[Music] now I’m going to present you my
now I’m going to present you my
now I’m going to present you my presentation so imagine that we’re in a
presentation so imagine that we’re in a
presentation so imagine that we’re in a big box and we need to figure our way
big box and we need to figure our way
big box and we need to figure our way out of it everyone can see the doors but
out of it everyone can see the doors but
out of it everyone can see the doors but is this the only way out thinking
is this the only way out thinking
is this the only way out thinking outside of the box or looking beyond the
outside of the box or looking beyond the
outside of the box or looking beyond the formula actually mean the same thing but
formula actually mean the same thing but
formula actually mean the same thing but the difference is the aspect that you
the difference is the aspect that you
the difference is the aspect that you look at them so now I’m about to tell
look at them so now I’m about to tell
look at them so now I’m about to tell you something that you think of all the
you something that you think of all the
you something that you think of all the time when you go to bed when you wake up
time when you go to bed when you wake up
time when you go to bed when you wake up when you sleep when you eat let me tell
when you sleep when you eat let me tell
when you sleep when you eat let me tell you it’s math so some of you might be a
you it’s math so some of you might be a
you it’s math so some of you might be a little skeptical about this presentation
little skeptical about this presentation
little skeptical about this presentation but I promise to explain everything when
but I promise to explain everything when
but I promise to explain everything when I was grade 6 I had a very calm and
I was grade 6 I had a very calm and
I was grade 6 I had a very calm and unstressed life but the moment when I
unstressed life but the moment when I
unstressed life but the moment when I needed to prepare for examine the end of
needed to prepare for examine the end of
needed to prepare for examine the end of seventh grades ruin my whole time I mean
seventh grades ruin my whole time I mean
seventh grades ruin my whole time I mean I had so much tension for the homework
I had so much tension for the homework
I had so much tension for the homework that I needed to turn in time
that I needed to turn in time
that I needed to turn in time preparation lessons and stuff and this
preparation lessons and stuff and this
preparation lessons and stuff and this suddenly started changing my mindsets
suddenly started changing my mindsets
suddenly started changing my mindsets I knew that have a lot of
I knew that have a lot of
I knew that have a lot of responsibilities and I need to deal with
responsibilities and I need to deal with
responsibilities and I need to deal with them in some way so I thought in my case
them in some way so I thought in my case
them in some way so I thought in my case the language bulgarians that I studied
the language bulgarians that I studied
the language bulgarians that I studied back then and other subjects like
back then and other subjects like
back then and other subjects like physics chemistry and biology I cannot
physics chemistry and biology I cannot
physics chemistry and biology I cannot say that I’m not learning about them
say that I’m not learning about them
say that I’m not learning about them very deeply because they have a lot of
very deeply because they have a lot of
very deeply because they have a lot of specifications but the big question came
specifications but the big question came
specifications but the big question came what about math I mean there are 1
what about math I mean there are 1
what about math I mean there are 1 million different formulas for both
million different formulas for both
million different formulas for both algebra and geometry and how I’m
algebra and geometry and how I’m
algebra and geometry and how I’m supposed to learn them and instead of
supposed to learn them and instead of
supposed to learn them and instead of doing instead of learning them I did
doing instead of learning them I did
doing instead of learning them I did some mathematical operations to figure
some mathematical operations to figure
some mathematical operations to figure out if they have something in common I
out if they have something in common I
out if they have something in common I mean there’s so many so genius idea down
mean there’s so many so genius idea down
mean there’s so many so genius idea down me that’s they have very big
me that’s they have very big
me that’s they have very big relationship between them and now I
relationship between them and now I
relationship between them and now I decided to share it to someone so this
decided to share it to someone so this
