Integers and Absolute Values - By Anywhere Math
Transcript
| 00:0-1 | Car has a velocity of 35 mph and carby has | |
| 00:05 | a velocity of negative 40 mph . Which car has | |
| 00:09 | the greater speed . Mhm . Welcome to anywhere , | |
| 00:30 | Math . I'm Jeff , Jacobson . And today we're | |
| 00:32 | gonna talk about integers and absolute value . Alright , | |
| 00:36 | let's talk about those cars . But before we do | |
| 00:38 | , we need to determine what's the difference between velocity | |
| 00:42 | and speed . Ah speed . You should know . | |
| 00:45 | Well it's how fast something's going , but velocity you | |
| 00:48 | might not know . And philosophy is very similar to | |
| 00:51 | speed . It says how fast something is going , | |
| 00:54 | but it also tells you the direction it's going . | |
| 00:58 | Which is why uh in the example one car was | |
| 01:01 | going a negative velocity . So let's talk about that | |
| 01:05 | car a had a velocity of 35 mph . Carby | |
| 01:16 | had a velocity of Negative 40 mph . Okay , | |
| 01:25 | yeah , this one's positive . The velocity here is | |
| 01:28 | positive and the velocity here is negative . And basically | |
| 01:32 | what you can think of is , well , this | |
| 01:34 | car is going forward which is why it's positive . | |
| 01:38 | This was negative . It's the opposite which means it | |
| 01:40 | would be going backwards or in reverse . Um So | |
| 01:44 | that's the velocities . Now let's figure out what the | |
| 01:47 | speed is because that was a question which had the | |
| 01:49 | greater speed . Well the speed here is simple . | |
| 01:53 | It's still 35 mph . Okay . That's that's how | |
| 01:58 | fast it's going . How about the speed for carby | |
| 02:03 | ? Remember with speed we don't care the direction , | |
| 02:05 | just how fast it's going in reverse . That's fine | |
| 02:10 | . It's going 40 mph . That's how fast it's | |
| 02:16 | going . So which car was faster or had the | |
| 02:19 | greater speed ? Uh huh . Car B All right | |
| 02:26 | . So today's lessons about absolute value and integers . | |
| 02:30 | Well , first let's talk about what what are integers | |
| 02:32 | . Are yet uh integers you can think of are | |
| 02:35 | just positive and negative . Whole numbers . Okay , | |
| 02:49 | so 1234 Those are integers and so on . But | |
| 02:56 | also the negative of those . Right ? We've got | |
| 02:58 | zero negative one , negative two negative three and so | |
| 03:03 | on . Those are also introduced . So it's pretty | |
| 03:06 | simple when you think introduces think positive and negative whole | |
| 03:09 | numbers . They don't include fractions . They don't include | |
| 03:12 | decimals , only whole numbers that are either positive or | |
| 03:16 | negative . Next let's talk about what absolute value is | |
| 03:20 | . Absolute value is simply the distance A number is | |
| 03:31 | from zero on a number line . It's just how | |
| 03:42 | far away is that number from zero ? Okay , | |
| 03:45 | that's all the absolute value is . And when you | |
| 03:48 | think about a distance distance is always going to be | |
| 03:50 | positive . Okay , So when you take the absolute | |
| 03:53 | value of a number , you're never gonna get a | |
| 03:55 | negative value because you can have a negative distance . | |
| 03:59 | If someone asks you , oh how far did you | |
| 04:02 | run today And you you're not going to say negative | |
| 04:04 | five miles . That doesn't make sense . Distance is | |
| 04:07 | always positive . And same thing when we take absolute | |
| 04:10 | values of numbers , you always get a positive number | |
| 04:13 | . Let's try some examples . All right , here's | |
| 04:15 | example . One find the absolute value of two . | |
| 04:19 | And if you remember absolute value , we're talking , | |
| 04:21 | how far away is that number from zero ? On | |
| 04:24 | a number line ? So let's draw a number line | |
| 04:28 | . Okay . Yeah . Yeah . So I'll just | |
| 04:31 | start here is maybe negative 101 and two . Okay | |
| 04:38 | . So too on the number line is going to | |
| 04:40 | be right here . Well , to figure out the | |
| 04:44 | absolute value of two , we just need to figure | |
| 04:46 | out how far away is that from zero ? Well | |
| 04:49 | , it's pretty simple here . zero . There's two | |
| 04:52 | . What is that distance ? It's too . So | |
| 04:56 | the absolute value of two is 2 . So when | |
| 05:00 | you write absolute value of a number , Yeah . | |
| 05:06 | You write like this with these two vertical lines and | |
| 05:09 | you read it . The absolute value of two is | |
| 05:15 | two . That's the distance . Okay , notice it's | |
| 05:18 | positive . Right ? How far away ? Let's try | |
| 05:21 | another example . All right . Here's another example . | |
| 05:24 | Find the absolute value of -3 . If you want | |
| 05:27 | to try this on your own first , go ahead | |
| 05:29 | and pause the video . Remember absolute value . How | |
| 05:32 | far away is negative three from zero on a number | |
| 05:35 | line . So , let's start with another number line | |
| 05:39 | . Uh negative three . I'll make that right there | |
| 05:42 | , negative to negative 101 Well , here's negative three | |
| 05:50 | right there . How far away is it from zero | |
| 05:56 | from here ? 20 What is that distance ? Well | |
| 06:01 | , pretty simple . That distance is three . So | |
| 06:06 | yeah , The absolute value of -3 is three . | |
| 06:16 | Okay . Again notice it's positive . Distance is always | |
| 06:20 | going to be positive . So when you take the | |
| 06:21 | absolute value of number , you're going to get something | |
| 06:24 | positive . Okay , here's some to try on your | |
| 06:27 | own . All right . Here's the last example compare | |
| 06:34 | one and the absolute value of negative fort again . | |
| 06:38 | If you want to try this on your own , | |
| 06:39 | go ahead and pause . Um So I don't think | |
| 06:42 | we need to draw um a number line again . | |
| 06:46 | But if you want to you can Well , we | |
| 06:48 | know one is one . That's fine . We just | |
| 06:51 | need to know well what is the absolute value of | |
| 06:52 | -4 ? And hopefully you remember again , How far | |
| 06:59 | away is that from zero ? Well , negative four | |
| 07:02 | is only four away from zero . So the absolute | |
| 07:04 | value of four . I'm sorry the absolute value of | |
| 07:07 | -4 is four . Okay , So hopefully you're starting | |
| 07:11 | to realize any time you take the absolute value of | |
| 07:14 | a number , you're going to get a positive number | |
| 07:17 | right ? So if you have a negative number here | |
| 07:21 | it would become positive . If you had a positive | |
| 07:23 | number here , the absolute value of positive number stays | |
| 07:26 | positive . Okay ? Um So then all we gotta | |
| 07:29 | do is compare one and four . Well one is | |
| 07:33 | less than four , therefore one is less than the | |
| 07:38 | absolute value of -4 . Okay , that's the last | |
| 07:44 | example . Here's something to try on your own . | |
| 07:50 | Thanks for watching and if you like this video please | |
| 07:53 | subscribe . Yeah . |
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