let's try to learn a thing or two about
ratios so ratios are just expressions
that compare quantities so that might
just be a fancy way let me do of saying
something that you may or may not
understand so let me give you actual
examples if I have 10 horses 10 horses
and I have five dogs five dogs and
someone were to come to me and say Sal
what is the ratio what is the ratio of
horses of horses to dogs so I want to
know how many horses do I have for some
number of dogs so I could say I have 10
horses I have 10 horses for every 5 dogs
so I could say the ratio of horses to
dogs is 10 - 5 or I could also write
that as a fraction I could say the ratio
of horses to dogs is 10 - 5 or I could
just write it out I could say it is 10 -
5 these all are saying the same thing
and the thing I write first or the thing
that I write on top is the number of
horses so this is the number of horses
right there that's the number of horses
and that's all the number of horses if I
want to talk about the number of dogs
this is the number of dogs that's the
number of dogs or that's the number of
dogs
I'm just these are all just expressions
that are comparing two quantities now I
just said I have 10 horses for every
five dogs but that what does that mean
that means I have five horses for every
one dog sorry not five horses for every
one dog that means I have two horses for
every one dog right if for five dogs I
have ten that means for every one of
these dogs there are two horses for
every one of these dogs there are two
horses for every one of every two of
these horses there's one dog and I just
kind of reasoned through that so this is
I have two horses for every one dog but
how do you get there
how do you get from ten to five to two
to one well you can think of what's the
biggest number that divides into both of
these numbers what's their greatest
common divisor I have all video on that
but the biggest number that divides
to both of these guys is five so you
divide both of them by five and you can
kind of get this ratio into a reduced
form now if I write it here it would be
the same thing as 2 to 1 or 2 or 2 to 1
and so it's interesting about ratios it
isn't literally or doesn't always have
to be literally the number of horses and
the numbers of dogs you have what a
ratio tells you is how many horses do I
have for every dog or how many dog do
how many dogs do I have for every horse
now just to make things clear
what if someone asked me what is the
ratio of o dogs to horses dogs to horses
so what's the difference in these two
statements here I said horses two dogs
here I'm saying dogs to horses dogs to
horses so since I've switched the ratio
X what I'm looking for I'm looking for
the ratio of dogs horses I switch the
numbers so dogs for every five dogs I
have 10 horses or if I divide both of
these by five for every one dog I have
five horses so the ratio of dogs to
horses is five to ten or one to five or
you could write it this way one two I
could write it let me write it down here
one to five or I could write one to five
and the general convention this wouldn't
be necessarily incorrect that's not
wrong but the general convention is to
get your ratio or your fraction if you
want to call it that into the simplest
form or into this reduced form right
there so let's just do a couple of other
examples let's say I have let's say I
have 20 apples I have 20 apples let's
say I have 40 oranges 40 oranges and
let's say that I have I don't know let's
say I have 60 60 strawberries
strawberries now what is the ratio of
apples to oranges to strawberries so I
can write it like this I can write what
is the ratio of all right like this
apples apples to oranges to oranges to
strawberries to strawberries
well I could start off by literally
saying well for 60 strawberries for
every 60 strawberries for every 60
strawberries I have 40 oranges I have 40
oranges and I have 20 apples so then
this would be legitimate you could say
the ratio of apples to oranges to
strawberry are 20 to 40 sorry 20 to 40
to 60 and that wouldn't be wrong but we
saw before we could put into reduced
form so we think of what's the largest
number that divides into all three of
these we can't just do it into two of
these now because now my ratio has three
actual quantities well the largest
number that divides into all of these
guys is 20 so if we divide all of them
by 20 we can then say for every one
Apple I now have you can divide this guy
by 20 I have two oranges and I have and
I have three strawberries so the ratio
of apples to oranges to strawberries is
one to two to three and I got that in
every case by just dividing these guys
all by 20 I divided by 20 I think you
get the general idea if someone were to
ask you what's the ratio of let me just
write it down because it never hurts to
have a little bit more clarification if
someone want to know the ratio of
strawberries to oranges we get into my
orange color strawberries to oranges to
apples to apples I thought I was going
to do that in yellow to apples what is
this race you're going to be well for
every three strawberries I have two
oranges to oranges and I have one Apple
so then it would be three to two to one
the general idea is what
to order someone asks you or the
