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Ratio
Mathematics, Grade 6
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Study Guide Ratio Mathematics, Grade 6
❮
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3
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RATIOS
What
are
ratios?
A
ratio
is
a
comparison
of
two
numbers.
The
two
numbers
must
have
the
same
unit
in
order
to
be
compared.
Ratios
can
be
written
three
ways,
4/5,
4:5
and
4
to
5.
Ratios
can
be
compared
to
other
ratios
as
long
as
the
units
are
the
same.
If
one
ratio
is
known
and
a
similar
ratio
needs
to
be
found,
a
proportion
can
be
used.
A
proportion
has
the
same
units
in
both
ratios.
A
proportion
is
used
to
find
equal
ratios.
To
solve
a
proportion,
cross
multiplication
is
used.
It
is
very
important
that
the
correct
units
are
lined
up
with
a
proportion
in
order
to
find
the
correct
result.
Similar
figures
also
use
proportions.
Similar
figures
are
figures
that
have
the
same
angle
measure
although
the
lengths
of
their
sides
are
different.
A
rate
is
a
fraction
in
which
the
units
are
different.
A
familiar
rate
is
miles
per
hour.
In
fraction
form,
it
would
be
miles/hour.
When
buying
items
from
a
grocery
store,
a
rate
is
used
to
determine
which
item
would
be
a
better
buy.
How
to
use
ratios:
•
A
ratio
is
used
to
compare
items
with
the
same
unit.
For
example,
if
School
A
won
18
out
of
24
games,
the
ratio
of
winning
games
to
total
games
would
be
3/4.
To
compare
this
to
School
B
that
won
36
out
of
48
games,
the
ratio
would
have
to
be
found.
The
ratio
of
winning
games
to
total
games
for
School
B
is
also
3/4.
Therefore
both
schools
have
the
same
ratio
of
winning
games
to
total
games.
•
A
proportion
is
used
when
one
ratio
is
known
and
only
part
of
another
ratio
is
known.
There
are
4
parts
to
a
proportion
and
it
can
be
solved
when
3
of
the
4
parts
are
known.
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Permission
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granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
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only.
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Example:
11
=
33
14
x?
Since
11
is
multiplied
by
3
to
get
33,
14
should
be
multiplied
by
3
to
find
the
answer
of
42.
•
If
the
numbers
in
a
proportion
are
too
large
to
figure
out
mentally,
cross
multiplication
should
be
used.
With
cross
multiplication,
two
ratios
are
set
up
equal
to
each
other
with
one
piece
of
the
proportion
missing
which
will
be
called
x.
The
numerator
of
the
first
ratio
is
multiplied
by
the
denominator
of
the
second
ratio.
It
is
set
equal
to
the
product
of
the
denominator
of
the
first
ratio
multiplied
by
the
numerator
of
the
second
ratio.
Then
algebra
is
used
to
solve
for
x.
Example:
18
=
45
18
·
x
=
27
·
45
27
x
18
·
x
=
1215
x
=
67.5
•
To
solve
similar
figures,
a
proportion
can
also
be
used.
It
is
important
to
make
sure
the
proper
sides
of
the
figure
match
up
with
the
proportion.
Example:
•
Rates
can
be
very
useful
in
everyday
life.
A
rate
is
a
fraction
with
different
units.
If
a
rate
of
pay
was
$22
per
hour,
the
amount
of
pay
for
6
hours
could
be
figured
out.
To
get
the
total
pay,
multiply
$22
by
6
hours
to
get
the
answer,
$132.
•
Rates
can
be
used
to
find
the
best
buy
at
a
grocery
store.
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
Example:
Cereal
A
is
$3.49
for
13
ounces.
Cereal
B
is
$3.99
for
16
ounces.
Which
is
the
better
buy?
Cereal
A
$3.49
=
.29/
ounce
Cereal
B
$3.99
=
.25/
ounce
13
oz.
16
oz.
In
this
case,
Cereal
B
is
a
better
buy
because
it
is
cheaper
per
ounce.
Try
this!
1.
Solve
the
ratio:
4/10
=
8/x
16/24
=
32/x
2.
Solve
the
proportion
by
cross
multiplication:
27/54
=
37/x
49/53
=
x/137
3.
Find
the
missing
side
in
the
similar
figures:
4.
Find
the
better
buy:
5
pop
bottles
for
$7
or
4
pop
bottles
for
$6
© Copyright NewPath Learning. All Rights Reserved.
Permission
is
granted
for
the
purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
Visit
us
at
www.NewPathLearning.com.
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