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Integers & Absolute Value
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Feb 19, 2025
In our class today, we'll transition from whole numbers and their operations to talking about integers and one of their characteristics, the absolute value. Chapters 00:00 Introduction 01:00 Negative numbers 01:20 Positive numbers 1:45 What's an integer? 02:58 Using integers to represent real life situations 05:25 How To compare integers 10:12 What's absolute value
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I'm recording I'm recording so by the
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way um resp I
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sent I sent you guys all uh an invite on
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Google Classroom right did you all get
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it or did you all respond to it I forgot
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to do something else I all right when
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you get a chance please join that so all
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the videos that we recorded are all
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there so if you want to go back and
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watch it and someone them fun if you
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want go watch and laugh show you know
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you can do that the one we were talking
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about functions and stuff I was
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I was laughing right so today we're
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going to start a new section so the new
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section is integers and absolute value
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again this is fun fun stuff right now
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integers first we need to understand
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what integers are right so the first
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thing I want to discuss
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is negative numbers right negative
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numbers so thus far we have not talked
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about negative numbers but I'm sure you
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guys know negative numbers right by
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definition negative numbers are that are
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less than what Z zero so they on the
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left side of the number line so if you
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have a number line all numbers on the
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left are called negative numbers all
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right so those are negative numbers -2
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-3 -4 those are all negative integers
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okay and then we have the positive of
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course the positive are anything 1 2 3 4
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five they're on the right side of the
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number line Beyond zero okay so negative
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so if you have your number
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line positives are here negatives are
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here NE this is pause right positive
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okay now what what's an integer by
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definition does anybody have the
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definition of an integer yes sir number
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a number okay is that
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sufficient is this just a
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number what is
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it what's the set of integer negative
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and positive right this the set of
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integers is a set of all positive and
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negative numbers right so all positive
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and negative numbers zero included are
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called integers so those are the
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integers so anything negative Infinity
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all the way to what positive Infinity
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that is a number okay it exclude
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decimals it excludes fractions it
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excludes rational numbers it excludes
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radicals so all of these are called
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integers -1 -2 5 0 1 2 3 all the way to
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positive infinity and all the way to
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negative Infinity
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right again if you if you look at like
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the set of real numbers the set of
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integers um this is stuff that we use on
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a day-to-day basis without the decimals
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okay
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now so we can write integers in real
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life situations okay inges are used
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sometimes to describe actual real life
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situation for example when I say 23 F
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below zero how would I write that if I
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was to reuse an integer
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yes3 -23 that would be the
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representation of 23 fhe below zero now
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is that freezing or what freezing
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freezing right so -3 23 so you see -23
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that's really cold it's freezing right
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so -23 and when I say 11 in more than
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normal what am I saying how would you
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represent that eer 11 in more than
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normal again how would you represent
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that as an
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integer think
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yeah 11 in more than normal what is
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normal POS 11 right so the normal so you
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have a normal so more than normal that
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means POS 11 cuz the normal is zero so
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postive 11 or just 11 you don't have to
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put plus 11 right you can just put 11
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now if you playing football right a loss
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of eight yards so how would you
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represent that everything is
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it a loss of eight
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yards you know football
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right- 8 right -
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8 now the Washington Redskins are used
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to losing your yards all the time they
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not that good of a team are
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they that's my my brother who's the
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commanders fan here commanders Redskins
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is my Wi-Fi password Redskins they the
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Redskins they're not the commander I
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like the
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red what's your what's your team
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Ravens Redskins you
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redin you don't watch it what I like the
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CHS you don't watch it
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I just like whatever I I just like what
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other team my brother likes I like I
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like the what Chiefs and Chiefs and
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patri patri all right that's what my
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brother's like you
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like CH Chiefs the 49ers all right
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anyway now we're going to learn how to
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compare what integers all right come on
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stay with me so we're going to use the
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number line to compare compare integers
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okay so now here's the thing he he hey
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hey hey
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quiet guys guys guys that's Chicago
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Bears a hockey team or a football team
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that's a football team okay all right so
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now we're going to learn how to compare
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integers right how do I compare integers
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I use less than more than or equal okay
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so if I have -2 and four hey I can hear
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your like I'm going to have to move you
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so you better hush up so -2 and four how
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would I compare these two
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numbers -2 and 4 yes uh you making -2
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positive I can't make it
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positive no we have to compare them
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right
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yes NE -2 is less than four does anybody
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agree there that -2 is less than four
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yes or no yes why is it less than four
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because -2 is where on the side of zero
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on the behind zero SO2 is obviously less
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than four what about
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-5 and
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-66 which one is so what would you what
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would you put
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there5 is greater or less than greater
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greater right because if you were to put
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down on a number line5 is here -6 is
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right behind it so5 is greater than -6
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okay so that's the negative integers so
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the negative integers so now you can
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compare positive that's pretty easy
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because you know what about
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this
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-2 and
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2 let's compare these two numbers -2 and
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two yeah equal yeah equal why are they
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equal because two I got double negatives
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that turns out to be what positive right
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I have two negatives here that gives me
