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Hard GED Math Questions and Answers to Help You Pass GED Math!

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help you level up with your GED math

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story time so this is a true story I was

once working with a student in person I

was tutoring her for GED prep and I gave

her one of these problems and she

actually it was so hard for her that she

was so demoralized that she actually

wanted to quit for the day after that

and I felt really bad so after that I

don't usually give these problems out to

students without giving them warning

first that hey these are problems

but if you're up for the challenge and

you really want to accelerate your GED

progress then give these problems a try

and I'll put a link to a downloadable

PDF version down below for those who

want to follow along on the PDF and also

let me know what you think of these

questions are they too hard are they too

easy are they just right and which

question do you think is the hardest let

me know down below let's get started

question asks you to find the area of a

circle given the circumference so it

says if the circumference of the circle

is 10 inches what is the area so pause

the video and try to do this now okay

let's go over how to do this so first of

all what is the circumference so the

circumference is just a fancy word for

the distance around the circle and the

formula for the circumference is C so C

represents circumference so C equals 2

times pi times R so what is this symbol

pi and what is R okay well pi is just a

number it's a symbol that represents a

number and you just have to remember

that it's approximately equal to 3.14

for your test so pi is approximately

3.14 and i say approximately because

there's a bunch of numbers it goes on

and on and on but you just have to

remember the first three numbers the

3.14 all right so that's what pi is but

oftentimes in math questions on the GED

you can just leave it as this PI symbol

you don't usually need to turn it into a

number but you can so we have C equals

to PI R and so the R stands for the

radius so if we start here on so if we

start here at a point on the outside of

the circle go all the way to

approximately 2 right into the halfway

point of the circle right which my

drawing is an approximation but imagine

this line is halfway into the center of

the circle okay so this line from the

end of the circle to the center of the

circle is what we would call the radius

all right and it's just a distance here

so the distance from a point on the end

of the circle to the center is the

radius all right so now let's also look

at the formula for the

area of a circle so a equals PI R

squared so what's the strategy here well

the strategy since we know we're that

the circumference is 10 all right we've

got to take this 10 and plug it in for C

so we're going to replace the C with 10

because you know the circumference is

equal to 10 and then we're gonna do some

algebra here and we're going to try to

figure out what R is and then once we

know what R is we can then take our area

formula here and we can substitute that

known value for R into R in our area

equation and that's going to spit out

the the area all right so here's how you

would do it so again we said that 10 is

going to replace C so we've got 10

equals 2 pi R ok and so the goal here is

to get this R by itself on one side of

our equation we want to solve this

equation for R so what we see here is 10

equals 2 times pi times R ok so the

opposite of multiplication is division

so if we want to get rid of the 2 in the

pi we want to divide here all right so

this will all cancel out but whatever we

do to one side we also do to the other

so we're now going to also divide by 2

PI over here so we've got 10 divided by

2 pi is equal to R because all of this

is getting cancelled out here right so

now what we can do is divide by 2 from

10 and that's going to leave us with 5

over pi equals R ok and we're just going

to leave PI as this symbol right here

we're not going to write 3.14 there's no

reason to right now so we now figured

out that R is 5 over pi and so now what

we're going to do is we're going to take

that formula for area and we're going to

substitute R into it so we know that the

area is equal to PI R squares so we take

that our ok the R remember is 5 over pi

ok and this is squared okay so here's

the trick so what we're going to do here

is we have to deal with this exponent

first before we do anything else so we

deal with so to do that ok let's treat

it as as if this is 5 squared and as pi

squared so here's what I mean so let's

say that we were rewriting this as pi

times

five squared divided by pi squared okay

and so five squared is equal to five

times five all right so we can write the

area now is being equal to PI because we

keep that little pi out front here and

five squared is just five times five so

let me just write that here five okay

five times another five now pi squared

is just equal to pi times another pi so

now that we've written it out this so I

hopefully you see that we can take one

of these PI's here and we can cancel it

with this pi up here because pi divided

by a pi is just going to cancel out so

pi divided by pi is there's going to be

one so we essentially have 1 times 5

times 5 divided by 5 and we don't need

to write that runt one so now we can

simplify this as area equals 25 divided

by pi okay and so now why is it 25 well

obviously because 5 times 5 is 25 here

alright and one another units that's

just inches squared all right next

question okay question number two what

is the domain and range of the following

function and here we have f of X is

equal to x squared plus 8x plus 16

divided by x squared plus 3x minus 4

pause the video and try to figure this

out ok let's go over how to do this so

what is the domain and what is the range

well the simplest way to think about it

is that the domain is all possible

inputs to a function and the range is

all possible outputs so what do I mean

by inputs and what do I mean by outputs

so basically we can input numbers into

this function here so for example we

could put in a 1 into the function all

right we could use 1 as our input and in

that case what we would do is all of

these X's here we would then replace

those with the number 1 or if two was

our input we would input 2 into the

function so we put 2 in for X and then

that would mean that we would substitute

all of these X's here into the equation

for twos and we would solve the question

and whatever number we get as a result

is our output all right so the domain is

all possible inputs and the range is all

possible output so how do we go about by

finding the domain well usually finally

to find the domain there's one main

concept you have to know and that's that

you cannot divide by zero okay so if you

ever put this into a calculator like for

example five divided by zero or any

number divided by zero 15 divided by

zero alright you're going to get an

error on your calculator because you

cannot divide by zero okay so one of the

main things you need to know for

figuring out where a function is

undefined or in other words which value

of x makes the function undefined is

whenever you get a 0 in the denominator

so what we want to do here essentially

is we're going to take the denominator

of this function here alright and the

denominator is just everything in the

lower portion of the fraction and the

numerators everything in the upper

portion of the fraction and we want to

set this equal to zero and we want to

find which values for X are going to

give us a zero in the denominator so

hopefully you noticed here if you've

been studying for a while that we have

two quadratic equations ok so a

quadratic equation is what we have in

the top in in the bottom and so we can

solve these quadratic equations by

factoring so we're gonna factor both the

top in the bottom here so we're gonna

get some practice with factoring and

we're also gonna find the domain and

range so how do we factor well let's

just focus on the top on the top

quadratic equation first so this x

squared plus 8x plus 16 let's factor

that so the way that we're going to

factor it is we're gonna take the the

number here okay the number here which

is like a 1 so there's an imaginary one

out in front here in front of this x

squared so we take that one so we take

the first term and multiply it by the

last term so we would do 1 times 16

which just gives us 16 okay so now what

we want to do is we want to find two

numbers that will multiply together to

give us 16 but we'll add up to give us 8

all right so what we can do is just

lists factors of 16 so what are some

