:02:14.300
I am going to move 8 spaces to the left because it is negative.
00:02:14.300 --> 00:02:16.300
Negative is going to make me go left.
00:02:16.300 --> 00:02:22.000
If this was a positive, I would move 8 spaces to the right.
00:02:22.000 --> 00:02:31.600
8 spaces to the left is going to be 1, 2, 3, 4, 5, 6, 7, 8.
00:02:31.600 --> 00:02:33.900
This is where I am going to land.
00:02:33.900 --> 00:02:37.400
That is -3 because it is -1, -2, -3.
00:02:37.400 --> 00:02:44.200
The number I land on is the answer; my answer here is -3.
00:02:44.200 --> 00:02:48.400
That is how you use a number line to add integers together.
00:02:48.400 --> 00:02:54.300
Again integers are all positive and negative whole numbers.
00:02:54.300 --> 00:03:03.400
No decimals, no fractions, just whole numbers and their opposites.
00:03:03.400 --> 00:03:14.000
Another way to add integers without using the number line... first let's remember that opposites add to 0.
00:03:14.000 --> 00:03:22.700
If I have +5 and I have a -5, then they are going to become 0.
00:03:22.700 --> 00:03:30.200
A 5 plus a -5 equals 0; 5 and -5 are opposites.
00:03:30.200 --> 00:03:38.700
As long as they are opposites, if I add opposites together, then my answer becomes 0.
00:03:38.700 --> 00:03:45.300
If both numbers are the same sign, then you are going to add the numbers and keep that sign.
00:03:45.300 --> 00:03:49.300
If they are opposite signs, we will talk about that in a second.
00:03:49.300 --> 00:03:58.200
But let's do an example of this one--if I have -2 plus -3.
00:03:58.200 --> 00:04:00.600
They are both negative; they have the same sign.
00:04:00.600 --> 00:04:05.400
This is negative and this is negative.
00:04:05.400 --> 00:04:09.700
I am just going to add up the numbers and I am going to keep that sign.
00:04:09.700 --> 00:04:13.200
My answer is -5.
00:04:13.200 --> 00:04:19.900
If I have -1 plus -10, then my answer is -11.
00:04:19.900 --> 00:04:25.100
As long as I have the same sign, I am adding two numbers to the same sign,
00:04:25.100 --> 00:04:29.300
then I am just going to add it and keep that sign; that is it.
00:04:29.300 --> 00:04:31.000
Same thing goes with positive numbers.
00:04:31.000 --> 00:04:38.100
If I have 3 plus 6, this is a positive number and this is a positive number.
00:04:38.100 --> 00:04:45.300
We know that 3 plus 6 is 9; +9; you kept the same sign.
00:04:45.300 --> 00:04:53.900
If the signs are opposite, the two numbers that you are adding together have opposite signs, then that becomes a little tricky.
00:04:53.900 --> 00:05:05.900
If I have 2 plus a -3, this one I know is a positive number because integers can only be positive or negative.
00:05:05.900 --> 00:05:08.300
There is no negative sign here so I know it is positive.
00:05:08.300 --> 00:05:13.300
It is +2 plus a -3.
00:05:13.300 --> 00:05:20.800
Since they are opposites, what I am going to do is take the absolute value of both numbers.
00:05:20.800 --> 00:05:26.000
The absolute value, if you don't remember absolute value, then take a look at the lesson right before.
00:05:26.000 --> 00:05:33.500
Absolute value asks me for the distance from 0.
00:05:33.500 --> 00:05:36.600
On the number line, how far away is 2 from 0?
00:05:36.600 --> 00:05:40.600
I know it is 2; the absolute value of 2 is 2.
00:05:40.600 --> 00:05:48.400
The absolute value of this is 3.
00:05:48.400 --> 00:05:57.600
I am actually going to take their absolute values... or I am going to subtract them.
00:05:57.600 --> 00:06:03.800
Basically I am going to just do 3... because the absolute value of -3 is 3... and -2.
00:06:03.800 --> 00:06:11.800
I am going to find the difference; that becomes 1; 3 minus 2 is 1.
00:06:11.800 --> 00:06:20.200
You are going to keep the sign of the number that is greater, with the greater absolute value.
00:06:20.200 --> 00:06:23.900
For this one, this has a negative sign.
00:06:23.900 --> 00:06:27.200
I am going to keep that negative sign; this is a little confusing.
00:06:27.200 --> 00:06:32.200
But just keep in mind that when you have the same sign,
00:06:32.200 --> 00:06:35.400
then it is like you are adding the two numbers and you are keeping that sign.