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what a positive okay soga -2 is the same
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as saying positive2 so that means 2 is
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equal to two so that that will be equal
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now we not there yet but we can still
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learn how to do that right so now what
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I'm going to ask you to do here is to
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order integers right so John and his
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friends played the question in the
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answer video game there scores were
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1-5
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01 2 and four right so what I want you
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to do now is put them in order from the
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least to the greatest so how would you
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do that
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you have
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1 -5 01 2 and then four and then so I
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want you to put them from the lowest to
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the highest number I want you to order
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these
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numbers got it
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so we are we are ordering this number
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okay I give you a list of integers we
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have one we have -5 we have 01 2 and
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then four so what we want to do is is we
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want to order them from the least to the
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greatest right to the least to the
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greatest so we can use the number line
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to do that right or if you feel like you
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don't need the number line you can also
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do without it cuz if you know your
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negative and you're positive but let's
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use the number line to be
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more so if you zero here what's one
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one is here right two will be right next
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to it right four will be somewhere here
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and then zero is here1 will be here and
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then five will be right here right so if
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you were to list
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them yeah on the left side of the
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zero no this side is a positive this is
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a positive
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zero and this is the negative side okay
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so the negatives are on the left side on
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my left side so if you are here is on my
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right side okay zero is here you go from
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left to right cuz we are from Saudi
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Arabia right you go from left to right
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so left negatives and then right
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positive right so
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-5 -1 0 1 2 and four so this is how we
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list it
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okay from the Leist
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to the greatest all right so I'm going
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to give you another one to do in a
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couple of minutes so now the next thing
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we're going to discuss is absolute
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value absolute value all right and a lot
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of times you guys have you guys done
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absolute value in uh in your previous
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classes you did all right so basically
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by
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definition the absolute value of a
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number is the distance of that number
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from zero this is why the absolute value
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of number is always what positive right
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so for example if you see this
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here that's a gap here right there's
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another Gap here so if I was to find the
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absolute value of -2 I'm technically
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saying what is how how far is two from
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zero that's what I'm looking for two
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units right can we have negative units
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no so this is why the absolute value of
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a number is always positive okay so the
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absolute value of -2 is two and the same
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thing goes for the absolute value of two
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the absolute value of two will be the
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distance from 0 to two which is again
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two unit is that making sense right so
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the absolute value of two is
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pos2 what's the absolute value of5
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alen what would be the value
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of five right five because the absolute
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value of a negative number is always
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what positive positive okay because the
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absolute value is actually saying the
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distance from that number to zero so
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this is why you can't have negative
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distances so the absolute value of a
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number is always positive uh Kenzie
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what's the absolute value of
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-10 not sure all right so the absolute
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value did you understand the definition
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I didn't see that you didn't see all
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right the absolute value of a number is
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the distance that that number is from
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zero does that make sense yeah all right
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so therefore what's the absolute value
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of-1 10 that's right 10 that's it
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right uh Daniel what's the absolute
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value
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of
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three is always what three three cuz
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it's always what positive is the
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distance that number is from zero it's
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always positive because you can't have
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negative distances right uh Kinley
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what's the absolute value of
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negative
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20 what's the after of
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20 20
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20 if I can put a billion zero billion
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negative is always going to be positive
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because the distance has to be always
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what a positive
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right what's the absolute value of
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negative
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negative
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Nega
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9 uh this yeah nine it doesn't matter I
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canot the consilion zero negatives it
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won't change your outcome because it's
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always the distance that that number is
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from zero which is always a positive
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number okay so it's always positive
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always positive now we're going to talk
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we're going to do some work now all
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right so actually before we do that let
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me let's work on a couple of things here
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we're going to talk about the absolute
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value of an expression can I eras
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this yes all
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right talk about the absolute
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value of an expression
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algebraic
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expression you guys remember what the
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this means algebraic expression you all
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remember what is it yeah yeah
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yeah
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expression that's right an expression
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that has an unknown or a variable in it
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right so for example if I want you to
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find the absolute value of x
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- 2 if x is -3 so how would you solve
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this I want you to find or I want you to
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evaluate the absolute value of x - 2 if
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x is2 so let's try and work on that you
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want to do
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it what is it one one how do you know
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it's one what do we do because if x is3
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the absolute value of3
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because it's three unit Z that's right 3
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- 2 which is one right so if I want you
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to evaluate this what I'm asking you to
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do is replace X by what -3 right and
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just like you say the absolute value of3
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is the distance of that number is from
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zero which is what positive 3 is always
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positive so that would be 3 - 2 that is
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one okay so we're going to do a bunch of
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problems like this to conclude the
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section and then
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um
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