WHOLE
NUMBERS
:
The
set
of
integers
is
comprised
of
natural
numbers
and
their
opposites
,
it
ie
positive
numbers
and
their
opposites
that
are
negative
.
Example
:
The
set
of
integers
is
defined
as
follows
:
Z
+
=
Positive
integers
Z
=
negative
integers
(
0
=
neutral
element
,
zero
is
neither
positive
nor
negative
)
ABSOLUTE
VALUE
:
If
a
number
is
positive
,
the
absolute
value
is
the
same
number
and
if
it
is
negative
its
absolute
value
is
the
opposite
.
The
absolute
value
is
never
negative
.
Example
:
-
3
=
3
reads
:
absolute
value
of
minus
three
three
5
=
5
reads
:
absolute
value
five
five
Operations
with
integers
:
SUM
:
The
sum
of
integers
is
divided
into
:
SUM
OF
____________________
integers
:
The
sum
of
____________________
positive
____________________
is
performed
in
the
same
way
that
two
natural
numbers
are
added
.
WHOLE
SUM
OF
NEGATIVE
:
The
sum
of
two
negative
integers
is
obtained
by
adding
the
absolute
values
?
?
of
the
____________________
and
putting
a
negative
sign
to
the
result
.
Procedure
:
to
.
We
place
the
numbers
to
be
added
in
parenthesis
b
.
We
add
their
____________________
values
c
.
The
result
will
put
a
minus
sign
Example
:
(
-
48
)
+
(
-
32
)
=
Numbers
to
add
I
-
I
-
32I
48I
+
=
add
their
absolute
values
-
80
=
As
a
result
we
put
a
minus
sign
SUM
OF
WHOLE
WITH
DIFFERENT
SIGNS
:
The
sum
of
two
integers
of
different
signs
is
obtained
by
subtracting
the
absolute
value
greater
whole
,
the
entire
lower
absolute
value
.
in
the
result
the
sign
of
integer
greater
absolute
value
is
written
.
Example
:
(
36
)
+
(
-
15
)
+
(
14
)
+
(
-
9
)
=
(
(
-
15
)
+
(
-
9
)
)
=
L
-
24l
=
L
-
24l
(
(
36
)
+
(
14
)
)
=
l
50
l
50
-
24
=
26
Operation
to
be
performed
We
add
negative
integers
and
the
result
we
add
its
absolute
value
.
We
add
the
positive
integers
and
its
outcome
will
find
absolute
value
.
We
subtract
these
two
results
and
let
the
result
the
sign
of
the
larger
number
having
greater
absolute
value
.
PROPERTIES
OF
THE
ADDITION
OF
WHOLE
NUMBERS
Clausurativa
:
The
sum
of
two
integers
gives
results
in
another
integer
.
Commutative
:
The
order
of
the
addends
does
not
change
the
result
.
Associative
:
When
you
add
more
than
two
integers
,
how
are
grouped
does
not
change
the
result
.
Modulativa
:
Adding
any
integer
zero
,
the
result
is
the
same
integer
.
PROPERTIES
EXAMPLES
Clausurativa
(
-
3
)
18
+
=
15
Commutative
(
-
33
)
+
(
-
142
)
=
(
-
142
)
+
(
-
33
)
-
175
-
175
=
Associative
(
(
-
2
)
+
12
)
+
(
-
5
)
=
(
-
2
)
+
(
12
+
(
-
5
)
)
(
10
)
+
(
-
5
)
=
(
-
2
)
+
(
7
)
5
=
5
Modulativa
(
-
3
)
+
0
=
(
-
3
)
ABDUCTION
:
In
operation
a
-
b
=
c
,
the
minuend
is
a
,
b
and
c
is
the
subtrahend
is
the
difference
.
Since
a
reverse
operation
is
subtraction
gives
the
addition
is
performed
as
follows
:
When
we
add
the
minuend
opposite
the
subtrahend
and
the
result
of
the
sum
is
the
difference
.
Symbols
:
Destruction
in
parentheses
12
-
8
+
(
36
-
7
+
10
-
15
)
+
9
12
-
8
+
36
-
7
+
10
to
15
+
9
67
-
30
=
37
Multiplication
:
Multiply
integers
abbreviated
means
adding
several
integers
either
identical
or
different
sign
.
Procedure
for
multiplying
integers
:
1
.
Multiply
the
numbers
as
if
they
were
natural
2
.
operate
the
signs
using
the
following
principles
Example
.
(
-
3
)
X
(
8
)
=
-
24
Properties
multiplying
integers
:
1
.
Clausurativa
:
The
multiplication
of
two
natural
numbers
as
a
result
gives
us
another
natural
number
.
2
.
commutative
:
The
order
of
the
factors
does
not
alter
the
product
.
3
.
Associative
:
Multiplying
over
two
natural
numbers
,
the
way
they
are
grouped
not
alter
the
product
.
4
.
Modulativa
or
neutral
element
:
Multiplying
any
natural
number
by
one
,
the
product
is
the
same
natural
number
.
5
.
Distributive
of
multiplication
with
respect
to
addition
:
The
product
of
a
natural
number
by
a
specified
amount
,
is
equal
to
the
sum
of
partial
products
of
the
whole
for
each
of
the
addends
.
EXAMPLE
PROPERTIES
Clausurativa
to
.
12
X
3
=
36
b
.
17
x
7
=
119
Commutative
6
x
53
=
53
x
6
318
=
318
Associative
(
7X49X8
=
7X
(
4X8
)
(
28
)
X8
=
7X
(
32
)
224
=
224
Neutral
element
2
,
574
x
1
=
2
,
574
1
X
2
,
574
=
2
,
574
The
distributive
multiplication
to
the
sum
4X
(
5
+
2
)
=
(
4x5
)
+
(
4x2
)
=
20
+
8
=
28
DIVISION
:
In
integer
division
may
be
the
case
that
both
numbers
are
positive
,
negative
or
both
are
having
different
sign
.
Considering
the
above
possibilities
can
draw
the
following
conclusions
:
1
.
The
quotient
of
two
positive
integers
is
a
positive
integer
(
15
)
/
(
3
)
=
5
2
.
The
negative
quotient
of
two
integers
is
a
positive
integer
(
-
24
)
/
(
-
6
)
=
4
3
.
The
ratio
of
the
division
of
two
integers
different
sign
is
a
negative
integer
.
(
-
24
)
/
(
6
)
=
-
4
In
integer
division
the
same
laws
that
are
used
for
multiplication
are
met
.
