CBSE NCERT Solutions for Class 8 Mathematics Chapter 1
Class- VIII-CBSE-Mathematics
Rational Numbers
CBSE NCERT Solutions for Class 8 Mathematics Chapter 1
Back of Chapter Questions
Exercise 1.1
1. Using appropriate properties find.
(i)
-2 ? 3 + 5 - 3 ? 1
35 2 56
(ii)
2 ? (-3) - 1 ? 3 + 1 ? 2
5
7
6 2 14 5
Solution:
(i) -2 ? 3 + 5 - 3 ? 1 = -2 ? 3 - 3 ? 1 + 5 (by commutativity)
3 5256 3 5562
2 -3 -3 1 5 =3?( 5 )+( 5 )?6+2
=
(-3)
5
(2
3
+
1)
6
+
5 2
(by
distributivity)
-3 5 5 = 5 ?6+2
-1 5 = 2 +2
-1 + 5 =2
4 =2
=2
Hence,
-
2 3
?
3 5
+
5 2
-
3 5
?
1 6
=
2
(ii) 2 ? (-3) - 1 ? 3 + 1 ? 2 = 2 ? (-3) + 2 ? 2 - 1 ? 3 (by commutativity)
5
7
6 2 14 5 5
7
14 5 6 2
=
2 5
(-3
7
+
1)
14
-
1 6
?
3 2
(by
distributivity)
2 -6 + 1 1 3 = 5 ( 14 ) - 6 ? 2
2 -5 1 1 = 5 (14 ) - 2 ? 2
2 (-5) 1 = 5 ? 14 - 4
Practice more on Rational Number
Page - 1
Class- VIII-CBSE-Mathematics
Rational Numbers
-2 1 = 14 - 4
-11 = 28
Hence,
2 5
?
(-3)
7
-
1 6
?
3 2
+
1 14
?
2 5
=
-11 28
2. Write the additive inverse of each of the following
(i)
2 8
(ii) -5
9
(iii)
-6 -5
(iv) 2
-9
(v)
19 -6
Solution:
We know that for any number , + (-) = 0, So, - is called the additive inverse of .
(i) Additive inverse of 2 is -2
8 8
(ii)
Additive
inverse
of
-5 9
is
5 9
(iii)
-6 = 6
-5 5
Hence,
additive
inverse
of
-6 -5
is
-6 5
(iv)
Additive
inverse
of
2 -9
is
2 9
(v)
Additive
inverse
of
19 -6
is
19 6
3. Verify that ? (? ) = for
(i)
x = 11
15
(ii) = - 13
17
Solution:
(i) The additive inverse of 11 is - 11
15
15
Practice more on Rational Number
Page - 2
Class- VIII-CBSE-Mathematics
Rational Numbers
Since
11 15
+
(-
11)
15
=
0
11
11
15 = - (- 15)
Hence verified.
(ii)
The
additive
inverse
of
-
13 17
is
13 17
Since
-
13 17
+
(13)
17
=
0
13
13
17 = - (- 17)
Hence verified.
4. Find the multiplicative inverse of the following.
(i) -13
(ii) - 13
19
(iii)
1 5
(iv) -5 ? -3
87
(v)
-1 ? -2
5
(vi) -1
Solution:
As we know that a rational number rational number if ? = 1
is
the
multiplicative
inverse
of
another
So,
=
Or
we
can
say
that
multiplicative
inverse
of
is
(i)
Multiplicative
inverse
of
-13
is
-1 13
Since -13 ? -1 = 1
13
(ii)
Multiplicative
inverse
of
-13 19
=
-19 13
Since -13 ? -19 = 1
19 13
(ii)
Multiplicative
inverse
of
1 5
is
5
Practice more on Rational Number
Page - 3
Class- VIII-CBSE-Mathematics
Rational Numbers
Since
1 5
?
5
=
1
(iv)
Multiplicative
inverse
of
-5 8
?
-3 7
=
15 56
is
56 15
Since
15 56
? 56 =
15
1
(v)
Multiplicative
inverse
of
-1
?
-2 5
=
2 5
is
5 2
Since 2 ? 5 = 1
5 2
(vi) Multiplicative inverse of -1 is -1
Since -1 ? -1 = 1
5. Name the property under multiplication used in each of the following
(i)
-4 ? 1 = 1 ? -4 = -4
5
55
(ii)
-13 ? -2 = -2 ? -13
17 7 7 17
(iii) -19 ? 29 = 1
29 -19
Solution:
(i) Multiplicative identity
(ii) Commutative property
(iii) Multiplicative inverse property
6. Multiply 6 by the reciprocal of -7.
13
16
Solution:
The
reciprocal
of
-7 16
is
-16 7
According to the question,
-16 6 -96 7 ? 13 = 91
Hence,
Multiplication
of
6 13
by
the
reciprocal
of
-7 16
7. Tell what property allows you to compute 1 ? (6 ? 4) as (1 ? 6) ? 4.
3
3
3
3
Solution:
By using associative property of multiplication,
? ( ? ) = ( ? ) ?
Practice more on Rational Number
Page - 4
Class- VIII-CBSE-Mathematics
Rational Numbers
8.
Is
8 9
the
multiplicative
inverse
of
-1
1 8
?
Why
or
why
not?
Solution:
-1
1 8
is
eqaul
to
-9 8
So,
multiplicative
inverse
of
-9 8
is
-8 9
Since, -9 ? -8 = 1
8
9
Hence,
8 9
is
not
the
multiplicative
inverse
of
-1
1 8
9.
Is
0.3
the
multiplicative
inverse
of
3
1 3
?
Why
or
why
not?
Solution:
3 0.3 = 10
As
we
know,
multiplicative
inverse
of
is
So multiplicative inverse of 3 is 10
10 3
Which is equal to 3 1
3
10. Write.
(i) The rational number that does not have a reciprocal.
(ii) The rational numbers that are equal to their reciprocals.
(iii) The rational number that is equal to its negative.
Solution:
(i) 0
(ii) 1, -1
(iii) 0
11. Fill in the blanks.
(i) Zero has ________ reciprocal.
(ii) The numbers ________ and ________ are their own reciprocals
(iii) The reciprocal of ? 5 is ________.
(iv)
Reciprocal
of
1 x
,
where
x
0
is
________.
(v) The product of two rational numbers is always a _______.
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Page - 5
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