is subtraction associative in rational numbers? explain with an example.
Answers
Answer:
No, subtraction is NOT associative in rational numbers.
Step-by-step explanation: We are asked to state whether subtraction is associative in rational numbers or not. To explain with an example.
Let a, b and c be three rational numbers. Then, according to the associative property, we must have
(a-b)-c=a-(b-c).(a−b)−c=a−(b−c).
The subtraction is NOT associative in rational numbers.
For example, let us consider that
a=\dfrac{1}{2},~b=\dfrac{3}{2},~c=\dfrac{5}{2}.a=
2
1
, b=
2
3
, c=
2
5
.
Then,
\begin{gathered}L.H.S.=(a-b)-c=(\dfrac{1}{2}-\dfrac{3}{2})-\dfrac{5}{2}=-1-\dfrac{5}{2}=\dfrac{-2-5}{2}=-\dfrac{7}{2},\\\\\\R.H.S.=a-(b-c)=\dfrac{1}{2}-(\dfrac{3}{2}-\dfrac{5}{2})=\dfrac{1}{2}-(-1)=\dfrac{1}{2}+1=\dfrac{3}{2}.\end{gathered}
L.H.S.=(a−b)−c=(
2
1
−
2
3
)−
2
5
=−1−
2
5
=
2
−2−5
=−
2
7
,
R.H.S.=a−(b−c)=
2
1
−(
2
3
−
2
5
)=
2
1
−(−1)=
2
1
+1=
2
3
.
So, L.H.S. ≠ R.H.S.
Hence, subtraction is NOT associative in rational numbers.
Answer:
subtraction is not possible in associatve with rational numbers