decided to share it to someone so this opportunity pop up and Here I am saying
opportunity pop up and Here I am saying
opportunity pop up and Here I am saying them in front of you so the topics that
them in front of you so the topics that
them in front of you so the topics that we’re going to explore today are
we’re going to explore today are
we’re going to explore today are commutative law of addition distributive
commutative law of addition distributive
commutative law of addition distributive law of division and a simple formula
law of division and a simple formula
law of division and a simple formula difference of squares and
difference of squares and
difference of squares and forgot in the end there’ll be a little
forgot in the end there’ll be a little
forgot in the end there’ll be a little test for you so don’t get too frustrated
test for you so don’t get too frustrated
test for you so don’t get too frustrated I promise to help so the first topic
I promise to help so the first topic
I promise to help so the first topic that we’re going to look at is
that we’re going to look at is
that we’re going to look at is commutative law of addition I believe
commutative law of addition I believe
commutative law of addition I believe everyone here has been in second grade
everyone here has been in second grade
everyone here has been in second grade right yeah and knows it’s mathematical
right yeah and knows it’s mathematical
right yeah and knows it’s mathematical application for those that don’t it’s on
application for those that don’t it’s on
application for those that don’t it’s on the board so commit the flow of addition
the board so commit the flow of addition
the board so commit the flow of addition the big question is how do we use math
the big question is how do we use math
the big question is how do we use math now in this specific moment and in this
now in this specific moment and in this
now in this specific moment and in this presentation so let’s it in other words
presentation so let’s it in other words
presentation so let’s it in other words that doesn’t sound so fancy what are we
that doesn’t sound so fancy what are we
that doesn’t sound so fancy what are we going to put first your shirt or your
going to put first your shirt or your
going to put first your shirt or your shoes it really doesn’t matter I mean
shoes it really doesn’t matter I mean
shoes it really doesn’t matter I mean your shoes on your feet and they share
your shoes on your feet and they share
your shoes on your feet and they share it is up on your body but in other case
it is up on your body but in other case
it is up on your body but in other case like what are you going to put first
like what are you going to put first
like what are you going to put first your socks or your shoes if you put your
your socks or your shoes if you put your
your socks or your shoes if you put your socks and then your shoes it’s fine but
socks and then your shoes it’s fine but
socks and then your shoes it’s fine but if you put your shoes first it’ll be
if you put your shoes first it’ll be
if you put your shoes first it’ll be ridiculous to try to put your socks of
ridiculous to try to put your socks of
ridiculous to try to put your socks of course so to tell you what actually
course so to tell you what actually
course so to tell you what actually commutative law looks like it’s a plus B
commutative law looks like it’s a plus B
commutative law looks like it’s a plus B equals B plus a so I have a little
equals B plus a so I have a little
equals B plus a so I have a little problem for you three plus four as you
problem for you three plus four as you
problem for you three plus four as you see on the board equals four plus how
see on the board equals four plus how
see on the board equals four plus how much congratulations to toe that said
much congratulations to toe that said
much congratulations to toe that said the correct answer is three so I’ll tell
the correct answer is three so I’ll tell
the correct answer is three so I’ll tell you a little story a long time ago there
you a little story a long time ago there
you a little story a long time ago there was a young man or let’s say a kids
was a young man or let’s say a kids
was a young man or let’s say a kids named Gauss which in fourth grade was
named Gauss which in fourth grade was
named Gauss which in fourth grade was supposed to solve the sum of the numbers
supposed to solve the sum of the numbers
supposed to solve the sum of the numbers from 1 to 100 imagine for the whole
from 1 to 100 imagine for the whole
from 1 to 100 imagine for the whole period because their teacher decided to
period because their teacher decided to
period because their teacher decided to give him something to do so after a
give him something to do so after a
