NCERT Solutions for Class 7 Maths Chapter 9 Rational Numbers InText Questions

Class 7 Maths NCERT Solutions Chapter 9 Rational Numbers InText Questions

Try These (Page 174)

Question 1.
Is the number ‘rational? Think about it.
Solution:
Yes, it is a rational number, because we know that a number that can be expressed in the form , where p,q are integers and q ≠ 0 is called a rational number.

Question 2.
List ten rational numbers.
Solution:
Ten rational number may be taken as
, , , , , , , , , and

Try These (Page 174)

Question 1.
Mention five rational numbers each of whose
(a) Numerator is a negative integer and denominator is a positive integer.
(b) Numerator is a positive integer and denominator is a negative integer.
(c) Numerator and denominator both are negative integers.
(d) Numerator and denominator both are positive integers.
Solution:
(a) Five rational numbers having numerator as negative integer and denominator as positive integer may
be taken as , , , , and
(b) Five rational numbers having numerator as positive integer and denominator as negative integer may be taken as
, , , ,and
(c) Five rational numbers having numerator and denominator both negative integers may be taken as
, , , , and
(d) Five rational numbers having numerator and denominator both positive integers may be taken as
, , , , and

Question 2.
Are integers also rational numbers?
Solution:
We know that, 1 = , 2 = , 3 = , etc.
Also, – 1 = , – 2 = , – 3 = etc. The integer 0 can also be written as
0 = or , etc.
i.e., any integer p can be written as p = , which is a rational number. Thus, every integer is a rational number.

Try These (Page 175)

(i)

Solution:
In order to fill the required box, we have to express 5 as a rational number with a denominator 16. For this, we first find an integer which when multiplied with 4 gives us 16.
Clearly, such an integer is 16 ÷ 4 = 4
Multiplying the numerator and denominator of by 4, we have
= =
Thus,

Again, for , we should multiply the numerator and denominator of by 25 ÷ 5, i.e., 5, we have
= =
Thus,

Also, for , we should multiply the numerator and denominator of by (-15) ÷ 5 = – 3, we have

Thus,

From (1), (2), and (3), we have

(ii)

Solution:
In order to fill the required box, we have to express -3 as a rational number with a denominator 14. For this, we first find an integer which when multiplied with 7 gives 14.
clearly, such as integer is 14 ÷ 7 = 2
Multiplying the numerator and denominator of by 2, we have
= =
Thus,

Similarly, we have

and

From (1),(2), and (3), we have

Try These (Page 175)

Question 1.
Is 5 a positive rational number?
Solution:
We know that 5 = , where 5 and 1 are both positive.
So, 5 is a positive rational number.

Question 2.
List five more positive rational numbers.
Solution:
Five more positive rational numbers may be taken as
, , , , and

Try These (Page 176)

Question 1.
Is – 8 a negative rational number?
Solution:
We know that – 8 = , where 8 is negative and 1 is positive .
∴ – 8 is a negative rational number.

Question 2.
List five more negative rational numbers.
Solution:
Five more negative rational numbers may be taken as , , , ,

Try These (Page 176)

Question 1.
Which of these are negative rational numbers?
(i)
Solution:
In , numerator and denominator are of opposite signs. Therefore, is a negative rational number.

(ii)
Solution:
In , numerator and denominator are of same signs. Therefore , is possitive rational number.

(iii)
Solution:
In , numerator and denominator are of opposite signs. Therefore, is a negative rational number.

(iv) 0
Solution:
The number 0 is neither a possitive nor a negative rational number.

(v)
Solution:
In , numerator and denominator are of same signs. Therefore , is possitive rational number.

(vi)
Solution:
In , numerator and denominator are of same signs. Therefore , is possitive rational number.

Try These (Page 178)

Find the standard form of
(i)
Solution:
The denominator of the rational number is positive. In order to express it in the standard form, we divide the numenator and denominator by the H.C.F of 18 and 45. is 9
Dividing the numenator and denominator of by 9, we have = =
Thus , the standard form of is

(ii)
Solution:
The denominator of the rational number is positive . In order to express it in the standard form, we divide the numenator and H.C.F. of 12 and 18 is 6.
Dividing the numenator and denominator of by 6, we have = =
Thus, the standard form of is

Try These (Page 181)

Can you list five rational numbers between and ?
Solution:
Let us convert the given rational numbers with same denominator 21. (∵ L.C.M. of 3 and 7 = 21)
= = and = =
We have, < < < < < <
Thus, , , , and are five rational numbers between and

Try These (Page 181)

Question 1.
Find five rational numbers between and
Solution:
We have, = =
and, = =
We know that,

Hence, five rational numbers between and may be taken as , , , and

Try These (Page 185)

Question 1.
+ +
Solution:
We have, + = = = – 1
and, + = =

Try These (Page 185)

Question 1.
+
Solution:
To find +
clearly, denominators of the given numbers are positive. the L.C.M. of denominators 7 and 3 is 21.
Now, we express and into forms in which both of them have the same denominator 21.
We have, = =
and, = =
∴ + = + = =

Question 2.
+
Solution:
To find +
clearly denominators of the given numbers are positive. The L.C.M. of denominators 6 and 11 is 66.
We have , = =
and, = =
∴ + = + = = =

Try These (Page 186)

Question 1.
What will be additive inverse of ? ? ?
Solution:
The additive inverse of is – =
The additive inverse of is – =
The additive inverse of is – =

Try These (Page 187)

Question 1.
Try to find – , – in both ways. Did you get the same answer?
Solution:
To find –

Thus, in both ways, the answer is the same.

To find –

Thus, in both ways, the answer is the same.

Try These (Page 187)

Question 1.
(i) –
Solution:
– = + = =

(ii) –
Solution:
– = + additive inverse of = + = = =

Try These (Page 187)

Question 1.
Find × 3 , × 4 using both ways. What do you observe?
Solution:
I method:
On the number line, × 3 means three jumps of to the left

We reach at so, × 3 =

II method:
× 3 = =
We observe that in both ways, the product is the same.
To find × 4

I method:

On the number line, × 4 means four jumps of to the left. We reach at . so , × 4 =

II method:
× 4 = =
We observe that in both ways, the product is the same.

Try These (Page 188)

Question 1.
(i) × 7 ?
Solution:
× 7 = =

(ii) × (-2) ?
Solution:
× (-2) = =

Try These (Page 188)

Question 1.
(i) ×
Solution:
we have, × = =

(ii) ×
Solution:
We have, × = =

Try These (Page 189)

Question 1.
What will be the reciprocal of ? and ?
Solution:
The reciprocal of is i.e.,
and, the reciprocal of is i.e.,

Try These (Page 189)

Question 1.
Try dividing by both ways and see if you get the same answer.
Solution:
I method:
÷ = × reciprocal of latex]\frac{-5}{7}[/latex]
= × = = =

II method:
Here, ÷ = x =
∴ ÷ = –

Try These (Page 190)

Question 1.
(i) ×
Solution:
we have, x = =

(ii) ×
Solution:
× = =