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
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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
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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
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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,
? ( ? ) = ( ? ) ?
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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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Class- VIII-CBSE-Mathematics
Rational Numbers
(vi) The reciprocal of a positive rational number is ________.
Solution:
(i) Zero has no reciprocal
(ii) The numbers 1 and -1 are their own reciprocals
(iii)
The
reciprocal
of
-5
is
1 -5
(iv)
Reciprocal
of
1
,
where
0
is
(v) The product of two rational number is always a rational number.
(vi) The reciprocal of a positive rational number is positive.
Exercise 1.2
1. Represent these numbers on the number line
(i)
7 4
(ii)
-5 6
Solution:
(i)
7 = 13
4
4
(ii)
Let
M
=
-5 6
2.
Represent
-2 11
,
-5 11
,
-9 11
on
the
number
line.
Solution:
Let -2 = C,
11
-5 11
=
B
and
-9 11 = A
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Class- VIII-CBSE-Mathematics
Rational Numbers
3. Write five rational numbers which are smaller than 2.
Solution:
The rational numbers smaller than 2 are
(i)
1 3
(ii)
2 3
(iii)
5 3
(iv)
4 3
(v)
1 2
4.
Find
ten
rational
numbers
between
-2 5
and
12.
Solution:
Rational numbers are -2 and 1
5
2
Here, L.C.M of 5 and 2 is 10.
So,
-2 5
=
-2 5
?
2 2
=
-4 10
Also,
1 2
=
1 2
?
5 5
=
5 10
Again, -4 = -4 ? 2 = -8
10 10 2 20
and,
5 10
=
5 10
?
2 2
=
10 20
Hence, -2 = -8 and 1 = 10
5 20
2 20
Ten rational numbers between -2 and 1 are -7 , -6 , -5 , -4 , -3 , -2 , -1 , 0, 1 , 2
5
2 20 20 20 20 20 20 20 20 20
5. Find five rational numbers between
(i)
2 3
and
4 5
(ii)
-3 2
and
53.
(iii) 1 and 1
4
2
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Class- VIII-CBSE-Mathematics
Rational Numbers
Solution:
(i) 2 and 4
3
5
L.C.M. of 3 and 5 is 15
So,
2 3
=
2 3
?
5 5
=
10 15
and 4 = 4 ? 3 = 12
5 5 3 15
Again,
10 15
=
10 15
?
4 4
=
40 60
and
12 15
=
12 15
?
4 4
=
48 60
Hence,
2 3
=
40 60
and
4 5
=
48 60
Five rational numbers bewteen 2 and 4 are 41 , 42 , 43 , 44 , 45
3
5 60 60 60 60 60
(ii)
-3 2
and
5 3
LCM of 2 and 3 is 6
So, -3 = -3 ? 3 = -9
2 23 6
and
5 3
=
5 3
?
2 2
=
10 6
Hence,
-3 2
=
-
9 6
and
5 3
=
10 6
Five
rational
numbers
bewteen
-3 2
and
5 3
are
-2 6
,
-1 6
,
0,
1 6
,
2 6
(iii)
1 4
and
1 2
LCM of 4 and 2 is 4
So,
1 4
=
1 4
?
1 1
=
1 4
&
1 2
=
1 2
?
2 2
=
2 4
Again,
1 4
=
1 4
?
8 8
=
8 32
and
2 4
=
2 4
?
8 8
=
16 32
Hence,
1 4
=
8 32
and
1 2
=
16 32
Five
rational
numbers
bewteen
1 4
and
1 2
are
9 32
,
10 32
,
11 32
,
12 32
,
13.
32
6. Write five rational numbers greater than ? 2
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