give him something to do so after a couple of minutes the young man went to
couple of minutes the young man went to
couple of minutes the young man went to his teacher which already solves problem
his teacher which already solves problem
his teacher which already solves problem and the teacher was just amazed whoa how
and the teacher was just amazed whoa how
and the teacher was just amazed whoa how did the young men manage to solve this
did the young men manage to solve this
did the young men manage to solve this difficult problem and after time like
difficult problem and after time like
difficult problem and after time like when they realized that it was a very
when they realized that it was a very
when they realized that it was a very smart method its Gauss used the method
smart method its Gauss used the method
smart method its Gauss used the method was named after him after gasps don’t
was named after him after gasps don’t
was named after him after gasps don’t answer the teacher so to show you how it
answer the teacher so to show you how it
answer the teacher so to show you how it looks like our next problem example one
looks like our next problem example one
looks like our next problem example one we don’t have the numbers from 1 to 100
we don’t have the numbers from 1 to 100
we don’t have the numbers from 1 to 100 we have the numbers from 1 to 29 and
we have the numbers from 1 to 29 and
we have the numbers from 1 to 29 and since I’m supposed to show something
since I’m supposed to show something
since I’m supposed to show something tricky not because you can find the
tricky not because you can find the
tricky not because you can find the method of girls in the Internet
method of girls in the Internet
method of girls in the Internet and from 1 to 100
and from 1 to 100
and from 1 to 100 there are a hundred numbers right and in
there are a hundred numbers right and in
there are a hundred numbers right and in our case we have from 1 to 29 which is
our case we have from 1 to 29 which is
our case we have from 1 to 29 which is odd amount of numbers so as we see here
odd amount of numbers so as we see here
odd amount of numbers so as we see here what girls did was he combined the last
what girls did was he combined the last
what girls did was he combined the last number and the first number in our case
number and the first number in our case
number and the first number in our case 29 plus 1 and he found that that the sum
29 plus 1 and he found that that the sum
29 plus 1 and he found that that the sum of 29 plus 1 is the same as 28 plus 2
of 29 plus 1 is the same as 28 plus 2
of 29 plus 1 is the same as 28 plus 2 and he tried this for all the numbers
and he tried this for all the numbers
and he tried this for all the numbers like 27 plus 3 then he went far to 16
like 27 plus 3 then he went far to 16
like 27 plus 3 then he went far to 16 plus 14 and he found it it was 30 in
plus 14 and he found it it was 30 in
plus 14 and he found it it was 30 in this case 101 what’s in our case 30 but
this case 101 what’s in our case 30 but
this case 101 what’s in our case 30 but the big question is what do we do with
the big question is what do we do with
the big question is what do we do with the 15 in the middle you see that we
the 15 in the middle you see that we
the 15 in the middle you see that we have groups of two numbers that have a
have groups of two numbers that have a
have groups of two numbers that have a sum of 30 but for 15 what 15 plus how
sum of 30 but for 15 what 15 plus how
sum of 30 but for 15 what 15 plus how much it gives us 30 15 of course I know
much it gives us 30 15 of course I know
much it gives us 30 15 of course I know just trying but in order to figure out
just trying but in order to figure out
just trying but in order to figure out the groups of two numbers we need to
the groups of two numbers we need to
the groups of two numbers we need to divide the amount of numbers in our case
divide the amount of numbers in our case
divide the amount of numbers in our case 29 divided by 2 so we have around 14.5
29 divided by 2 so we have around 14.5
29 divided by 2 so we have around 14.5 groups that means the 0.5 did we have a
groups that means the 0.5 did we have a
groups that means the 0.5 did we have a half group which is our number 15 so to
half group which is our number 15 so to
half group which is our number 15 so to show how the solution for this problem
show how the solution for this problem
show how the solution for this problem looks like it’s this it’s long right but
looks like it’s this it’s long right but
looks like it’s this it’s long right but I’ll explain so the first roles you can
I’ll explain so the first roles you can
I’ll explain so the first roles you can see that we have the thing that I
see that we have the thing that I
