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How To Divide Integers Of The Same And Opposite Signs
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Feb 19, 2025
Welcome back to our study of integers, in today's section we're going to talk about how to divide integers and focus mainly on the quotient of integers of the same and opposite signs, as well as learn how to evaluate expressions involving quotients. Chapters 00:00 Introduction 00:42 How to divide 2 integers of the same sign 01:43 How to divide 2 integers of opposite signs 02:54 Evaluating algebraic expressions involving quotients 06:18 real world example ( application)
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0:02
okay all right so we are starting a new
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section we're going to talk about this
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again this is pretty pretty simple right
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we're going to talk about um this week
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on Tuesday we talk about
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subtracting multiplying integers
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right now I'm going to talk about
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dividing integers right the principle is
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the same it's not any
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different want and division they have
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the same type of uh
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process right
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so the first thing we going to talk
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about is when you have two integers of
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the same sign how do you divide them
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what happens to their ass signs okay so
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again quotient mean division right so
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the quotient of two integers of the same
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sign is always what a positive number
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the outcome is always going to be
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positive
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example
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-10 / -2 is POS 5 and then 10 / 2 is 5
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because they are the same sign we are so
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used to using positives all the time so
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you already know this right now we have
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two negatives what do you get a positive
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because Division and multiplication they
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have the same process yeah of the same
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side would be negative say it again I of
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the same sign would be negative yeah
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well you have a
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-10 and then a -2 so two integers of the
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same sign they're each negative right so
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if you divide them you get a positive
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all right and then the next thing is
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opposite signs and when you do opposite
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signs it's the same thing it's not I
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mean it's the same as as uh
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multiplication the quotient of two
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integers of opposite signs is always
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negative
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example
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-9 / 3 is -3 right and then 15 /5 is -3
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so if you want to make a table you can
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do that if you want so if you put a
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table here you build it right so if you
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have a negative ided by negative you get
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what positive you can if you want yeah I
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made one already right and then negative
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/ positive is a
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negative and then a positive / a
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negative is a negative
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and then two Nega a positive and a
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positive give you a positive when you
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divide it all
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right so that's that so this really like
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I said this is really simple
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right what you laughing at okay all
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right so now we going to learn how to
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evaluate an expression all right so say
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we
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have if x is -6
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and Y is -3 I want you to find 12 y / X
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so here all you're doing is substitution
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so we're going to
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replace let me erase this here we're
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going to replace now again some of you
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guys are still doing this like you see
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this and you go 12 and then six that's
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the 126 when you have 12 and Y always if
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you don't if you forget just put make
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sure you put a what put a dot there to
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remember this is a multiplication right
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so this is 12 * -6
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/ -3 now we have two things going on at
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the same time right we have a
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multiplication and we have a division so
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I have 12 * -6 what is that going to
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give
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me something what is
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it what is that
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something is it it 12 * 3 12 * -6 right
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is oh y you're right Y is -3 thanks for
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catching that right and then this is -6
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so 12 * -3 what do that equal 36 36 36
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because the positive * a negative is a
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negative right - 36 and now you divid
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about -6 what do we get 6 we get a posi
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six right we get a positive six or just
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six okay because you doing 12 * -3 that
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is the law of multiplication when it
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comes to negatives you have a positive
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and a negative you get a negative and
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divided by negative you get a Nega a
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positive
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good I don't again go sit next
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to can I go my lock get some yeah all
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right and then now we
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have -5x
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y right no
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I'm -5x / y so it's the same process
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it's going to be -5 time what time -6 *
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-6 right and I choose to put this in
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parenthesis because I do not want to
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have any problems with my negative and
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I'm divided by y what's
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y y
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is -3 right now I have three things
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going on at the same time What is5 *
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-6 emily5 *
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-6 I have two
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negatives no positive right because this
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is two right and now I have 30 I know
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and I divide it by -3 yes 10 huh 10 10
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10
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10 because this is positive and in
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negative right positive and negative
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now now here's what's going to go on
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here so now we
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have a word problem which I know you
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guys love right love now the wind chill
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right temperatures in fah heit for 7
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days where -65 2 -10 1 9 and six they
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want you to find the mean temperature
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given this data here right so how do we
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do that remember for the last 10 days we
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had a lot of rain right but it wasn't
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this
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cold but it was just raining it was like
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like 50s yeah so how would you find the
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mean temperature yeah I want to say we
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add them we add them and then do
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what divid by seven days so divide by
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what by s seven right by seven not two
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but you have the right idea so we have
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seven temperatures we want to find the
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average temperature for those seven days
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we have to add them all up together and
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divide by seven right so now you see
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what's going on we have -6 + what + -5 +
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2 + -10 + 1 and then plus 9 and then + 6
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all that we are dividing by seven that's
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a little fast right so now the question
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is as you can see this almost like a
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recap of everything that we've been
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talking about we have a bunch of
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negatives okay we have some positive so
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how you going to go about doing this we
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will have to use the pendas right so go
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ahead and tell me what you got
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calculator uh no no calculator you do by
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hand let's go step by step right what's
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-6 +5
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30 I mean -6 +5
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I'm sorry 11 11 right and then I'm going
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to have now I'm going to do this two
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together what's 2 +
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-108 right my go what's 1 +
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988 and then plus 6 right and now we
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have what's ne1
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+8 19 and what is 8 +
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62 -2 right so now we have -19 + -2 over
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7 what's 9 +
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-2 21 - 21 over
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7 and that's three that
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is3 sorry de F was he cold was he hot or
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was he what this is freezing because
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it's below what zero below zero so
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that's freezing temperature right and
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some some places it's so cold that even
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when you spit before the spit gets to
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the ground it turns into what ice that'
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be crazy right imagine going out there
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going I I sick disgusting yeah I know
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right like out so this is pretty much
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division we just wrapped up that chapter
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so what I want us to do now is we can go
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ahead and work on some uh sample
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problems in the book and then we're
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going to close this up all right so this
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is