numbers that we know that will multiply

together to give us 16 well one pair is

two and eight and another pair is four

and four so we want to add these up and

see which pair is going to give us eight

so obviously if we do four plus four

that's going to give us eight

so this is our pair so when we factor

this okay what we do is we're just

taking this the top part of the equation

here alright and we would then rewrite

this x squared plus 8x plus 16 all right

as as X plus 4

and as X oops X +4 and also X +4 all

right we've got X plus 4 and X plus 4

all right so that the top part of the

fraction here is officially factored so

now let's factor the bottom portion here

so this x squared plus 3x minus 4 so

again let's take the let's take the

first number that we see here with the x

squared term which is again a 1 we don't

usually write it but imagine that

there's an imaginary one out here so we

would do 1 times the last number here

which is negative 4 so 1 times negative

4 is just negative 4 so now what we want

to do is we want to list numbers that

will multiply together to give us

negative 4 but that will add up to

positive 3 all right so what are some

combinations of numbers here that will

multiply together to give us negative 4

well 1 would be negative 1 and 4 so if

if we add these up if we add negative 1

plus 4 that is going to give us positive

3 so we've already found our pair here

all right so now what we do is we would

just take this bottom and this bottom

portion here in the denominator and

we're just going to rewrite this now as

X minus 1 and X plus 4 all right so what

kind of quickly we factored that so this

simplifies things down quite a bit all

right and so now we've got or we've got

the numerator and the denominator

denominator we've taken two quadratic

equations and factored them all right

but we're not even close to being done

yet so we still need to find that domain

so again what we want to do is we want

to take the whole bottom portion of the

fraction now and set these equal to zero

so we want to take this X minus 1 set

that equal to zero and then we're gonna

take X plus 4 and set these both equal

to zero here all right so let's do that

so let's try X minus 1 first so let's

set that equal to zero so if we do X

minus 1 and we set that equal to zero

and solve for X just like you would for

an algebra question right so we want to

get X by itself here we want to isolate

this X so since it's X minus 1 we do the

opposite of minus which is plus so we

then also have to add 1 to the other

side so we would see that x equals 1

okay and so now let's do the same with

this X plus

four so we take our X plus four and we

want to set that equal to zero as well

so we do our X plus four okay

and again we're setting that equal to

zero and we want to get the X by itself

on the left hand side of the equation so

since we've got this plus four here we

do the opposite of addition which is

subtraction and whatever you do to one

side you also do it to the other so

we're then left with x equals negative

four

all right x equals negative four so when

X is equal to 1 and when X is equal to

negative four where the function is

gonna be undefined so let me just show

you with an example of what I mean here

so let's just say that the top part of

the fraction I'm just gonna call

everything in the top part a just just

to prove a point here all right so let's

say that the X is equal to one okay so

we're gonna leave the denominator the

same here all right and I'm just going

to plug a 1 in for X here so I'm gonna

plug in 1 in for both of the X's down

here and I just left the top part is a

because I'm just proving a point here so

if we subject you to 1 in for X we would

have 1 minus 1 and then we would have 1

plus 4 okay so 1 plus 4 is going to be 5

but here's the problem all right 1 minus

0 1 minus 1 is going to be 0 so if I

rewrite this we were going to have 0

times 1 plus 4 which is 5 so we have 0

times 5

ciara times 5 is just 0 so we would end

up with a divided by 0 and we're going

to get it a divided by zero error here

because you can't divide by zero so

that's why we know the function is

undefined where x equals 1 all right and

so now let me clear this out of the way

here and I'm not going to walk through

this for the sake of time with 4 with

negative 4 but the same thing won't

happen if I plug in negative 4 for X all

right so let's say I take this negative

4 plug it in here for X all right

negative 4 plus positive 4 is going to

give us 0 here all right and so just

because we have that zero here zero

times this over here is going to make

the whole denominator equal to zero and

therefore the you can't do the problem

anymore because you're going to get a

divided by zero error in your calculator

because you can't divide by zero all

right so that so we know that the domain

is going to be all real numbers except

for x equals 1 and x equals negative 4

all right so that's the that's how you

would get the domain but what about the

range all right so again the domain is

going to be all numbers x

to where x equals negative 4 and x

equals 1 so remember that the range is

just all of the outputs all right so the

range is all the possible outputs so we

know that all inputs will work we can

put in any number here except for 1 or

negative 4 for X ok but what about the

the output so here's here's kind of a

concept here that I want to clear some

road some room out of the road here

because this is very very important to

understand here okay and this is semi

complicated but you guys are really

smart so you can get this so what we see

here if we go back to the the original

part of the problem here where I took

the two quadratic equations and I

factored them so we see that we've got X

plus 4 and X plus 4 so we can actually

since we've got an X plus 4 up here in

our numerator and an X plus 4 down here

in our denominator we can actually

cancel these out ok and so when we

cancel these out we can rewrite our

function ok so we can rewrite f of X as

equal to X plus 4 divided by X minus 1

okay and this is really where the magic

happens okay so so since we've got X

minus 1 down here and we've got X plus 4

up here all right no matter what happens

so well no matter what X is right can't

you see that the numerator in the

denominator they're never going to be 1

we're never going to get an even ratio

so if we've got 1 if we've got any

number up top and if we've got that same

exact number in the bottom of the

fraction ok the fraction is just going

to be equal to 1 because anything

divided by itself it's gonna be 1 all

right but no matter what we put in for X

here we're never going to be able to get

we're never going to be able to get that

alright so for example let's say we plug

in 2 for X all right so if we plug in 2

for X we would have 2 plus 4 ok up top

and then down here we're going to have 2

minus 1 okay and so this is obviously

going to be equal to 6 divided by 1

which is 6 over 1 ok so no matter what

happens this can never be 1 all right

and the reason is because of the way we

see that X plus 4 in the top and X minus

1 on the bottom so what you have to

understand here is that the range is

going to be all real numbers so you can

get any possible output here except 1

this function will never be equal to 1

ok so question 3 solve the equation for

X without using a calculator so we see

squared equals 50 find what X is equal

to without using a calculator pause the

video and try to do that now okay let's

go over how to do this so first of all I

want to point out a very common mistake

here so what some students might do is

they might think that well I want to get

x squared so x squared is equal to 50

squared + 50 squared to get that I just

do 50 times 50 and this is actually

incorrect that's not how you would find

X here in this situation so if you did

this that's okay give yourself a pat on

the back for trying all right I admire

your effort but this is actually the

wrong approach all right so let me cross

this out so we know that this is the

wrong approach and this is a common

question I get from GED test takers so

you're definitely going to want to

understand this concept here because

it's very important because I get this

question a lot but people who are

confused about about this they think x

squared equal to some number they think

they just square that number and that's

actually incorrect so we want to find

this X all right so we want to solve the

equation for X but right now we see that

we have x squared all right so we don't

want to solve the equation for x squared

it's already solved for x squared we

want to solve for X so the important

thing to understand here is that if you

take the square root of any number

that's squared it's just going to give