see that we have the thing that I explained you about the combination of
explained you about the combination of
explained you about the combination of the numbers and then when we go down to
the numbers and then when we go down to
the numbers and then when we go down to here we can figure out we have 14 groups
here we can figure out we have 14 groups
here we can figure out we have 14 groups as I already said of sums of 30 right
as I already said of sums of 30 right
as I already said of sums of 30 right and then we need to add our last number
and then we need to add our last number
and then we need to add our last number which is 15 and finally we get our
which is 15 and finally we get our
which is 15 and finally we get our answer of 435 I know that we got too
answer of 435 I know that we got too
answer of 435 I know that we got too serious but it’s math then our next
serious but it’s math then our next
serious but it’s math then our next problem is this one it’s example with
problem is this one it’s example with
problem is this one it’s example with even amount of numbers so we can see how
even amount of numbers so we can see how
even amount of numbers so we can see how girls found out the sums without the
girls found out the sums without the
girls found out the sums without the tricky part with the left out number in
tricky part with the left out number in
tricky part with the left out number in the middle so we’ll check it again 30
the middle so we’ll check it again 30
the middle so we’ll check it again 30 plus 1 equals 31 29 plus 2 equals 31 28
plus 1 equals 31 29 plus 2 equals 31 28
plus 1 equals 31 29 plus 2 equals 31 28 plus 3 still equals 31 then 17 plus 14
plus 3 still equals 31 then 17 plus 14
plus 3 still equals 31 then 17 plus 14 31 16 plus 15 31 no middle number
31 16 plus 15 31 no middle number
31 16 plus 15 31 no middle number everything’s fine so we have 5th
everything’s fine so we have 5th
everything’s fine so we have 5th in groups because 30 divided by 2 is 15
in groups because 30 divided by 2 is 15
in groups because 30 divided by 2 is 15 times 31 easy 465 and as you saw here I
times 31 easy 465 and as you saw here I
times 31 easy 465 and as you saw here I gave you a couple of examples to see for
gave you a couple of examples to see for
gave you a couple of examples to see for yourself that commutative law is not
yourself that commutative law is not
yourself that commutative law is not only in math and in these presentations
only in math and in these presentations
only in math and in these presentations but this in life and you even I believe
but this in life and you even I believe
but this in life and you even I believe you don’t think when you use it and the
you don’t think when you use it and the
you don’t think when you use it and the most important thing that I want you to
most important thing that I want you to
most important thing that I want you to learn from this presentation is that
learn from this presentation is that
learn from this presentation is that math isn’t just a science you need to
math isn’t just a science you need to
math isn’t just a science you need to manipulate or adapt the problems in a
manipulate or adapt the problems in a
manipulate or adapt the problems in a way that’s more suitable for you
way that’s more suitable for you
way that’s more suitable for you so now going back to the topic next
so now going back to the topic next
so now going back to the topic next distributive law of division
distributive law of division
distributive law of division it sounds pretty fancy right laws
it sounds pretty fancy right laws
it sounds pretty fancy right laws division stuff but it really looks like
division stuff but it really looks like
division stuff but it really looks like 1 plus 1 in parentheses divided by 2
1 plus 1 in parentheses divided by 2
1 plus 1 in parentheses divided by 2 gives us one right with the appropriate
gives us one right with the appropriate
gives us one right with the appropriate thing of course but to give you a more
thing of course but to give you a more
thing of course but to give you a more casual example in your everyday life
casual example in your everyday life
casual example in your everyday life when you go to the cinema with one of
when you go to the cinema with one of
when you go to the cinema with one of your friend friends only one because
your friend friends only one because
your friend friends only one because we’re not that popular of course like
we’re not that popular of course like
we’re not that popular of course like Stefan you buy popcorn one bucket per
Stefan you buy popcorn one bucket per
Stefan you buy popcorn one bucket per person right when you go to the movie
person right when you go to the movie
person right when you go to the movie you set the tension from the movie
