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properties of fractions
If
a
a
,
b
b
,
c
c
,
d
d
, and
k
k
are real numbers, and if there is nothing being divided by
0
0
, then the following
properties of fractions
apply:
a
b
=
c
d
a
b
=
c
d
if and only if
a
d
=
b
c
a
d
=
b
c
a
1
=
a
a
1
=
a
and
a
a
=
1
a
a
=
1
a
k
b
k
=
a
b
⋅
k
k
=
a
b
a
k
b
k
=
a
b
⋅
k
k
=
a
b
−
(
a
b
)
=
−
a
b
=
a
−
b
-
(
a
b
)
=
-
a
b
=
a
-
b
a
b
=
a
⋅
k
b
⋅
k
a
b
=
a
⋅
k
b
⋅
k
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⎡
⎢
⎣
x
2
1
2
√
π
∫
x
d
x
⎤
⎥
⎦
[
x
2
1
2
π
∫
x
d
x
]
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