you that number

all right so for example all right the

square root of x squared is just equal

to X it doesn't matter what number you

put under here you could put in you

could put in 80 doesn't matter if I

Kenny random number and square that

number so this so a T squared what's the

square root of 80 squared it's just 80

all right again you could put in any

number literally you could do 20 22

let's say we've got 22 squared the

square root of 22 squared just gives us

that 22 okay so that's the idea here all

right we've got this x squared and if we

take the square root of x squared it's

just going to give us X all right but

whatever we do to one side of an

equation we also have to do it to the

other so we're also gonna have to take

the square root of 15 and we're gonna

have to find out what the square root of

50 is without using a calculator all

right so that's the strategy here and so

how are we gonna do that well in order

to do that you want to know these what I

call common square roots all right and

this is a good list to put down in your

notes and review it every couple days or

so or memorize it you can use flashcards

however you want to do it but you

definitely want to know this if you want

to score well on the GED so there's some

common square root so I'm not going to

read the whole list here but you're more

than welcome

pause the video when and study these

more in depth here but you've got the

square root of 1 is just 1 square root

of 4 is 2 square root of 9 is 3 the

square root of 16 is 4 of the square

root of 25 is 5 and so on and so forth

but these are all good numbers that you

want to have memorized so the strategy

here is we're gonna take 50 and we're

going to break it down into two numbers

that will multiply together to give us

50 okay and so we want to take we want

to find pairs of numbers that will

multiply together to give us 50 and we

want to find a pair in which one number

in that pair okay is one of the numbers

I have written here underneath the

square root symbols alright so for

example we want to find a number that's

either a 4 or a 9 or a 16 or 25

something that has a common square root

alright this will make more sense when I

show you the example so to get started

we want to list factors of 50 all right

factors of 50 so in other words two

numbers that multiply together to give

us 50 all right so let's just list pairs

here all right so what about first of

all the obvious one would be 50 and one

all right now there's also five in 10 so

somebody might be thinking well I

thought you said we want to find numbers

that appear on the left hand side of the

list here right in other words numbers

that have a square root that's a common

number all right well we do but the ones

not gonna help us out here so 50 and one

you might say well the square root of

one is just one so that doesn't help us

but good dot process if you were

thinking that so here's another pair

what about 2 and 25 well this actually

is hits us right it hits the bull's eye

because we see that the square root of

25 is 5 all right so see how I did that

again to find the square root of 50 I

just started by thinking of pairs of

numbers that will multiply together to

give us 50 and we found 2 and 25 and we

see that we wanted to find a pair that

had one of the numbers that has a common

square root so in other words one number

in the pair we want it to appear

underneath the square root symbol on our

list of common square roots and we see

that 2 and 25 would be the trick because

25 has a common square root all right in

other words the square root of 25 gives

us a common number which is 5 all right

and so now what we're gonna do is we're

going to take the square root of 50 okay

and now let's rewrite this okay so the

square root of 50 is equal to the square

root of 25

- and this little dot means

multiplication so the square root of 50

is equal to the square root of 25 times

2 okay so now we can go even further

here right because we know the square

root of 25 it's a common number it's a 5

it's not going to give us some weird

decimal or some weird number like the

square root of 2 would be all right so

we know the square root of 25 so square

root of 25 is 5 so I'm just gonna

rewrite this out here as 5 and I'm gonna

leave the 200 the square root all right

and so the answer here is that x equals

5 square root 2 okay 4 what is the

equation of a line that passes through

the points negative 2 negative 1 and 16

4 go ahead and pause the video and try

to figure this out so I've written 3

equations up here and I don't want you

to be intimidated because we're gonna

explain what these means it's really not

that complicated once we break it down

so first of all let me draw your

attention to this equation right here y

equals MX plus B so y equals MX plus B

this is the equation of a straight line

alright and what this means this little

M represents the slope so the M symbol

it's just represents the slope the slope

of a line okay and B is our y-intercept

okay so the y-intercept is on a graph

where the line crosses the y-axis so let

me just break this down quickly here so

this would be this is just an example of

a graph okay and so the line that goes

up and down here is what we call the

y-intercept and the line that goes left

and right here or horizontal is our

x-intercept so here's our X or it's not

the x intercept the x axis I should say

so the line going up and down again is

the y-axis and the line going left and

right is or x-axis all right and so

let's say we've got an equation of a

line here right we've got a line that

goes and passes all right across the

graph so right here at this point okay

where we see that the line crosses the y

axis remember the y axis goes up and

down so where the line crosses the y

axis we call that the y-intercept okay

and where the line crosses the x axis we

would call that the x-intercept okay so

now we see that we've got a line here

and whenever you've got a line you can

find the equation of that one

if you know the slope and two points

that are on that line here so for

example this negative 2 and negative 1

these would be two points on a line the

same with the 16 in 4 okay so another

thing that you want to know here about

slope is the general concept okay so

let's say that imagine that you are

gonna run down a big hill okay now I'm

sure you're much better-looking than the

stick bigger but you get the point here

so let's say that this is a hill that

you want to run down all right which

Hill would you run down faster okay a

hill like this or let's say a hill that

looks like this okay so obviously if you

were gonna run down a hill

all right the hill that is steeper is

going to you're gonna go down it faster

right so imagine if I gave you something

like this okay a hill that looks like

this that's practically straight up and

down okay you're gonna run down it so

fast cuz it's so steep right but you

know this hill here this looks like it's

gonna take you longer to run down

because it's so much it's not nearly as

steep all right so that's what the

concept of slope is it's just a number

that tells us something about the

steepness of a line so the slope you

could think of a concept is just it just

gives us a snapshot of the steepness of

that line okay and so you might also

have heard the slope called the rise

over the run and what that means is

remember we said that the y-axis goes up

and up and down and the x-axis goes left

and right okay well what that means is

you know the rise would be going up here

alright so we might rise let's say we've

got this is 1 and this is 2 all right so

we might say hey you know on this line

we rise up 2 and we could call this 1

this 2 in this 3 for example 1 2 3 all

right so for this line we would say hey

well the rise is 2 and the run is 3 and

we would write the slope as 2 over 3 so

that's another way to think about the

slope as the rise over the run ok so

another important thing to understand

about lines here ok when you see an

equation of a line is there are both

positive and negative slopes so whenever

you see a line that goes down so when

you go from left to right like it starts

high and it goes down a downward line

like this the slope will always be a

negative number

ok now whenever you've got a slope that

going from left

right it goes up so it starts low and

goes up that's gonna have a positive

slope okay so now a wine that is

horizontal like this so here's our

x-axis a line that runs like this just

kind of parallel to that x-axis

okay this line is going to have a slope

of 0 now if you have a slope though

that's vertical and that's straight up

and down alright this is gonna be

undefined all right you can't have a

slope in this situation if your line is