different items you put the ratio is
going to be in that same exact order now
and all of the examples so far I gave
you the number of quantity the quantity
of things we had and I we figured out
the ratio what if it went the other way
what if it went the other way
what if I told you a ratio what if I
said the ratio the ratio of boys to
girls in a classroom boys to girls is
let's say the ratio of boys to girls is
two to three which I could have also
written as two to three just like that
so for every two boys I have three girls
or for every three girls I have two boys
and let's say that there are there are
forty students students in the classroom
in the classroom and then someone were
to ask you how many girls are there how
many girls are in in the classroom so
this seems a little bit more convoluted
than what we did before we know the
total number students we know the ratio
but how many girls are in the room so
let's think about it this way the fact
that the ratio of boys to girls I'll
write it like this boys maybe I'll be
stared difficult with the colors the
ratio of boys to girls is equal to is
equal to two two to three need to be so
stereotypical but it doesn't hurt two to
three the ratio of boys to girls is two
to three so this says for every three
girls there's two boys for every two
boys there's three girls what does it
also say it also says for every for
every five students for every five
students there are what there are two
boys and three girls
there are two boys and
and three girls now why is this help
this statement helpful
well how many groups of five students do
I have I have 40 students in my class
right there right I have 40 students in
my class and for every five students
there are two boys and three girls so
how many groups of five students do I
have so I have total of forty students
let me do it in this purple color I have
40 students students and then there are
five students per group five students
per group and I figured out that group
just by looking at the ratio for every
five students I have two boys and three
girls so how many groups of five
students do I have so that means that I
have eight groups
40 divided by five I have eight groups
of five students now we are wondering
how many girls there are so each group
is going to have three girls each group
has three girls so each group has three
girls each group has three girls so how
many girls do I have I have eight groups
each of them have three girls so I have
8 groups times 3 girls per group is
equal to 24 girls 24 girls in the
classroom and you could do the same
exercise with boys how many boys are
there there's a couple of ways you could
do it you could say for all for every
group there are two boys there's eight
groups there's sixteen boys or you could
say look there's forty students 24 of
them are girls 40-24 is sixteen so
either way you could get to sixteen boys
and if you want to think about kind of a
fast way to do it and it would be
identical you'd say look two plus three
is five so for every five students two
boys three girls how many groups are
there you say 40 divided by 5 is equal
to 8 groups every group has 3 girls so
you do 8 times 3
is equal to 24 girls let's do one that's
a little bit harder than that a little
bit harder than that let's do one where
I say that the ratio the ratio of let's
say well let's let's go back to let's go
to the farm the farm example the ratio
of sheep I'll do sheep and white the
ratio of sheep - I don't know chickens -
chickens - I don't know what's another
farm animal - pigs the ratio of sheep to
chicken - pigs
maybe I should just say chicken right
there the ratio of sheep to chicken -
pigs or chickens let's just say chickens
is let's say the ratio is 2 to 5 2 to 10
and notice I can't reduce this anymore
there's no number that divides into all
of these so this is the ratio of sheep
to chickens to pigs and let's say that I
have a total of 51 animals so I have a
total of 51 animals and I want to know
how many chickens do I have how many
chickens how many chickens do I have
what we do the same idea for every two
sheep I have five chickens and I have 10
pigs that tells me for every 17 animals
so for every 17 animals so every group
of 17 animals what do I have and where
did I get 17 from I just added two plus
five plus 10 so for every 17 animals I'm
going to have let me pick a new color
I'm going to have two sheep two sheep
five chickens five chickens and 10 pigs
10 pigs now how many groups of
17 animals do I have I have a total of
51 animals so if there's 17 animals per
group 51 animals divided by 70 animals
per group
I have three groups of 17 animals three
groups of 17 animals now I want to know
how many chickens every group has five
chickens every group has five chickens
we already know that and I have three
groups so I have three groups every
group has five chickens so I'm going to
have three times five chickens which is
equal to 15 chickens 15 chickens not too
bad all I did is add these up and says
for every 17 animals I've got five
chickens I've got three groups of
seventeen so for each of those groups I
have five chickens three times five is
fifteen chickens you could use the same
process to figure out the number of
sheep or pigs you might have