00:06:35.400 --> 00:06:40.200
When you have opposite signs, it is like you subtract the numbers.
00:06:40.200 --> 00:06:49.600
Then you take on the sign with the greater absolute value.
00:06:49.600 --> 00:06:56.500
Another way you can do this is think of positive numbers as dogs.
00:06:56.500 --> 00:06:59.200
I like to use dogs and cats; you can use anything.
00:06:59.200 --> 00:07:08.900
You can use stars; you can use different colors.
00:07:08.900 --> 00:07:16.600
Let's say positive numbers are like dogs and negative numbers are cats.
00:07:16.600 --> 00:07:21.700
If I am adding dogs and cats together, I am going to add a D for dog and C for cat.
00:07:21.700 --> 00:07:27.300
It is going to be dog and a dog because there is 2 of them, and then 3 cats.
00:07:27.300 --> 00:07:33.500
That is cat, cat, and cat; because it is -3, it is 3 cats.
00:07:33.500 --> 00:07:40.100
Each dog and cat cancels out; they are like opposites, add to 0.
00:07:40.100 --> 00:07:44.900
Dog and cat cancels out; these cancel out; what do I have left?
00:07:44.900 --> 00:07:51.900
I have 1 cat; remember a cat is a negative number; it is a -1.
00:07:51.900 --> 00:07:55.000
I can also use colors.
00:07:55.000 --> 00:07:58.500
If I have a positive, then let's say I am going to use blue.
00:07:58.500 --> 00:08:08.200
Blue circle, blue circle; -3 is going to be red circles.
00:08:08.200 --> 00:08:14.400
Each time I have a blue and a red, I am going to cancel it out; cancel it out.
00:08:14.400 --> 00:08:21.300
What do I have left?--1 red; that makes a negative.
00:08:21.300 --> 00:08:27.400
Let's do a few more examples; add the integers.
00:08:27.400 --> 00:08:36.400
If I have -4 plus -2, I am adding two negative numbers together.
00:08:36.400 --> 00:08:40.600
You can just add up the two numbers and keep the same sign.
00:08:40.600 --> 00:08:49.100
-4 plus -2 is going to be -6.
00:08:49.100 --> 00:09:01.400
If I want to draw it out, -4... red circles because it is negative; -4 plus a -2.
00:09:01.400 --> 00:09:06.800
I don't cancel this out because I only cancel out a blue and a red or opposites.
00:09:06.800 --> 00:09:09.300
These are not opposites; they are the same.
00:09:09.300 --> 00:09:12.800
I can't cancel them; instead I have to add them all together.
00:09:12.800 --> 00:09:19.500
1, 2, 3, 4, 5, 6; 6 and it is red; it is -6.
00:09:19.500 --> 00:09:31.000
Next one, I have -3 plus 8; 3, negative, that is red.
00:09:31.000 --> 00:09:42.500
Then +8; +8 is blue; 1, 2, 3, 4, 5, 6, 7, 8.
00:09:42.500 --> 00:09:49.000
The blue and the red cancels out; cancels out; cancels out.
00:09:49.000 --> 00:09:58.100
Then I have 1, 2, 3, 4, 5 left; blue is positive; it is +5.
00:09:58.100 --> 00:10:03.000
I can leave it like this; or I can write +5.
00:10:03.000 --> 00:10:07.800
Again another way to think of this, you can take the absolute value of each number.
00:10:07.800 --> 00:10:11.200
The absolute value of this is going to be 3.
00:10:11.200 --> 00:10:16.100
The absolute value of this is 8; I just find the difference.
00:10:16.100 --> 00:10:23.600
I subtract them; I can just do 8 minus 3 is 5.
00:10:23.600 --> 00:10:28.900
I take on the sign of the greater number which is 8.
00:10:28.900 --> 00:10:34.500
That is a positive so this becomes a positive.
00:10:34.500 --> 00:10:39.500
The next couple of examples; find the sum; that just means to add them up.
00:10:39.500 --> 00:10:49.800
-15 plus -10; we have a negative number and a negative number.
00:10:49.800 --> 00:10:59.800
I just add them up; my answer is also a negative number, -25.
00:10:59.800 --> 00:11:05.800
The next one, I have a positive number and a negative number.
00:11:05.800 --> 00:11:07.500
Again I take the absolute value.
00:11:07.500 --> 00:11:20.600
I am just going to think of both of these as positive numbers; 37 minus 25 which is 12.
00:11:20.600 --> 00:11:30.200
I take the sign of this number because 37 is bigger than 25.
00:11:30.200 --> 00:11:31.400
That has a sign of negative.
00:11:31.400 --> 00:11:33.700
That means I am going to give this that same sign.
