verify computing of additional or rational of numbers for -11/5 and 4/7?
Answers
Explanation:
Answer: Verified.
Step-by-step explanation: We are given to verify all the properties of rational numbers by taking any two rational numbers as example.
We know that a rational number is of the form \dfrac{p}{q},~q\neq 0
q
p
, q
=0 and p, q are integers.
So, let the two rationals be \dfrac{1}{2},~~\dfrac{3}{2}.
2
1
,
2
3
.
The properties are as follows:
(i) Closure property : Addition and multiplication of two rational numbers is again a rational number.
We have
\begin{gathered}\dfrac{1}{2}+\dfrac{3}{2}=2,~\textup{a rational},\\\\\dfrac{1}{2}\time\dfrac{3}{2}=\dfrac{3}{4},~\textup{a rational}.\end{gathered}
2
1
+
2
3
=2, a rational,
2
1
\time
2
3
=
4
3
, a rational.
(ii) Commutative property : Addition and multiplication of rational numbers is commutative.
We have
\begin{gathered}\dfrac{1}{2}+\dfrac{3}{2}=2=\dfrac{3}{2}+\dfrac{1}{2},\\\\\dfrac{1}{2}\times\dfrac{3}{2}=\dfrac{3}{4}=\dfrac{3}{2}\times\dfrac{1}{2}.\end{gathered}
2
1
+
2
3
=2=
2
3
+
2
1
,
2
1
×
2
3
=
4
3
=
2
3
×
2
1
.
(iii) Associative property.
(iv) Distributive property.
One can also verify the last two properties because by taking a third rational number.
Hence completed