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How To multiply integers of the same and opposite signs
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Feb 19, 2025
Welcome back to chapter 2.4 of our section on integers. In today's lesson, we're going to be talking about the multiplication of integers of the same and opposite signs. We'll also talk about how to multiply more than 2 integers as well as discuss evaluating expressions involving the multiplication of integers. Chapters 00:00 introduction 00:36 how to multiply Integers with opposite signs 02:35 how to multiply Integers of the same signs 03:17 multiplication table of signs for integers 03:49 Real word problem ( application ) 06:52 How to multiply more than 2 integers 09:36 How to simplify algebraic expressions
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0:01
so now we are talking so the first thing
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I want you all to do is you have to take
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notes right you have to take notes
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because if you don't take notes you
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can't understand the material if you
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don't take notes and if you don't do
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your homework that is not going to help
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you have to take a lot of notes and I'm
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recording these videos for a purpose so
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that you can go back and watch it this
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is your own class you see what I'm
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saying so that you can go back and watch
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it again right and then do your homework
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now we're going to talk about
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multiplying integers right first one
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first
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section integers with opposite signs
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right what does that mean when I say
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opposite
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signs what am I saying yeah posi and a
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negative a positive and a negative or a
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negative and a positive vice versa right
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so if you have two integers that do not
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have the same signs and you multiply
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them what do you get right so the
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general rule is this the product or the
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multiplication of of two integers of
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opposite sides is always what negative
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right if you multiply to integers that
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do not have the same signs the result is
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always going to be negative no matter
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where you go it's always going to be
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negative right so if I do 2 * -5 that is
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-10 and then -3 * 10 is -30 that's what
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I'm saying because this is negative
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right this is this is negative and this
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is positive so a positive * a negative
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always equals a negative yes all right
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here thank you all right and in the same
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way likewise a negative times a
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positive always gives a negative that's
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just how it is that's just a rule right
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so a a negative * a positive equals a
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negative and a positive * a negative is
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always a negative okay so 3 * -2 is -6
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-2 * 3 is -6 because multiplication is
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what what's the rule that we learn about
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multiplication yeah commutative
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commutative right CU you can reverse it
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doesn't matter it's always going to give
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you a negative right now
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second when you have two integers of the
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same sign right the same sign what's
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funny you
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you laughing all right so the product of
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two integ of the same sign is always
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what positive right if I have a negative
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and I multiply that negative by another
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negative I get a
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positive and if I have a positive * a
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positive is a positive that is something
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that you know because 2 * 3 is 6 you
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know about positive and positive now the
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new one is negatives right so if I have
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-3 * -3 I get pos3 so a negative time a
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negative always equals a positive and a
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positive time a positive is a positive
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so same signs you always get a positive
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all right so same signs that's always
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going to give you a positive that's just
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a given right and I give you a little
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table here so let's say you
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forget right just remember same signs
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positive opposite signs negative if you
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can remember that it'll be easy for you
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right same signs the outcome is always
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positive when it comes to multiplication
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and opposite signs the outcome is always
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what negative all right so positive
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negative negative and a positive does
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that make sense all right now let me
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give you a quick problem here let's see
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if you can figure this out right does
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anybody have scuba
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di you interested in
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SCU huh you want a scuba ey no yes no
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yeah I mean I I I don't think I want a
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scuba ey just cuz I don't know what's
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under I just I'm
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thinking you know so I don't really like
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but you know it's fun my new friend you
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do huh yeah yeah I thought you wanted do
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scuba
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dive all right so it says here
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right a scuba diver the same from the
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surface at a rate of 7 ft per minute
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right so he's descending at this rate
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what was his death at 15 minutes right
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so he's diving every 1 minute he goes
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down how many feet 7t right if he's
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going down what does that say is he a
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negative rate or a positive rate
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negative rate so his rate is negative so
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let's say rate is -7 Right feet per
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minute
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ft now I want to know how deep is this
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guy after 15 minutes how do I solve
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this 7 * 15 right thank you so 7
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-7 *
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15 right so how much do I get what's 7 *
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15 7 * 5 is what 35 right you 10 37 and
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one is so that's so he's how how he's
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about 100
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ft below what SE below sea level so this
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really deep in the water that's pretty
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deep that's like this room is about
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having like about let's
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say about maybe I'm six so six and maybe
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this one about six maybe 7 and 7 and5
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right so he's 105 ft below sea level
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that's like how many times it's about 15
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times is De that's pretty deep I you
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know I don't want to do that scary right
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so he about 150 ft and make sure he's a
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negative cuz you're going down right so
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every time you you hear the word the
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saying you're going down it's it's going
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down that means it's negative when I I
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say I'm doing what positive positive cuz
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I'm going up right remember when at the
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resurrection what did Jesus do before he
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left his
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disciple say
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again he went to the sky he ascended
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right they saw him when he just