straight up and down all right because

there's no we don't see this rise of a

run okay we don't see we don't have a

rise of a run there ok so just some

things to keep in mind here all right

and so also these different numbers we

see that we've got these negative signs

here right and we've got a positive sign

so what do I mean by this well usually

if we were on a graph here right the

numbers going out here would be positive

numbers like we could have positive 1

positive 2 now if we go the other way

right so if we start right at the center

of the graph which right here in the

center ok we call this the origin

because the coordinates are 0 in 0 right

here so there's 0 on the x axis and 0 on

the y axis so in a coordinate pair you

always write the x value first and the Y

value second okay so if we go in the

left direction we would see a negative 1

all right then negative 2 and so on and

so forth okay so the same thing going

down alright so let me clear that out of

the road so we can see a little bit

better here right so if we're going down

say for example the numbers also get

negative right so if we go down here

this would be for example negative 1 and

negative 2 all right but if we start at

the origin and go up the numbers get

positive so this could be for example

positive 1 and positive 2 here okay

and so here's what we can say about the

different quadrants so we can divide

these up into what we call quadrants

right so he can have a quadrant here

here here and here so there's four

different quadrants and so over here

okay we would say all of the x-values

okay will always be negative ok and the

Y's over here are always going to be

positive ok all right so any point on a

graph that you find up in this quadrant

here the X will be negative and the Y

will be positive so over here we would

have positive and positive so our X

values so any points over here in this

quadrant would be positive and positive

all right so down here we would have a

pause

of X value but a negative Y value okay

and so over here we would have both

negative x and negative y okay so just

something to keep in mind here just to

give you kind of a snapshot all right

and so like I said in any coordinate

pair you always list the negative number

for you always list the X number first

and the Y number second okay so just to

give you some context here to what we're

doing but the point here is that this

equation here this y equals MX plus B

this is going to give us the equation of

a wine alright so now that we've got the

concept out of the way here how do we

find that well first of all we're gonna

use this formula down here so this is

what we call the point-slope formula all

right and so we use this formula okay

when we know the slope and we have at

least one of the coordinate pairs and

this will tell us the equation of the

line so in order to get this this y

equals MX plus B okay as long as you

know the slope and as long as you know

at least one of the the coordinate pairs

right so one of the pairs to line you

can use this formula Y minus y1 equals

slope times X minus x1 and that's going

to give you the equation of the line

okay so how do we get the slope well

that's what this up here is this M

equals y2 minus y1 divided by x2 minus

x1 that is our equation for the slope

okay so this all might sound a little

bit complicated but once we break down

this example here it's really not that

hard so first of all the first thing

that I'm gonna do here I'm gonna label

these coordinate pairs alright so let's

call this number x1 all right the first

number we'll call x1 and the second

number and this pair will call y1 all

right and so here we'll call this 16

okay let's call the 16 let me rewrite

this over here so we're gonna call our

16 is going to be our X 2 and our 4 is

our Y 2 so 4 is our Y 2 all right so to

find the slope all we're gonna do is

we're gonna take these numbers and

substitute them into the formula so what

I mean by that is so our Y to write our

four we substitute that into our

equation for y 2 alright and so our Y 1

again which is negative 1 we just slept

the tooth that in 4 or Y 1 same with the

X's so we take the value for X 1 which

is negative 2 substituted in here for

it's for our X 1 and this X 2 which is

teen substitute this in here 4x2 so I'm

gonna clear this out of the road here

because it's gonna get a little bit

stuffy on the board but hopefully you're

seeing the point here so the first step

here to find the equation of the line we

need to find the slope and then once we

found our slope we then use this formula

so first we use M equals y2 minus y1

divided by x2 minus x1 to get the slope

then we use the formula the point-slope

formula y minus y1 equals slope times X

minus x1 let's go ahead now and

calculate our slope here so we need our

y2 so our y2 is for and we need to

subtract our y1 so our y1 is just minus

1 here so we're gonna be doing 4 minus

negative 1 so whenever you do minus a

negative 1 minus a negative number okay

it becomes a plus so 4 minus negative 1

is the same as 4 plus 1 okay and so now

we want to do or let me make this a

little bit smaller but the next step

here is to do x2 minus x1 all right and

so our X 2 is 16 and or x1 is negative 2

so again 16 minus negative 2 is the same

as 16 plus 2 so whenever you do minus a

negative it just becomes a plus and of

course let me put the slope symbol here

all right so what we've done is again

we're calculating the slope and we do y2

minus y1 divided by x2 minus x1 and the

reason that these look like these are

pluses here is because whenever you

subtract a negative number it becomes a

plus so instead of doing 4 minus

negative 1 we would just write that as 4

plus 1 all right it's the same thing all

right so now we can calculate the slope

so what's 4 plus 1 that's 5 and what's

16 plus 2 that is 18 so our slope is 5

over 18 all right so we're on the so

we're on the right track here we've got

5 over 18 as your slip all right so now

what we want to do is use this formula

here Y minus y1 equals M times X minus

x1 and this is going to give us the

equation of the line okay so let's start

off here so y minus y1 so our y1 is

negative 1 so we're just gonna fill

these numbers in here Y minus y1 all

right so we do Y minus negative 1 so

again any number okay minus and negative

you just make that plus so Y minus

negative 1 that becomes Y plus 1 so

that's equal to our slope okay which is

5/18 okay so we've got our Y minus or Y

one is equal to the slope times X and

we're just gonna write an X here minus x

one okay so what's our x one well we

just look up here and we see that that's

negative two so again X minus negative

two we can just write that as X plus two

keep life simple okay so now what are we

gonna do well we're gonna solve our

equation here okay so there's a couple

ways so the first thing you could do is

you could subtract one over to the side

of the equation but I'm gonna save that

step for right now all right so what

we're gonna do here is we're going to

distribute this five over 18 so first

we're going to take the five over 18

multiply it by X then we're gonna take

the five over 18 and multiply it by our

two okay so in other words we are going

to distribute it all right so let me

rewrite this so we've got y plus 1 is

equal to 5 divided by 18 now it's times

X because that does not look like an 8

but pretend that's an 8 so we've got 5

divided by 18 times X plus 5 over 18

times 2 okay so what's 5 times 2 5 times

2 is 10 so we can just write that as 10

divided by 18 okay and so we can

actually simplify this fraction now

right so what if we divide both of these

by 2 so what is 10 divided by 2 10

divided by 2 is 5 and what's 18 divided

by 2 well 18 divided by 2 is 9 okay so

we can simplify that to 5 over 9 so we

now have 5x divided we have y plus 1

equals 5x divided by 16 plus 5 over 9

and so now what we're going to do is

we're going to subtract this one all

right

so we'll have y equals 5x hopefully you

guys are with me here 5x divided by 18

if you're with me then you're doing an

excellent job right now so props to you

y equals 5x divided by 18 all right plus

5 over 9 minus 1 okay so

we're almost done we can do one more

simplification here so we've got five

over nine minus one okay so what we can

do now is we can we can subtract one so

five over nine minus one now well you

can just do that in your calculator but

we could I like to keep it as a fraction

here so we know that any number okay

just written as a number is really that

number over one so if I pick any random

number like say 99 and I just say hey

here's a 99 okay you can really think of

it as 99 over one but there's really no

reason to write that normally speaking

but in this case we're gonna write it

over one so we've got five over nine