00:11:33.700 --> 00:11:39.000
It is going to be -12.
00:11:39.000 --> 00:11:43.200
Find the value; this one right here, I am looking for x.
00:11:43.200 --> 00:11:51.500
To find x here, -2 plus something is going to give me -7.
00:11:51.500 --> 00:12:01.900
-2 plus what is going to give me -7?
00:12:01.900 --> 00:12:10.300
If I give myself 5 circles or 5 cats, what do I have to add to this?
00:12:10.300 --> 00:12:18.000
Plus what is going to give me 7?--how many more do I need?
00:12:18.000 --> 00:12:24.000
I have 5 here; I have 7 here; how many more do I need?
00:12:24.000 --> 00:12:28.100
I need 2 more, 2 more red.
00:12:28.100 --> 00:12:41.400
That is -2 because red I know is negative; I have to add -2 more.
00:12:41.400 --> 00:12:47.100
The next example, the absolute value of 15 plus the absolute value of -9.
00:12:47.100 --> 00:12:58.200
The absolute value of 15 is 15; the absolute value of -9 is 9.
00:12:58.200 --> 00:13:03.800
My answer is 24; that is a positive.
00:13:03.800 --> 00:13:08.200
Again if it is a positive number, you don't have to write the plus sign, the positive sign.
00:13:08.200 --> 00:13:11.100
You can just leave it as 24.
00:13:11.100 --> 00:13:15.900
The next couple, add the integers.
00:13:15.900 --> 00:13:20.100
Again we have a negative number here plus a negative number here.
00:13:20.100 --> 00:13:27.300
As long as they have the same sign... in this case, they both have a negative sign.
00:13:27.300 --> 00:13:33.300
Then we can just add the numbers together, 12 and 20.
00:13:33.300 --> 00:13:35.300
Or you can add the absolute values together.
00:13:35.300 --> 00:13:40.400
It is 12 plus 20 which is 32.
00:13:40.400 --> 00:13:42.800
You are going to give it the same sign.
00:13:42.800 --> 00:13:51.100
Negative plus a negative equals a negative; -12 plus -20 equals -32.
00:13:51.100 --> 00:13:54.500
The next one, 8 plus -6.
00:13:54.500 --> 00:13:58.200
Again 8 is a positive number even though there is no sign written there
00:13:58.200 --> 00:14:01.900
because numbers can only be positive or negative.
00:14:01.900 --> 00:14:10.700
We know it is not negative so it has to be positive... plus a negative number.
00:14:10.700 --> 00:14:21.700
Again if I want to draw a visual representation of this, this is going to be 2, 3, 4, 5, 6, 7, 8.
00:14:21.700 --> 00:14:27.500
The blue represents the positive number; that is +8.
00:14:27.500 --> 00:14:35.500
My red is going to represent the negative number, -6; 3, 4, 5, 6,
00:14:35.500 --> 00:14:40.600
Each time I have a blue and a red, an opposite, I am going to cancel it out.
00:14:40.600 --> 00:14:47.200
All of these cancel out; what do I have left?--2.
00:14:47.200 --> 00:14:52.700
That is positive because blue is positive; it is +2.
00:14:52.700 --> 00:14:57.200
Or you can just take the absolute value of these numbers.
00:14:57.200 --> 00:15:02.700
The absolute value of 8 is 8; the absolute value of -6 is 6.
00:15:02.700 --> 00:15:08.900
We are going to subtract those numbers; 8 minus 6 is going to be 2.
00:15:08.900 --> 00:15:13.900
This is only when the signs are opposite; so 2.
00:15:13.900 --> 00:15:20.400
Then this was an absolute value of 8 and this was 6.
00:15:20.400 --> 00:15:25.600
The bigger number is 8; that has a sign of positive.
00:15:25.600 --> 00:15:31.900
You are going to give that same sign to the answer which is 2.
00:15:31.900 --> 00:15:34.700
It is going to become +2.
00:15:34.700 --> 00:15:39.400
Again you take the absolute value of each number; subtract them.
00:15:39.400 --> 00:15:43.700
It is 8 minus 6 because absolute value of 8 is 8.
00:15:43.700 --> 00:15:48.300
Absolute value of -6 is 6; 8 minus 6 is 2.
00:15:48.300 --> 00:15:55.200
Then you are going to give it the same sign as the bigger number.
00:15:55.200 --> 00:15:59.800
That is a positive; your answer becomes +2.
00:15:59.800 --> 00:16:02.800
That is it for this lesson on adding integers.
00:16:02.800 --> 00:16:05.000
We will see you next time; thank you for watching Educator.com.