RATIOS
Reasons
One
reason
is
a
____________________
between
two
or
more
quantities
.
This
comparison
is
made
by
a
____________________
(
division
)
,
which
can
be
written
in
any
of
the
following
ways
:
And
it
reads
"
is
ab
"
,
since
in
this
case
are
____________________
two
magnitudes
(
b
)
having
the
same
nature
,
that
is
,
generally
fractions
are
considered
an
"
abstract
"
reason
to
be
meaningful
,
it
____________________
the
numbers
____________________
in
it
represent
some
extent
,
such
as
:
number
of
people
,
number
of
objects
,
units
of
time
(
hours
,
____________________
,
seconds
)
,
distance
units
(
meters
,
millimeters
,
dm
,
etc
.
)
____________________
others
.
Example
1
Staple
boxes
2
cm
wide
____________________
in
packs
of
12
cm
.
How
many
boxes
fit
on
each
package
?
To
____________________
this
question
it
is
____________________
to
divide
12
by
2
,
which
will
give
the
number
of
boxes
.
The
ratio
is
called
____________________
and
indicates
that
12
is
six
times
greater
than
two
.
Example
2
In
a
room
there
are
40
students
,
of
whom
25
are
women
and
15
are
men
,
then
the
ratio
of
women
to
men
is
:
The
reason
is
,
that
is
25
____________________
are
five
thirds
of
15
men
in
the
group
.
Example
3
What
is
the
ratio
of
6
mm
and
four
centimeters
?
,
to
respond
,
you
need
to
compare
two
numbers
in
the
same
unit
of
____________________
,
such
as
millimeters
.
This
is
,
then
is
the
reason
,
that
is
,
there
are
three
twentieths
6mm
4
____________________
.
Proportions
If
it
is
observed
____________________
,
it
can
be
deduced
that
more
____________________
having
the
same
reason
,
for
example
,
the
ratio
of
48
and
8
,
is
also
six
(
as
in
the
first
example
)
,
which
____________________
that
,
it
is
said
that
12
2
,
48
and
8
form
a
proportion
.
The
numbers
a
,
b
,
c
and
d
form
a
____________________
if
the
ratio
b
is
equal
to
the
ratio
between
c
and
d
.
Which
is
written
:
As
shown
,
a
ratio
is
formed
of
four
numbers
called
terms
,
____________________
b
and
c
and
d
are
the
ends
,
____________________
the
media
.
Fundamental
property
of
proportions
At
a
____________________
the
product
(
multiplication
)
of
the
____________________
is
equal
to
the
product
of
the
media
.
Example
4
To
check
if
the
____________________
and
forms
a
____________________
or
not
?
As
3
x
20
=
60
and
5
x
12
=
60
,
these
ratios
form
a
proportion
.
This
property
others
,
which
are
detached
named
below
:
?
In
all
____________________
you
can
swap
the
locations
of
the
media
,
thus
obtaining
another
proportion
.
For
example
,
in
the
proportion
,
the
media
is
5
to
12
and
to
move
them
(
including
)
is
obtained
which
is
a
ratio
as
____________________
the
fundamental
property
.
?
In
all
proportion
can
be
inverted
thus
obtaining
the
two
reasons
other
proportion
.
For
example
,
if
the
terms
of
each
reason
____________________
the
proportion
invested
in
a
new
ratio
is
obtained
____________________
it
meets
the
____________________
property
2
x
42
=
84
and
7
x
12
=
84
.
?
In
all
proportion
the
sum
of
the
first
and
second
,
is
the
second
as
the
sum
of
the
third
and
fourth
term
is
the
fourth
.
Consider
the
following
ratio
:
____________________
it
is
added
to
4
(
the
first
term
)
3
(
second
term
)
and
compared
with
the
same
second
term
;
after
the
third
(
12
)
and
fourth
term
(
9
)
is
added
,
and
compared
with
the
fourth
term
,
ie
,
which
would
be
a
new
ratio
is
as
7
x
9
=
63
and
3
x
21
=
63
.