okay minus one over one and so we need

to get a common denominator here so we

want to do 5 minus 9 5 over 9 minus 1

over 1 so to do that we want to get a

common denominator so the denominator is

the bottom number in a fraction and top

number in the fraction is called the

numerator so to get a common denominator

we want to get the same number in both

of our denominators here so we've got a

nine and we've got a 1 so we've got to

multiply the denominator by 9 and

whatever you do to be denominator you're

gonna do it to the top number as well so

we love to multiply both by 9 here okay

so really we can now really write this

as y equals 5x divided by 18 and then

we're now adding that to 5 over 9 minus

9 over 9 so what is 5 minus 9 well

actually we're taking 5 minus 9 so

that's gonna give us negative 4 right

because 5 is smaller than 9 so if we do

5 minus 9 that's negative 4 okay so

basically what we're going to end up

with is our final answer up here so I'm

going to write it big right in the

center we've got y equals 5x divided by

18 and then that's + and are actually

now that's - so it's - right 4 over 9

okay and so then we're done case so now

the question is find the value of the

following number without using the

calculator and we see the fraction 17

over 4 and I've given you multiple

choice answers so go ahead pause the

video try to figure it out is it a B C

or D alright let's go over this

hopefully you had a chance to try this

one

so the first thing that we have to do

understand here is that we want to do

this without using the calculator and so

we've got to recognize what kind of

fraction this is so this is an example

of an improper fraction okay it's an

improper fraction all right and the

reason is because the top number and the

fraction is bigger than the bottom

number so the top number in a fraction

again is called the numerator and the

bottom number is called the denominator

and one way to remember that is to think

hey the denominator

well denominator that sounds like in the

dungeon or downstairs so the denominator

is downstairs or in the dungeon the way

I tell people to remember the top number

in a fraction is really silly but I tell

them think of Newman salad dressing so

if you've ever had Newman's salad

dressing you know that Newman's salad

dressing goes on top of the food the

numerator is the top part of the

fraction so it's kind of silly but

hopefully that helps you remember it

alright so an improper fraction has a

numerator that's bigger than the

denominator again numerator top number

in the fraction denominator is the

bottom number in the fraction all right

so now on the other hand if if this

looked the other way right if this was

instead for over 17 all right then we

would have a proper fraction so for a

normal regular everyday average proper

fraction okay the the proper word is

proper fraction pun intended

the top number would be smaller than the

bottom number for a proper fraction but

that's not what we have here okay so

we've got to work with this improper

fraction seventeen over four now

the good thing about improper fractions

is that we can turn them into what's

called a mixed number okay and so a

mixed number it's got a whole number and

a fraction okay and so we're gonna look

at how to do that now so we want to turn

this mixed number which is we want to

turn this fraction 17 over four into a

mixed number alright so that's the goal

here so how do we do that well to turn a

improper an improper fraction into a

mixed number okay the first thing that

we have to understand is that we keep

the same denominator so the denominator

of the improper fraction and the mixed

number are going to be the same so we

keep our four in our denominator so

there's gonna be a big number that's

going to go out here okay we're not

necessarily a big number but it's gonna

look big and compare us into the number

down here and the number down here

because it's a whole number so we put a

whole number right out front here in the

fraction then we also put a number in

their numerator so how do we know what

goes where ok well what we want to do is

we want to

think of a number that we can multiply

the denominator by that's going to give

us a number that's close to 17 but

that's not quite 17 okay so let me say

that again here so we want to put some

number out here so I'm just going to put

an A for now okay and we want to

multiply four by that number okay and we

want the result to be a number that's

close to 17 but not quite 17 it's got to

be a little bit smaller than 17 all

right so one way to do this is just

guess and check so let's just go through

our 4-times tables quickly so what's 4

times 3 4 times 3 is 12

all right what about 4 times 4 well 4

times 4 is what 16 and now 4 times 5 I'm

going to pause to give you a quick quiz

here 4 times 5 is what 20 all right and

so 5 would be too big because we want a

number that's close to 17 but it's not

quite 17 so 5 would be too big but 3 is

going to be too small because we can get

a little bit closer all right with 16 so

4 is gonna be the perfect answer here

all right so instead of an a we're gonna

put a 4 so let me drag this whole mess

down here so again we keep the 4 in the

denominator and we're gonna put a 4 out

here so 4 x 4 is 16 16 plus 1 is 17 so

we put a 1 up here all right

and so now we've got our mixed numbers

so you can you should be able to go from

mixed numbers to improper fractions and

from improper fractions to mixed numbers

fairly simply so this is a mixed number

here we've got our whole number out

front and we've got our fraction here

and so how do we go back to a an

improper fraction so the way that you do

that is you take the number in the

denominator multiply it by the whole

number and add the number in the

numerator so we would do 4 times 4 which

is 16 plus 1 gives us 17 and remember

the denominator is the same alright so

that's a way to guess to check that

we've got the mixed number correct here

all right so again make sure that you're

you know how to go between an improper

fraction and a mixed number fast and

make sure you can do going both ways

from an improper to mixed numbered mixed

number to improper fraction okay so now

we're almost to our answer so this 4 and

1/4 is really helpful here so right off

the bat okay the fact that we've got a 4

out here that should cue you in that C

is the right answer here but how do we

then that it's point 25 well 1/4 really

is equal to 0.25 all right so this is

another point that you'll want to know

all right for the GED but also for

general math okay so you want to know

some basic decimal values that are gonna

come up over and over again okay so I'm

gonna write some out here for you these

are really important to add to your

notes okay or even better yet just

memorize them so okay so the first thing

to understand here is that point 25 is

equal to 1/4 okay so we're looking at

fraction decimal equivalents here all

right in point 50 is equal to 2/4 all

right or 1/2 okay and point 75 is equal

to 3/4 okay and so now 1 all right is

just equal to 4/4 all right and so the

best way to think about this is to think

about quarters okay so if you've got one

quarter you've got 25 cents you've got

two quarters you've got 50 cents if

you've got three quarters you've got 75

cents if you've got four quarters you've

got a dollar here okay so that's the

best way to think about it whenever you

see fourths in the bottom right so if

you see that you've got four all right

or you've got 1/4 or two fourths or

three fourths just think about quarters

hey if I had three quarters I'd have 75

cents so 3/4 is equal to 0.75 all right

and so if you just memorize these values

here all right you'll see that 4 and 1/4

is the same as 4 point 25 all right and

so now also a way to do it is you can

put these in your calculator anytime

here all right so if you had been able

to use your calculator you could have

really sidestepped all of this you could

have put 17 divided by 4 in your

calculator that would give you the same

answer here all right but that that

wasn't the point the point is I wanted

to just take this improper fraction and

convert it to a mixed number then once

you had that mixed number to see that

this 1/4 is equal to 0.25 which is why

we got the point to 4.25 here all right

this doesn't add a little bonus to this

question let me give you something else

that's really common all right so

another really common fraction to

decimal equivalent is 1/3 all right so

one-third is equal to point three three

three three just a bunch of repeating

threes okay so another way to write that

it's just point three three and I'll put

a little sign up here this little line

means

repeating so if you do 1/3 in your