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oops now you you want to see that some
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just going again disappearing I mean
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that's insane right but he did all right
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now now that we've talked about
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multiplying inges of the same signs so
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far we've only seen like two integers
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two just two right now we going up and
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now we talking about more than two
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integers right so now we have three
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integers and then we want to multiply
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them so how would you do this uh Kinley
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we have -4 3
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* so how do you think you're going to
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solve
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this knowing the rules that we've learn
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right so how would you solve this we
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have -4 * 3 *
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5 -4 * five okay so you can do
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that all right what's that going to give
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you 20 what's the rule oh positive
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because they are what
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same same and then what are you do after
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that 20 * * three and that
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is 60 60 right so you do the two first
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or you can go in order right you can do
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now she use what she use here to do this
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she used the associative law right this
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times this times this you can do that if
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she want right or you can go in order4 *
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6 going to give you what
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-2 right4 * 3 that gives you -2 and then
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times by5 what do you get 6 60 it's the
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same thing
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right so first you can go this two and
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whatever you get times it by the last
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one all right now I have three negatives
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-2 * 5 *
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-6 no how would I do
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this all right 10 okay
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is -60 so I want you to come to see
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something here how many negatives do I
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have three right three is it odd or even
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odd so anytime you have an odd number of
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negatives the outcome is always going to
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be
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what negative right cuz I have three
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negatives so I know that the outcome is
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going to be negative but when I have an
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even number of negatives the outcome is
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going to be what
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positive right say I have -1 * -3 * -4
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* * -6 how many negatives do I have here
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five five so therefore the outcome is
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going to be what negative because it's a
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odd number of negatives right so this is
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how you figure out negatives especially
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multiplication and division are pretty
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easy to figure out the only thing that
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gets hard is when you have like um that
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and then you trying to add on
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uh variables and and stuff now here
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we're going to talk about simplifying
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algebraic expressions right so I have -2
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* an X and then * -6 this is an
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expression because you have what you
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have a variable right an unknown so this
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this is therefore an expression so how
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would you solve this -2 * x * X yes
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first of all is the X positive or
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negative we don't know the X does it
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matter right it doesn't matter the x
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value does not matter right all we know
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this an X yes combine like terms start
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with okay -2
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* which
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is POS 12 right2 you can rearrange it
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right and then
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um 12 * X which is 12x 12x right so this
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should be 12x right does that make sense
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cuz we have again if I feel like this is
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too overwhelming I'm like okay I have
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two negatives so I know that my outcome
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is going to be what positive right I
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have two negatives so I know I'm going
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to get a positive number so 2 * 6 is 12
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and then X because the multiplication is
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12x right 12x now here I have
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-7x * 4
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y -7x * 4 y uh Dexter what do you think
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-7x * 4
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y 2x y - 28x y right because I have one
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negative so I know the outcome is going
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to be negative I have a negative and a
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positive so - 28x y all right so this is
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pretty simple so now what I want to talk
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about is the last thing I want to talk
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about in this chapter is
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uh when you have an expression and now
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they asking you to like let's assume
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that
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X is -3
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Y is -4 and then
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Z is uh 10 and I want you to
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find
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2x Y how would you do this I want you to
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find
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2xy I want somebody else Vicki I want
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you to find 2x y if x is -3 Y is -4 and
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Z is 10 I want you to find 2
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XY first what does that
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mean say it
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again 2 * -4 *
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y let's go in order right X is equal to
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what so it's 2
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* oh sorry I thought
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was 2
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* and then
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time4 right so 2xy means you multiplying
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two by -3 and then
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by4 that make sense right so now you
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have multiple options you have at least
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three options to solve this KY what's
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one of
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them
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um3 * all right that
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is um
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I don't know 12 12 you say 12 yeah all
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right and then times what two two which
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is 24 24 right so 2x y will be 24
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because you're doing 2 * -3 * 4 now I
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want you to find x y z what's
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XYZ uh somebody else uh wasn't spoken
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there oh I get
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XYZ um
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* 10 * 10 right so do you think the
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resultant number is going to be positive
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or negative negative why is it
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negative it's an odd number how many
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negatives do I have oh two two positive
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right I don't have this is not an odd
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number this is a I have even number of
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negatives right so therefore what do I
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get -3 * 4 is
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is 12 right and then this is 120 all
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right so this is this is pretty simple
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stuff okay so now I'm going to assign
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some work for you guys to do in class
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now we have a 15 minutes we can still
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work on those we can start off here all
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right
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