Chapter 9: Rational Numbers
Exercise: 9.1 (10)
Question: 1
List five rational numbers between:
(i)
(ii)
(iii)
(iv)
Solution
Rational number is any
number that can be expressed in the form of p/q, where p and q are
integers and q ≠ 0.
(i)
We need to find five rational number between
So, we can write as rational numbers with denominator .
Therefore, five rational numbers
between would be
(ii)
We need to find five rational number between
Let us write as rational numbers with denominator .
Therefore, five rational numbers
between would be
(iii)
Let us write as rational numbers with the same denominators.
Therefore, five rational numbers
between would be
(iv)
Let us write as rational numbers with the same denominators.
Therefore, five rational numbers
between would be
Question: 2
Write four more rational numbers in each of the following
patterns:
(i)
(ii)
(iii)
(iv)
Solution
(i)
We observe that numerator is
multiple of 3 and denominator is multiple of 5.
Therefore, the next four rational
numbers of this pattern would be
(ii)
Therefore, the next four rational
numbers of this pattern would be
(iii)
Therefore, the next four rational
numbers of this pattern would be
(iv)
Therefore, the next four rational
numbers of this pattern would be
Question: 3
Give four rational numbers equivalent to:
(i)
(ii)
(iii)
Solution
(i)
Next four
Therefore, four equivalent
rational numbers are
(ii)
Therefore, four equivalent
rational numbers are
(iii)
Therefore, four equivalent
rational numbers are
Question: 4
Draw the number line and represent the following rational
numbers on it:
(i)
(ii)
(iii)
(iv)
Solution
(i)
Given fraction
represent 3 parts out of 4 equal parts. Hence, the space between the integers 0
and 1 on the number line must be divided into 4 parts.
(ii)
Given fraction
represent 5 parts out of 8 equal parts. Negative sign represents that it is on
the negative side of the number line. Hence, the space between the integers -1
and 0 must be divided into 8 equal parts on the number line.
(iii)
We can write
given fraction as
This fraction
represents 1 full part and 3 part out of 4 equal parts. Therefore, each space
between the integers 0 and -1 and also between -2 and -1 must be divided into 4
equal parts on the number line.
(iv)
Given fraction represents 7 parts out of 8
equal parts. Therefore, space between the
integers 0 and 1 and also between 1 and 2 must be divided into 8 equal
parts on the number line.
Question: 5
The points P, Q, R, S, T, U, A and B on the number line are
such that, TR RS SU and AP PQ QB. Name the rational numbers represented by
P, Q, R and S.
Solution
In the given number line, each part which is between the two
numbers is divided into parts.
Distance between U and T = 1 Unit
It is divided into 3 equal parts.
Similarly,
AB = 1 unit, and it is divided into 3 equal parts.
Therefore,
Thus, the rational numbers represented P, Q, R and S are respectively.
Question: 6
Which of the following pairs represent the same rational
number?
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Solution
(i)
[Converting
into lowest term]
As , therefore and does not represent same rational number.
(ii)
[Converting into lowest term]
therefore and represent same rational numbers.
(iii)
[Converting
into lowest term]
therefore ,
and represent same rational number.
(iv)
[Converting
into lowest term]
(v)
[Converting
into lowest term]
(vi)
[Converting
into lowest term]
(vii)
[Converting
into lowest term]
Question: 7
Rewrite the following rational numbers in the simplest form:
(i)
(ii)
(iii)
(iv)
Solution
(i)
[H.C.F.
of and is ]
(ii)
[H.C.F. of and is ]
(iii)
[H.C.F.
of and is ]
(iv)
[H.C.F. of and is ]
Question: 8
Fill in the boxes with the correct symbol out of and .
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Solution
(i)
Since, the
positive number is always greater than the negative number.
Hence,
(ii)
Making
denominator same for both the rational number.
As, -25 > than -28
(iii)
Making
denominator same for both the rational number.
(iv)
Making
denominator same for both the rational number.
(v)
Making
denominator same for both the rational numbers.
(vi)
(vii)
Since, 0 is
greater than every negative number.
Question: 9
Which is greater in each of the following:
(i)
(ii)
(iii)
(iv)
(v)
Solution
(i)
Making
denominator same for the rational numbers.
Since
Therefore
(ii)
Making
denominator same for both the rational numbers.
Since
Therefore
(iii)
Making
denominator same for both the rational numbers.
Since
Therefore
(iv)
Since positive number is always greater than
negative number.
(v)
Since
Therefore
Question: 10
Write the following rational numbers in ascending order:
(i)
(ii)
(iii)
Solution
(i)
(ii)
[Converting these into like fractions]
(iii)
[Converting these
into like fractions]
Exercise: 9.2 (4)
Question: 1
Find the sum:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Solution
(i)
(ii)
[L.C.M. of ]
(iii)
[L.C.M.
of ]
(iv)
[L.C.M. of ]
(v)
[L.C.M. of ]
(vi)
(vii)
[L.C.M. of ]
Question: 2
Find
(i)
(ii)
(iii)
(iv)
(v)
Solution
(i)
[L.C.M. of ]
(ii)
[L.C.M. of ]
(iii)
[L.C.M. of ]
(iv)
[L.C.M. of ]
(v)
[L.C.M. of ]
Question: 3
Find the product:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Solution
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Question: 4
Find the value of:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)
Solution
(i)
(ii)
(iii)
(iv)
(v)
(vi)
(vii)