you set the tension from the movie
you set the tension from the movie starts and you start eating right and
starts and you start eating right and
starts and you start eating right and you have two options either put a pocket
you have two options either put a pocket
you have two options either put a pocket in the middle between your you and your
in the middle between your you and your
in the middle between your you and your friends and eat it then when you eat you
friends and eat it then when you eat you
friends and eat it then when you eat you take the other one and put it in the
take the other one and put it in the
take the other one and put it in the middle and eats again or take a pocket
middle and eats again or take a pocket
middle and eats again or take a pocket per person and be sure that you eat the
per person and be sure that you eat the
per person and be sure that you eat the same amount of popcorn so these are the
same amount of popcorn so these are the
same amount of popcorn so these are the two main options that you have if you
two main options that you have if you
two main options that you have if you want to keep it simple but in other
want to keep it simple but in other
want to keep it simple but in other cases like this one it won’t be that
cases like this one it won’t be that
cases like this one it won’t be that simple let me read it for you to see how
simple let me read it for you to see how
simple let me read it for you to see how difficult is this problem negative 452
difficult is this problem negative 452
difficult is this problem negative 452 and 17 28 divided by 7 and 5/8 plus 574
and 17 28 divided by 7 and 5/8 plus 574
and 17 28 divided by 7 and 5/8 plus 574 and 17 28 divided by 7 and 5/8 I didn’t
and 17 28 divided by 7 and 5/8 I didn’t
and 17 28 divided by 7 and 5/8 I didn’t memorize this I have it on the screen
memorize this I have it on the screen
memorize this I have it on the screen down here but the thing is how are you
down here but the thing is how are you
down here but the thing is how are you going to solve this any ideas
going to solve this any ideas
going to solve this any ideas don’t be shy yes I’ll tell you live
don’t be shy yes I’ll tell you live
don’t be shy yes I’ll tell you live calculator calculator you don’t need to
calculator calculator you don’t need to
calculator calculator you don’t need to solve this calculator but if you don’t
solve this calculator but if you don’t
solve this calculator but if you don’t have one you use our simple law as the
have one you use our simple law as the
have one you use our simple law as the Mohi to say but I interrupted him
Mohi to say but I interrupted him
Mohi to say but I interrupted him and what are you going to do Yahveh
and what are you going to do Yahveh
and what are you going to do Yahveh common factor 7 and 5/8 and our next
common factor 7 and 5/8 and our next
common factor 7 and 5/8 and our next step
step
step come on here it would look like this you
come on here it would look like this you
come on here it would look like this you have in the numerator the numbers 574
have in the numerator the numbers 574
have in the numerator the numbers 574 and 1728 – 452 and 1728 over our
and 1728 – 452 and 1728 over our
and 1728 – 452 and 1728 over our contactor and after you solve this hard
contactor and after you solve this hard
contactor and after you solve this hard numbers you will get this 122 and 61
numbers you will get this 122 and 61
numbers you will get this 122 and 61 over 8 this is 7 and 5/8 within a
over 8 this is 7 and 5/8 within a
over 8 this is 7 and 5/8 within a fraction so when we do our mathematical
fraction so when we do our mathematical
fraction so when we do our mathematical operation which we learned in eighth
operation which we learned in eighth
operation which we learned in eighth grade let’s see you get our simple
grade let’s see you get our simple
grade let’s see you get our simple number 16 so that difficult right it’s
number 16 so that difficult right it’s
number 16 so that difficult right it’s not like 2 million 52 or a fraction and
not like 2 million 52 or a fraction and
not like 2 million 52 or a fraction and here I prove to you as well that’s not
here I prove to you as well that’s not
here I prove to you as well that’s not that difficult to use simple laws and
that difficult to use simple laws and
that difficult to use simple laws and second grades and math problems which
second grades and math problems which
second grades and math problems which you probably solved in 10th grades so to
you probably solved in 10th grades so to
you probably solved in 10th grades so to go to our next topic as I said
go to our next topic as I said
go to our next topic as I said difference of squares this is our
difference of squares this is our