calculator you're just gonna get 0.333

and a bunch of threes that repeat okay

all right and so if you do 2/3 ok what

you're gonna get is you're gonna get

repeating sixes okay you're going to get

6 you're gonna get 6 so I'm gonna put

this repeating symbol here all right and

so those are two other numbers that are

important to have memorized here okay so

hopefully this all makes sense and

hopefully you got 4.25 and you didn't

get D you had no clue but if you did hey

that's okay

at least you're here at least you didn't

give up even if you pick D here that you

had new clue that's better than giving

up and not picking so another bonus

lesson here is on the GED test always

pick for a multiple choice answer don't

have really a multiple choice question

blank it just guess anything even if

you're stuck on it six says if the mean

of the following data set is 115

what's the missing number and we see a

data set here with 14 19 x2 in 16 all

right so pause the video and try to find

the mean okay let's go over how to do

this so this is another type of question

here that it's not really that or once

you see how to do it but a lot of

students don't get the concept until

they've been shown how to do it so let's

go through let's go through this now so

give yourself a pat on the back again

for being here in this video right now

trying to improve your life by passing

the GED test so what we're going to what

I want you to think of here is the mean

so what really is the mean what do I

mean when I say mean all right pawn 100%

intended so the word mean here is

another word for average so the mean

means the average so whenever you hear

the word mean mean means the average so

whenever you get a question say on mean

median mode and range you'll know that

that mean just means the average okay

and so in this case we see that it says

if the mean of the following data set is

150 what's the missing number we should

right away think hey we see the word

mean mean means the average so since

mean means the average we would just

find the mean in the same way that we

find the average because they're the

same thing the mean means the average

right you're probably getting tired of

hearing me say that but hopefully you're

getting it that the mean means the

average all right and so the way you

find the average is you take all the

numbers in a number set you add them up

and you divide by the total number of

numbers in that data set all right so

here let's pretend that we don't know

what the mean is because they told us

what the mean is they told us the mean

is 150 so let's just pretend that we

don't know what it is so how would we

find the average

well what we would do is we would take

all of our numbers in our number set

right and we would add them up so we

would do our 14 19 X 2 and 16 then we

would divide by the total number of

numbers and our number set all right or

the total number of data points to words

for the same thing so let's count them

we've got one two three four five all

right so we would divide by 5 and so now

basically all right we see now the

problem becomes evidence so we could not

solve for the mean in this situation

because we don't know what this X is

okay we don't know what this missing

number is so this is how you would find

the mean if we didn't know the mean and

we knew what this X was okay you would

add these up in divide by 5 but

unfortunately that's not the case here

all right so we don't know what the mean

is so or we do know what the mean is we

don't know what that X is so we

fortunately do know what the mean is all

right the mean is 150 all right and so

we can put on under 50 in there and now

hopefully it becomes obvious to you that

we have to solve for this X so the way

we're going to do this is just using

basic algebra we're gonna we're gonna

pull out or wheeling and dealing skills

as far as dealing with solving equations

here and we're going to solve the

equation for x so when I say solve the

equation for x we want to basically get

this X by itself on one side of the

equation here all right so hopefully

you've been taught what PEMDAS is before

if not then today's the day that you're

gonna learn all right so PEMDAS please

excuse my dear Aunt Sally so the P

stands for parenthesis and the e stands

for exponents in square roots the M

stands there multiplication the d stands

for division the a is for addition and

the S is for subtraction so this is your

order of operations so when you've got

equations to solve alright you want to

solve them using this order of

operations meaning you would do what's

in the parentheses first

all right you would do what's what has

exponents your square root second you

would then multiply you would then

divide and the order of addition and

subtraction is fairly arbitrary you

could subtract before you add it's not

going to change the answer but we

usually just say say a s first because

PEMDAS it sounds better than pamda s a

whatever that would would mean right but

anyway I mean I usually do addition

before subtraction just because

remember that way but that's not that

important it's in but what is important

is doing your multiplication in division

before you move on to addition and

subtraction and making sure you start

with what's in the parenthesis and

making sure that you do the exponents

and square words before you jump into

your multiplication division addition

subtraction etc etc all right so I have

a video on PEMDAS if this is a foreign

concept to you but I'm gonna explain

what you need to know here so there's

one more caveat to this all right

so whenever you've got a division bar

here all right you treat the division

bar like a parenthesis and you might be

thinking what does that mean why would I

treat the division bar like a

parenthesis okay well I'm gonna show you

how so you would treat this since you've

got this division bar here as if there's

parentheses around the top number and

parenthesis around at the top not in the

number the top part everything in the

top part of the fraction here so all of

these numbers here and you would treat

it like there's parentheses to run the

bottom number two all right and so now

that we have this division bar we know

we've got to treat the division bar like

parentheses so now we would then

following our PEMDAS rules we would do

everything in the parentheses first

before we move on to the rest of the

question and so this is one caveat to

PEMDAS that a lot of people don't don't

understand is that p is for parenthesis

but you treated division bar like

parentheses so basically what we're

gonna do here is we're going to simplify

everything up here for so we would do 14

plus 19 plus 2 plus 16 alright and if

you do that in your calculator you'll

find that that equals 51 so let's let's

bring this all down here sometimes I

can't talk right but hopefully I can

talk right for the rest of this question

so we've got 150 equals 51 plus X

divided by five so hopefully you guys

are really smart so I'm sure you're

falling but if if you weren't able to

follow that all I did was I did 14 plus

19 plus 2 plus 16 in my calculator that

was equal to 51 and we still have plus X

here all right and so we're dividing by

five all right so now remember this

division bar means that you've got to

treat the everything on the top and

everything in the bottom like it's

surrounded by parenthesis so we would in

theory simplify what's going on up top

in the fraction and simplify what's

going on on the bottom first but since

we've already done that we can't add 51

to X so we don't know what X is then

we're good we'll leave the top as it is

and we now want to multiply both sides

of our equation by five so why do we

multiply both sides by

well because we see that we've got 51

plus X divided by five we want to get X

by itself alright and we can't do

anything with a 51 we can't subtract the

51 all right we can't do that right now

because we've got to forgot to deal with

this five first down here alright so we

can't do any more simplifications all

right so now we can't add 51 to X and

we've done everything in the parenthesis

that we can so now we will move on to

multiplication and division all right

and so now we multiply by five on both

sides of the equation because whatever

you do to one side you do to the other

so since we've got 51 plus X divided by

five we multiply by five five divided by

five is just one so we'd have 51 plus X

times one who cares about the one we

okay so five times 150 is 750 so now

what we have is 750 is equal to 50 one

plus X and so now since we want to get X

by itself we see if you do 1 plus X so

we want to subtract 51 from both sides

of our equation alright and so 750 minus

51 is going to give us 699 sorry for

that dramatic pause my calculator was

