be subtracted from
to get
3
6
. (1) Which rational number is its own additive inverse?
(11) Is the difference of two rational numbers a rational number?
(ii) Is addition commutative on rational numbers?
(iv) Is addition associative on rational numbers?
(v) Is subtraction commutative on rational numbers?
(vi) is subtraction associative on rational numbers?
(vii) What is the negative of a negative rational number?
Answers
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Answer:
i. Let us consider a number
b
a
The additive inverse of
b
a
is −
b
a
such that,
b
a
+
b
−a
=0
∴0 is the number which is additive inverse of its own.
ii. Let us consider two rational numbers i.e.
b
a
and
d
c
where, b
=0
Now let's subtract
b
a
−
d
c
By taking LCM of b and d i.e. bd
bd
ad−bc
Where, bd
=0
We can say
bd
ad−bc
is a rational number
Hence, the difference of two rational numbers is a rational number.
iii. Let us consider two rational numbers i.e.
b
a
and
d
c
where, b
=0 and d
=0
By using commutative law
b
a
=
d
c
=
d
c
+
b
a
∴ Yes, Addition is commutative on rational numbers
iv. Let us consider three rational numbers i.e.
b
a
,
d
c
and
f
e
where, b
=0,d
=0 and f
=0
By using associative law
b
a
+(
d
c
+
f
e
)=(
b
a
+
d
c
)+
f
e
∴ Yes, Addition is associative on rational numbers
v. Let us consider two rational numbers i.e.
b
a
and
d
c
where, b
=0 and d
=0
By using commutative law
b
a
+
d
c
=
d
c
+
b
a
∴ No, Addition is not commutative on rational numbers
vi. Let us consider three rational numbers i.e.
b
a
,
d
c
and
f
e
where, b
=0,d
=0 and f
=0
By using associative law
b
a
+(
d
c
+
f
e
)
=(
b
a
+
d
c
)+
f
e
∴ No, Addition is not associative on rational numbers
vii. The negative of a negative rational number is the number itself without the negative sign.
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Answer:
1) 0
2) Yes
3) Yes
4) Yes
5) No
6) No
7) itself without the negative sign