difference of squares this is our formula that I was talking about
formula that I was talking about
formula that I was talking about in fact we go way back to seventh grade
in fact we go way back to seventh grade
in fact we go way back to seventh grade which is long time ago but you need to
which is long time ago but you need to
which is long time ago but you need to at least remember something and my
at least remember something and my
at least remember something and my question is a squared minus B squared
question is a squared minus B squared
question is a squared minus B squared how much does it equal let me tell you
how much does it equal let me tell you
how much does it equal let me tell you this of course I mean you need to have
this of course I mean you need to have
this of course I mean you need to have the formula to figure it out but the
the formula to figure it out but the
the formula to figure it out but the thing is this is one of the most
thing is this is one of the most
thing is this is one of the most commonly used formulas at all and it
commonly used formulas at all and it
commonly used formulas at all and it really makes math easier I’ll tell you
really makes math easier I’ll tell you
really makes math easier I’ll tell you why because of this problem you have
why because of this problem you have
why because of this problem you have some big numbers and as I already said
some big numbers and as I already said
some big numbers and as I already said you solve it with a calculator of course
you solve it with a calculator of course
you solve it with a calculator of course don’t make your life too difficult but
don’t make your life too difficult but
don’t make your life too difficult but you use this formula for this problem
you use this formula for this problem
you use this formula for this problem because I showed you before you have two
because I showed you before you have two
because I showed you before you have two numbers which are squared and you need
numbers which are squared and you need
numbers which are squared and you need to find their difference in this case we
to find their difference in this case we
to find their difference in this case we have 196 squared minus 154 squared over
have 196 squared minus 154 squared over
have 196 squared minus 154 squared over 28 squared minus 7 squared so what is
28 squared minus 7 squared so what is
28 squared minus 7 squared so what is our first step of course we need to find
our first step of course we need to find
our first step of course we need to find the difference of the numbers multiplied
the difference of the numbers multiplied
the difference of the numbers multiplied by their sum
by their sum
by their sum to look like this so when we find it
to look like this so when we find it
to look like this so when we find it with a calculator the numbers in this
with a calculator the numbers in this
with a calculator the numbers in this one this one this one and this one we
one this one this one and this one we
one this one this one and this one we will get this I ordered for you so you
will get this I ordered for you so you
will get this I ordered for you so you can see that 350 divided by 35 equals 10
can see that 350 divided by 35 equals 10
can see that 350 divided by 35 equals 10 and 42 divided by 21 equals 2 so
and 42 divided by 21 equals 2 so
and 42 divided by 21 equals 2 so actually our answer will be 20 so if we
actually our answer will be 20 so if we
actually our answer will be 20 so if we go back to the main idea of this
go back to the main idea of this
go back to the main idea of this presentation how do you use math now I
presentation how do you use math now I
presentation how do you use math now I will give you an example okay let’s say
will give you an example okay let’s say
will give you an example okay let’s say that you have money in a bank and your
that you have money in a bank and your
that you have money in a bank and your growth of the money monthly is
growth of the money monthly is
growth of the money monthly is exponential which can hardly happen but
exponential which can hardly happen but
exponential which can hardly happen but you have a loan in the same Bank it has
you have a loan in the same Bank it has
you have a loan in the same Bank it has the same properties as the deposit that
the same properties as the deposit that
the same properties as the deposit that you have and you need to figure out your
you have and you need to figure out your
you have and you need to figure out your the profit that you have every month so
the profit that you have every month so
the profit that you have every month so you’re going to square your deposit then
you’re going to square your deposit then
you’re going to square your deposit then you take it out take out the square low