lagging and that's the reason but 699 is

X so the value of x the missing number

was 699 all along did you get this right

let me know in the comments if you did

so right now as you sit there listening

to this you might be wondering why does

this question say it 121 well the reason

is because I pulled this one directly

out of my book the GED math champions

guide it's a B its guide to winning on

the GED test math section so if you're

interested in that and you like these

hard problems definitely check out that

book I've got a link to it down below if

you want to look at it but anyway that's

why the number says 121 so this is a

very challenging problem and this is

really going to test your understanding

of geometry so let me just add one note

in here this is a right triangle

so it says the following figure consists

of a square a triangle and a rectangle

what is the perimeter an area of the

figure below both ran into the nearest

whole number

all right pause the video and let's see

if you can get this okay let's go over

this so first of all this problem is

asking you to find two things the

perimeter in area so we don't want to

just find one so let me put a p here for

a perimeter right is that the end we're

going to make sure we found both so

whenever you've got a multi-faceted

question like this you want to make sure

you do both things

and this a obviously is for area so at

the end we'll make sure that we found

both here all right so to break this

down we see that it says the figure

consists of a square a triangle and a

rectangle all right so first let's

identify the the square triangle and

rectangle so hopefully all right you see

here that we've got the square right

here so a square is a four-sided plain

figure it's got a 90 degree angle in

each of the corners here so this little

box type thing just represents a 90

degree angle why is it a 90 degree angle

well let's say that you've got two lines

like this and they intersect in form a

90 degree angle we call these lines

perpendicular lines perpendicular lines

intersect and creat this 90 degree angle

which looks like a little box type thing

all right so that is a 90 degree angle

in any way in each of the four corners

of square in for a rectangle we're gonna

see these little box type things alright

and so the right triangle here so this

is our triangle okay I'm tracing our

triangle here and it has this little box

type thing in the corner which means

that that is or our ninety degree angle

here okay so the good thing about

squares that you need to know is that

all sides are the same line so every

side of the square is the same length so

if this is inches meters we don't really

know it doesn't really matter but we

know that for a square each side is

gonna be a length 10 okay and so with

the rectangle alright

the opposite sides are the same length

so let's say we've got 11 here all right

and so for the rectangle we would have

called this 11 as well and this side

over here would be 32 as well all right

so for a rectangle

you've got science that are opposite in

they're the same length so just by

seeing this 32 here we know that this

side is also 32 and by saying that this

side here is 11 we know that this side

is 11 - so the good news is that our

draw for our triangle we know two sides

for the triangle so we know that this

line here for the triangle is also going

to be length 10 so that this side of the

square is also the side of the triangle

so they're both 10 and down here we see

that our rectangle our 8 shares a side

with the triangle so for the rectangle

this is side this side is length of

Lebanon same with the triangle this side

it's going to be like 11 for our

triangle so the only side that we don't

know is this big line right here in our

triangle alright so we don't know the

length of this line alright and this

line on the triangle is called the

hypotenuse so the hypotenuse is the side

of the triangle that's that's directly

across from or opposite from our right

angle which is this little box type

thing so the 90-degree angle is across

from or hypotenuse all right the

hypotenuse is again is the biggest side

of that triangle and I'll explain why

that is in just a second

so in order to find the perimeter we

just have to add up the sides all right

we just have to add up the length of

each side here all right now to find the

area is gonna be a little bit trickier

all right so for the perimeter we just

have to add up all these sides but the

thing is that we don't know we don't

know what the side of this triangle is

so the hypotenuse of the triangle we

don't know what that is so how can we

find that well let me just pull this

triangle out here and we'll look at this

more in depth here because this is

extremely important to know for your

test all right so as you listen to this

right now

all right first of all give yourself a

huge big round of applause for being

right here with me right now working

towards your GED good for you and also

for sticking it through the video you

don't want to be a quitter you want to

be a champion all right and I want to

help you get through the GED so we've

got side ten and we've got Sun eleven

here and obviously we need to find this

side over here all right so this is

really a Pythagorean theorem question

and this is something you definitely

need to know for the GED test all right

so let me call this side a and let me

call this side B so whenever we've got a

right triangle right triangle is a

triangle where we've got this right

angle which again the little box type

thing is a right angle okay we can use

the following equation which is called

the Pythagorean theorem all right so a

squared plus B squared all right a

squared plus B squared equals C squared

all right so it's just that simple a

squared plus B squared equals C squared

okay and so we can use this relationship

here to help us find side C so since

this is side a alright so side a of the

triangle is going to be 10 in this case

alright and our side B is going to be 11

so we can use this Pythagorean theorem

relationship in order to find what the

hypotenuse or the missing side or the

side C whatever you want to call it is

all right so we've got a squared plus B

squared equals C squared so we've got 10

squared all right

plus 11 squared and that's going to

equal C squared all right so there's so

much so much stuff here in this question

that is just really helpful to

understand for your GED so you're

getting so much bang for your buck with

this question because there's there's

more than just one idea a little idea

being expressed rate there's a ton of

ideas so 10 squared is 100 and hopefully

you remember that 10 squared is the same

as 10 times 10 same with 11 so 11

squared is just 11 times 11 or 8 so

we've got 100 plus 11 times 11 which is

121 all right so we've got 100 plus 121

equals C squared okay so now we would

then have to do 100 plus 121 and that's

going to be 221 so we now see 221 and

that that is equal to C squared so now

what we have to do is we've got to find

the square root of C squared and so this

is this situation right here this two to

one equals C squared

I love that this came up in this

question here because remember earlier

on in the video we had that square root

question right where I told you that

whenever you see a number equal to a

variable squared a variable is just

another term for an unknown that we

solved that by taking the square root of

both sides so we want to just get C we

don't want C squared all right we just

need to get this C so we've got C

squared how do we get to see well we

take the square root of that and in

order to do that we've got to take the

square root by the other side as well so

let me just figure out what this is real

quick so we've got 221 and we want to do

the square root I'm putting this in my

calculator square root of 221 and that

gives us fourteen point eight six seven

let's say so let's say that C is equal

to fourteen point eight six seven okay

and so you know what we can we can round

that up that let's just round that up to

15 just to make life nice and simple all

right so to make life easy we're just

going to say that C side C is equal to

15 so we don't need this question mark

here anymore all right the question is

solved this side is equal to 15 all

right so hopefully you see how I got all

this so far all right so if you want to

take any notes now would be a good time

to pause the video all right because I'm

going to clear some

face out here so we've got some room to

work it so I hope you've got that stuff

in your notes if you wanted to if not

then you can rewind the video make sure

that you get that because that's all

important but I want to touch on another

really really important part of the

