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Fraction Operations
Mathematics, Grade 7
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Study Guide Fraction Operations Mathematics, Grade 7
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3
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FRACTION
OPERATIONS
Fraction
operations
are
the
processes
of
adding,
subtracting,
multiplying
and
dividing
fractions
and
mixed
numbers.
A
mixed
number
is
a
fraction
with
a
whole
number.
Adding
fractions
is
common
in
many
everyday
events,
such
as
making
a
recipe
and
measuring
wood.
In
order
to
add
and
subtract
fractions,
the
fractions
must
have
the
same
denominator.
If
the
fractions
do
not
have
the
same
denominator,
a
common
denominator
must
be
found
before
the
fractions
can
be
added
or
subtracted.
Once
the
fractions
have
the
same
denominator
the
fractions
are
added,
by
adding
the
numerators
only
and
leaving
the
denominators
the
same.
Multiplying
fractions
is
the
operation
of
multiplying
two
or
more
fractions
together
to
find
a
product.
Multiplying
fractions
is
used
when
finding
the
area
of
various
shapes.
Dividing
fractions
is
the
operation
of
dividing
two
fractions
or
mixed
numbers
to
find
a
quotient.
Mixed
numbers
can
be
used
in
all
operations,
but
a
mixed
number
must
be
changed
into
an
improper
fraction
first
before
performing
the
operation.
All
fractions
should
be
in
simplified
form.
Equations
may
contain
fractions
and
must
be
solved
using
inverse
operations.
How
to
use
fraction
operations
When
adding
or
subtracting
fractions,
the
denominators
must
be
the
same.
If
the
fractions
have
the
same
denominator,
they
can
be
added
or
subtracted.
If
the
fractions
do
not
have
the
same
denominator,
one
must
be
found
before
the
fractions
can
be
added
or
subtracted.
Ex.
Add
4/18
+
3/9
→
4/18
+
6/18
=
10/18
=
5/9
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Permission
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granted
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purchaser
to
print
copies
for
non-commercial
educational
purposes
only.
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www.NewPathLearning.com.
When
multiplying
fractions,
simply
multiply
the
numerators
first
to
find
the
resulting
numerator
and
then
the
denominators
to
find
the
resulting
denominator.
When
multiplying
fractions,
the
resulting
fraction
should
always
be
reduced
to
lowest
terms
if
possible.
When
dividing
fractions,
the
first
fraction
stays
the
same,
the
sign
changes
to
multiplication
and
the
second
fraction
is
changed
to
its
reciprocal.
A
reciprocal
is
the
fraction
flipped
so
when
the
two
fractions
are
multiplied
together,
the
result
is
1.
Ex.
Multiply:
5/6
·
4/5
=
20/30
=2/3
Divide:
1/3
÷
4/7
=
1/3
·
7/4
=
7/12
When
evaluating
mixed
fractions,
the
mixed
fraction
must
be
changed
into
an
improper
fraction
before
evaluating.
The
same
rules
apply
to
mixed
fractions.
When
operating
with
mixed
fractions,
the
result
may
be
an
improper
fraction,
which
would
then
have
to
be
changed
back
into
a
mixed
number
for
the
final
answer.
Ex.
Add:
1
2/3
+
3
7/8
=
5/3
+
31/8
=
40/24
+
93/24
=
133/24
=
5
13/24
© 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.
Try
This!
1.
Add
the
fractions:
3/5
+
7/15
=
?
8/14
+
3/28
=
?
2
2/3
+
6
1/5
=
?
4
7/8
+
1
3/4
=
?
2.
Subtract
the
fractions:
8/9
-
2/3
=
?
15/16
-
4/8
=
?
5
9/10
-
3
2/5
=
?
4
4/8
-
1
1/4
=
?
3.
Multiply
the
fractions:
6/10
· 2
/3
=
?
7/9
·
4/5
=
?
2
6/9
·
3
1/4
=
?
1
1/2
·
2
2/3
=
?
4.
Divide
the
fractions:
6/7
÷
2/3
=
?
8/12
÷
3/4
=
?
5
1/2
÷
1
1/2
=
?
6
2/3
·
4
1/4
=
?
5.
Solve
the
equations
for
x:
x
+
3/4
=
11/12
x
-
2
3/20
=
2
4/5
1
7/9
·
x
=
4/18
2
5/6
÷ x
=
1
5/12
© 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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