you take it out take out the square low
you take it out take out the square low one and you get the profit that you have
one and you get the profit that you have
one and you get the profit that you have for the money that you own to the bank
for the money that you own to the bank
for the money that you own to the bank because the laws are too big so now we
because the laws are too big so now we
because the laws are too big so now we get to the most interesting part of our
get to the most interesting part of our
get to the most interesting part of our lesson the test I mean you have the
lesson the test I mean you have the
lesson the test I mean you have the option not to participate but since you
option not to participate but since you
option not to participate but since you have nowhere to go I think you should
have nowhere to go I think you should
have nowhere to go I think you should and now this will this problems that I
and now this will this problems that I
and now this will this problems that I have for you here our summary of
have for you here our summary of
have for you here our summary of everything that I explained and we will
everything that I explained and we will
everything that I explained and we will see how my explanations affected you in
see how my explanations affected you in
see how my explanations affected you in a way and probably not embarrass myself
a way and probably not embarrass myself
a way and probably not embarrass myself of course so that’s why I’ll help first
of course so that’s why I’ll help first
of course so that’s why I’ll help first problem you want me to read it for you
problem you want me to read it for you
problem you want me to read it for you yeah I’ll do this part of the script so
yeah I’ll do this part of the script so
yeah I’ll do this part of the script so 1 times 2 times 3 plus 4 x 2 x 4 x 6 I’m
1 times 2 times 3 plus 4 x 2 x 4 x 6 I’m
1 times 2 times 3 plus 4 x 2 x 4 x 6 I’m sorry plus 4 times 8 times 12 plus 7
sorry plus 4 times 8 times 12 plus 7
sorry plus 4 times 8 times 12 plus 7 times 14 times 20 a 1 over 1 times 3
times 14 times 20 a 1 over 1 times 3
times 14 times 20 a 1 over 1 times 3 times 5 plus 2 times 6 times 10 plus 7
times 5 plus 2 times 6 times 10 plus 7
times 5 plus 2 times 6 times 10 plus 7 plus x so 21 times 35 pretty long so I
plus x so 21 times 35 pretty long so I
plus x so 21 times 35 pretty long so I won’t read you my solutions because
won’t read you my solutions because
won’t read you my solutions because they’re still long but I will point to
they’re still long but I will point to
they’re still long but I will point to you how do we solve this if we go and
you how do we solve this if we go and
you how do we solve this if we go and look in front of the parenthesis we have
look in front of the parenthesis we have
look in front of the parenthesis we have a common multiple which is 6 or 2 times
a common multiple which is 6 or 2 times
a common multiple which is 6 or 2 times 3 the way that you prefer it
3 the way that you prefer it
3 the way that you prefer it in the denominator we have the same
in the denominator we have the same
in the denominator we have the same thing three times five so if we look the
thing three times five so if we look the
thing three times five so if we look the parentheses very closely you will see
parentheses very closely you will see
parentheses very closely you will see that they’re the same and since we have
that they’re the same and since we have
that they’re the same and since we have division there probably when we divide
division there probably when we divide
division there probably when we divide the same numbers you’ll get one and the
the same numbers you’ll get one and the
the same numbers you’ll get one and the solution for this will be 2 over 5
solution for this will be 2 over 5
solution for this will be 2 over 5 because 3 we have it in the numerator
because 3 we have it in the numerator
because 3 we have it in the numerator and denominator and the parentheses have
and denominator and the parentheses have
and denominator and the parentheses have the same so crisscross applesauce where
the same so crisscross applesauce where
the same so crisscross applesauce where is everything ready so 2 over 5 or 0.4
is everything ready so 2 over 5 or 0.4
is everything ready so 2 over 5 or 0.4 it the way that you prefer our next
it the way that you prefer our next
it the way that you prefer our next problem still from the test will be this
problem still from the test will be this
problem still from the test will be this it’s slightly different it the one
it’s slightly different it the one
it’s slightly different it the one before so I’ll still read it for you to
before so I’ll still read it for you to
before so I’ll still read it for you to understand it 11 to the power of k plus
