Mula sa Wikipedia, ang malayang ensiklopedya
Mga pahati ng 10 na inilarawan ng Cuisenaire rods : 1, 2, 5, at 10 Sa sipnayan , ang sinasabing nahahati o pahati ang isang buumbilang
m
{\displaystyle m}
n
{\displaystyle n}
m
{\displaystyle m}
n
{\displaystyle n}
pagkahatiin ng mga bilang.
Sinasabing pahati ng isang bilang
n
{\displaystyle n}
m
{\displaystyle m}
k
{\displaystyle k}
n
=
m
k
{\displaystyle n=mk}
m
∣
n
{\displaystyle m\mid n}
at kung hindi,
m
∤
n
.
{\displaystyle m\not \mid n.}
Sa lahat ng buumbilang
a
,
b
,
c
{\displaystyle a,b,c}
Kung
a
∣
b
{\displaystyle a\mid b}
b
∣
c
,
{\displaystyle b\mid c,}
a
∣
c
;
{\displaystyle a\mid c;}
palipat ang pagkahatiin.
Kung
a
∣
b
{\displaystyle a\mid b}
b
∣
a
,
{\displaystyle b\mid a,}
a
=
b
{\displaystyle a=b}
a
=
−
b
.
{\displaystyle a=-b.}
Kung
a
∣
b
{\displaystyle a\mid b}
a
∣
c
,
{\displaystyle a\mid c,}
a
∣
(
b
+
c
)
{\displaystyle a\mid (b+c)}
a
∣
(
b
−
c
)
.
{\displaystyle a\mid (b-c).}
[ a]
a
∣
b
{\displaystyle a\mid b}
c
∣
b
,
{\displaystyle c\mid b,}
(
a
+
c
)
∣
b
{\displaystyle (a+c)\mid b}
2
∣
6
{\displaystyle 2\mid 6}
3
∣
6
{\displaystyle 3\mid 6}
a
∣
b
⟺
a
c
∣
b
c
{\displaystyle a\mid b\iff ac\mid bc}
c
{\displaystyle c}
k
a
=
b
⟺
k
a
c
=
b
c
{\displaystyle ka=b\iff kac=bc}
↑
a
∣
b
,
a
∣
c
{\displaystyle a\mid b,\,a\mid c}
⇒
∃
j
:
j
a
=
b
,
∃
k
:
k
a
=
c
{\displaystyle \Rightarrow \exists j\colon ja=b,\,\exists k\colon ka=c}
⇒
∃
j
,
k
:
(
j
+
k
)
a
=
b
+
c
{\displaystyle \Rightarrow \exists j,k\colon (j+k)a=b+c}
⇒
a
∣
(
b
+
c
)
.
{\displaystyle \Rightarrow a\mid (b+c).}
a
∣
b
,
a
∣
c
{\displaystyle a\mid b,\,a\mid c}
⇒
∃
j
:
j
a
=
b
,
∃
k
:
k
a
=
c
{\displaystyle \Rightarrow \exists j\colon ja=b,\,\exists k\colon ka=c}
⇒
∃
j
,
k
:
(
j
−
k
)
a
=
b
−
c
{\displaystyle \Rightarrow \exists j,k\colon (j-k)a=b-c}
⇒
a
∣
(
b
−
c
)
.
{\displaystyle \Rightarrow a\mid (b-c).}