question here all right so you need to

understand this Pythagorean theorem

because on your test you might get

something you might get a word problem

where they say hey it's a ladder like

you might have a ladder leaning up

against the wall where this could be

your wall this side could be the wall

and this could be your ground or your

floor or whatever they call it so this

side would be your ground that's

supposed to be a G and this whole thing

up here could be your ladder right so

they could say hey there's a ladder

leaning against a wall and you know

here's the ground and they might tell

you that hey there's a 90 degree angle

form between the wall and the ground and

you might have to either find the length

the ladder or find the length of the

wall or the ground or something like

that it could also be a pole it could

also be a tree doesn't matter but

there's there's different kinds of word

problems they can give you with this so

you just have to remember that this 90

degree angle right this little box type

thing all right that tells you that you

can use the Pythagorean theorem

relationship which is a squared plus B

squared equals C squared now another

common question I get is is see you can

always going to be the largest side and

the answer is yes it has to be so it

doesn't matter what numbers you put in

here for a or B C is always going to be

another number because whenever you take

a number and you add another number to

it you're always going to get something

bigger okay so like you know if a is 2

and B is 4 2 plus 4 is 6 you get a

bigger number all right now the thing is

this is always always always going to be

true even if we've got negative numbers

because these are both squares so even

if we do say for example negative 2

squared and we add that to say negative

1 squared all right so even if a is

negative 2 and B is negative 1 since

they're both squared alright we're still

going to end up with positive numbers so

negative 2 squared is still 4 right

because negative 2 squared is the same

as 2 as negative 2 times negative 2 a

negative times a negative gives a

positive all right same with negative 1

so negative 1 squared is the same as

doing negative 1 times negative 1 a

negative times a negative gives you a

positive number so you would would end

up with 4 plus 1 which is is 5 right so

C squared would be 5 in this case but

the point I want to make is that C

always has to be bigger so C is always

going to be the biggest side and the

triangle

all right and that's because you've got

a squared plus B squared so whatever

numbers you plug in for a and whatever

number you plug in for B you're always

going to get you know that you're always

going to get a positive because you're

just gonna have to square that number so

C is always going to be the biggest side

of the triangle all right so now let's

get back to our original question all

right now that we found the now that we

found that this was 15 now how do we

actually calculate the perimeter well

it's actually very simple we want to

take all these numbers on the outside

which I've underlined and we're just

going to add them up so we take all of

the numbers on the outside of the shape

and we add them up here so let me just

do the quick method here to write this

out here so we would do 10 starting with

this 10 down here let's do 10 plus

another 10 plus another 10 plus 15 plus

32 plus 11 plus another 32 and what is

this equal well if you do it in your

calculator you find that that equals 120

all right and I did that in my

calculator before I did this part of the

question so the perimeter is 120 so

again how do we get the perimeter of

this wicked shape here well we just look

at each number on the outside right so

we don't care about these numbers on the

inside just the numbers on the outside

all right and we add these all up and we

get 120 all right so that's our

perimeter but what about the area so the

area is a little bit different the area

is a little bit trickier here so

basically we want to get the area of the

entire shape so let's call this a and

I'm gonna put a little T here all right

so the total area T stands for total is

equal to your area of the square plus

the area of the rectangle plus the area

of our triangle here all right so the

area of the square a little less the

little S stands for square the little

art here stands for area the rectangle

and a little T the T stands for area of

the triangle and you know let me call

this little T or for triangle because we

already got this 80 out here and this a

T out here just is for the toll so

basically we defined the area of the

square the area of the rectangle and the

area of the triangle so now how are we

going to do that though so let's talk

about the area of the square so the area

of the square

is equal to side times side so let's say

the area of the square is equal to a

squared or we could say a times a so

let's call any side of the square okay

let's just call it length a because

every side of the square is the same

length so we could say a squared or a

times a is going to give us the area of

the square all right so to do that

calculation we would just do 10 times 10

and 10 times 10 is 100 all right so you

can either do that in your calculator

you can do it by hand where you can just

say hey we're multiplying by 10 here

we've got these two zeros so where the

answer is gonna have to two zeros

however you want to think about it

alright or just remember that 10 times

10 is 100 that's a good that's good to

memorize that times table so now let's

talk about the area of that rectangle or

our AR and so for the area the rectangle

okay the formula is just one side of the

rectangle times another side of the

rectangle so length of the rectangle

times width of the rectangle however you

want to think about it I just like think

about it as side times side so 32 could

be side a for example and 11 could be

site B it doesn't matter that how you

label you're just doing side times side

so here we've got 32 times 11 all right

so here's a little trick for multiplying

by 11 it's ready for this so as a bonus

because you made it this far into the

video I'm going to teach you a little

trick here so to multiply any two digit

number by 11 just take focus on these

two digits so we've got three and we've

got two so we're going to split them up

so we're going to write a three here I'm

gonna put a little space and we're gonna

write a two here now we're gonna add

them up so now let's do three plus two

that's going to give us five all right

so 350 to you so that's a quick trick to

multiply two-digit numbers by 11 that's

your little bonus for sticking with the

video so far alright so now what about

the triangle so the area of the triangle

or our 80 or is equal to two half times

side a times side B okay another way to

write that is just a times B divided by

2 so 1/2 times a B is the same as just

saying a times B divided by 2 so the

area of a triangle is

the side a times side B divide them by

two all right so let's do that here let

me write the work out here so we've got

a little bit more room to work here so

side a would be ten side B is 11 so

we've got a perfectly we can use your a

little trick here so let me draw this

line here as a divider so what we're

doing here is side a of the triangle

times side b of the triangle then we're

gonna have to remember to multiply by

two so we've got 10 times 11 so let's

use that little trick I taught you

actually this is actually almost don't

even need to but let's just say you

wanted to so we're going to take the two

digit number we're multiplying by 11 we

take 1 and we take 0 and we put a space

in between we're gonna split them up

we've got 1 and we've got a gap here

we've got a 0 so now we add this up

what's 1 plus 0 that is just 1 so we've

got we've got 110 is the answer to 10

times 11 now again since we're

multiplying by a 10 you could just put

and there's one zero here you could just

think hey you put a zero on the end

there and without using your calculator

and you would just remember hey we've

got 11 let me just put a zero there and

you could have gotten it in 110 that way

or you could do the 11s multiplying

trick doesn't really matter all right

but either way we have to divide this by

two and the answer is of course 55 and I

didn't do that in my head I just did in

the calculator before I film this

portion of the video but we know that

our perimeter is 120 our area is 35 now

if you've got this right without any

work let me know down in the comment

section because I really really think

that you're gonna pass I'd be shocked if

you got this right and without my help

and if you've got both the perimeter in

the area by yourself and you don't pass

the GED test I'd be shocked honestly