jwGwAwDxikc

so hello there and welcome to another
tutorial
my name is Tanner Bakshi and this time
we're going to be going over the second
revision for the integers tutorial that
I made a few weeks ago now this is going
to be really interesting as we go into a
bit more complex stuff which is
multiplication and division since last
time we covered addition and subtraction
so now as you can see here we have a
little diagram explaining exactly what
we've been taught and what we still have
to be taught so as you can see in
integers we've already taught you
addition and subtraction in part 1 and
now we're going to be teaching you
multiplication and division now you
might be thinking that these are simpler
than this and that's exactly why I said
now we're going to be going into the
complex stuff but you're wrong
I agree sometimes in school like mostly
in schools they do teach you addition
subtraction first then multiplication
and division but that's because there
are negative and positive numbers both
there's just positive numbers meaning
sometimes these could be considered
easier than these however when you get
negative numbers into the mix you're
looking for a more systematic and
foolproof way of doing this stuff and
that's where multiplication and division
come in which is basically much more
systematic way of doing things there's
one defined or set of rules that you
have to follow and in addition
subtraction which is much more abstract
basically so now I'm gonna be explaining
it to you and let's get to the drawing
board so as you can see I'm gonna draw a
simple question which is plus five x
plus four okay let's just use this as an
example just see here or actually now
that I think about it because we want
our division to be much simpler let's
use the numbers six and three okay
because that'll make our division much
simpler you'll see why in just a minute
so if we use six and three as you can
see we have six times three and actually
positive six times
three now you might be thinking how will
we solve this well first of all we want
to look at the numbers and ignore the
operators currently so if we take 6
times 3 just normally no operators
basically then we get the answer 18 so
what we can do is we can write down the
answer as 18 but then there's a slight
problem and let me explain what this
problem is and just let it becomes a
little bit easier for us I am going to
make a little bit more gap because
you'll see exactly why in a minute so
now what I'm gonna do is I'm going to
write down a set of rules that you
should also always follow when you are
doing multiplication or division with
integers which is if there's a positive
or positive it'll always come out or
actually a positive or positive or
negative and negative it'll always come
out to be a positive if it is a positive
or a negative or negative and a positive
then it'll always come out to be a
negative so essentially we're saying
that if they are the same operators in
the question then it'll come out or a
result to be positive if it there if
there are different operators then I
will always result in a negative result
so now if we were to look at this we
have a plus and a plus and those two are
the same so what does our you will say
our rule says that this should be a
positive number right there so as you
can see that's why I was making that
little gap because then we can put in
that plus really easily so now let's
just say we have plus 6 times minus 3
how do we go about doing this well we
have a plus and a minus a plus and minus
are not the same so they conflict with
each other and it becomes a minus so I
can do minus 18 for this answer okay now
let's do minus six x plus 3 why would
this be equal to let's see this again
minus and plus minus and plus are not
the same so what does that give us
negative so
it would be a negative 18 here lastly we
have one more question which is negative
six times a negative three
now the answer will obviously be
negative 18 yeah so that was all for
multiplication but wait just one minute
this was just to fool you to see if you
knew the answer this is actually
supposed to be positive I know your
instinct will say that negative and
negative makes a negative because
they're both negatives how can it make a
positive but if you follow the rule of
multiplication then this has to be a
positive because they're both similar so
now that we're done this you should know
the basic rule and you should be able to
do it with division so now you'll see
exactly why I chose six and three for
our numbers watch this
and so now all I need to do is put
division symbols here and then all I
need to do is put twos in these because
6 divided by 3 is 2 now if you look at
it this is the exact this is these are
real correct answers and the reason is 6
divided by 3 that's equal to 2 a plus
and a plus they're similar that comes
out to a positive so it's positive 2
plus minus that becomes negative 6
divided by 3 that's 2 so negative 2
minus the plus minus 6 and 3 2 so
negative 2 again then minus and a minus
comes out to be a plus because they're
similar again and 6 & 3 6 divided by 3
is 2 so positive 2 so that's exactly why
I said that this is actually very very
simple if you use the numbers 6 & 3
because then you only need to erase the
operators for the answers that's it and
so this is a really good way of
demonstrating how this rule actually
works because the same operators are
being used and you always get the same
operator result and
matter if you're using multiplication or
division that just shows that we're
actually using the rule now let's just
go into it a bit more let's say we're
asked a question like this okay let's
look at this for a sec we have a
question which is let's just say oh I
don't know negative positive 3 times
positive negative 4 what would this be
equal to
well what we have to do is just like in
fractions but not really you always
simplify fractions well you are gonna
simplify this question quite literally
using this very rule so I wanna simplify
we take this part okay and then you say
okay how are we taking this we have a
minus and a plus
these are not similar so we get a
negative so the first number is actually
just negative 3 ok now let's look at
plus and minus these are again not the
same meaning we get a negative output
meaning this is times negative 4 which
looks very similar to you because I just
taught you how to do this literally a
few minutes ago now if I say equal to
you should see that negative a negative
what does that equal positive because I
just taught you that 3 times 4 12 so the
in theory the answer should be positive
12 and this answer is correct now that
we have that out of the way we can
easily just erase this question mark and
say that we know this question and the
answer to this is plus 12 I'll just give
you one more example really quickly and
this time let's just use division since
you know the rule so I'm just going to
erase this part okay now let's do this
let's do something like plus
- 6 / - -2 is equal to you know let's
simplify this again as you can see we
have plus and minus so that would end up
to be a negative result meaning we have
a negative 6 here now we have a division
symbol of course and then we have two
negatives as we know that comes out to
be a positive answer and because it
comes out to me a positive answer
negative 6 divided by positive 2 which
is equal to again I just taught this to
you a few minutes ago let's look at this
- + not the same that means we get a
minus result now if we divide we see 6
divided by 2 is 3 so we just say 3 and
you say the operator is negative it's
that simple and we can again say that we
know how to solve this sort of a
question now I'm not giving you two
examples I think it should be quite
fluent with it and yeah that was really
all you had to learn in this part of
integers and yeah this was the last part
in the series if you do want some more
information maybe you can just leave it
in the comments and I'll take a look at
that you can even email me at Taji manye
gmail.com my email will be down in the
description if you have any troubles
will be in down in the description so
you can check it out you can email me
and please like the video if you liked
it and also subscribe if you're new to
my channel to get all the latest videos
that I release and that'll be it goodbye