understand it 11 to the power of k plus
understand it 11 to the power of k plus 3 minus xi ^ k plus 2 plus xi ^ k plus 1
3 minus xi ^ k plus 2 plus xi ^ k plus 1
3 minus xi ^ k plus 2 plus xi ^ k plus 1 in parentheses divided by 111 it will be
in parentheses divided by 111 it will be
in parentheses divided by 111 it will be very easy if we can divide 11 by 111 but
very easy if we can divide 11 by 111 but
very easy if we can divide 11 by 111 but no sorry so we still will use the same
no sorry so we still will use the same
no sorry so we still will use the same thing that we did before we rearranged
thing that we did before we rearranged
thing that we did before we rearranged the problem so it’s more suitable for us
the problem so it’s more suitable for us
the problem so it’s more suitable for us to solve it it will look like this xi ^
to solve it it will look like this xi ^
to solve it it will look like this xi ^ k plus 1 times the thing in the
k plus 1 times the thing in the
k plus 1 times the thing in the parentheses which is xi squared + xi
parentheses which is xi squared + xi
parentheses which is xi squared + xi minus 1 divided by say 110 11 and
minus 1 divided by say 110 11 and
minus 1 divided by say 110 11 and finally when we are simplified within
finally when we are simplified within
finally when we are simplified within the parentheses on the next line
the parentheses on the next line
the parentheses on the next line we’ll get this xi ^ k plus 1 times 1100
we’ll get this xi ^ k plus 1 times 1100
we’ll get this xi ^ k plus 1 times 1100 sings I’m sorry divided by a hundred
sings I’m sorry divided by a hundred
sings I’m sorry divided by a hundred soon xi and finally our answer will be
soon xi and finally our answer will be
soon xi and finally our answer will be this as you see here to conclude
this as you see here to conclude
this as you see here to conclude unfortunately our lecture that I enjoyed
unfortunately our lecture that I enjoyed
unfortunately our lecture that I enjoyed very much I need to say that from the
very much I need to say that from the
very much I need to say that from the perspective of a young man and a student
perspective of a young man and a student
perspective of a young man and a student surrounded by technology and its variety
surrounded by technology and its variety
surrounded by technology and its variety of users I never asked myself why do I
of users I never asked myself why do I
of users I never asked myself why do I follow some steps for writing an email
follow some steps for writing an email
follow some steps for writing an email or something they probably would sound
or something they probably would sound
or something they probably would sound logical if I think of it but I don’t so
logical if I think of it but I don’t so
logical if I think of it but I don’t so if we go back to the topic that it’s
if we go back to the topic that it’s
if we go back to the topic that it’s everything is about two different
everything is about two different
everything is about two different aspects of looking at things I figured
aspects of looking at things I figured
aspects of looking at things I figured out that I’m passionate about math
out that I’m passionate about math
out that I’m passionate about math because I’m not I don’t like only
because I’m not I don’t like only
because I’m not I don’t like only solving problems but I like the way that
solving problems but I like the way that
solving problems but I like the way that it effects me it taught me that I need
it effects me it taught me that I need
it effects me it taught me that I need to adopt everything in a way that’s more
to adopt everything in a way that’s more
to adopt everything in a way that’s more suited
suited
suited for me and I really found out that math
for me and I really found out that math
for me and I really found out that math isn’t just the science that employs
isn’t just the science that employs
isn’t just the science that employs figures theorems and other numbers or
figures theorems and other numbers or
figures theorems and other numbers or something that’s boring for you but it
something that’s boring for you but it
something that’s boring for you but it represents life in a different way and
represents life in a different way and
represents life in a different way and it provides the interpretation for the
it provides the interpretation for the
it provides the interpretation for the people that prefer this way of living
people that prefer this way of living
people that prefer this way of living just looking beyond the formula thank
just looking beyond the formula thank
just looking beyond the formula thank you very much
you very much
you very much [Applause]
”
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