Class – 7 CH-9 RATIONAL NUMBERS
MATHS NCERT SOLUTIONS
Exercise 9.1
Question 1:
(i) 1 and 0 (ii) 2 and 1
(iii) 4 2
and (iv) 1 2
and
List five rational numbers between:
5 3 2 3
SOLUTION 1:
(i) 1 and 0
Let us write 1 and 0 as rational numbers with denominator 6.
1 6 and 0 = 0
6 6
6 5 4 3 2 1
0
6 6 6 6 6 6
1 5 2 1 1 1 0
6 3 2 3 6
Therefore, five rational numbers between 1 and 0 would be
5 2 1 1 1
, , , ,
6 3 2 3 6
(ii) 2 and 1
Let us write 2 and 1 as rational numbers with denominator 6.
2 12 and 1 6
6 6
12 11 10 9 8 7 6
6 6 6 6 6 6 6
2 11 5 3 4 7 1
6 3 2 3 6
Therefore, five rational numbers between 2 and 1 would be
11 5 3 4 7
, , , ,
6 3 2 3 6
(iii)
(iv)
4 2
and
5 3
4 2
Let us write and as rational numbers with the same denominators.
5 3
4 36 2 30 and
5 45 3 45
36 35 34 33 32 31 30
45 45 45 45 45 45 45
4 7 34 11 32 31 2
5 9 45 15 45 45 3
4 2
Therefore, five rational numbers between and would be
5 3
7 34 11 32 31 2
, , , , ,
9 45 15 45 45 3
1 2
and
2 3
1 2
Let us write and as rational numbers with the same denominators.
2 3
1 3 2 4
and
2 6 3 6
3 2 1 1 2 3 4 0
6 6 6 6 6 6 6
1 1 1 1 1 1 2 0
2 3 6 6 3 2 3
1 2
Therefore, five rational numbers between and would be
2 3
1 1 1 1
, ,0, , .
3 6 6 3
Question 2:
Write four more rational numbers in each of the following patterns:
3 6 9 12
(i) , , , ,.........
1 2 3
(ii) , , ,..........
1 2 3 4
(iii) , , , ,.........
6 12 18 24
2 2 4 6
(iv) , , , ,..........
3 3 6 9
SOLUTION 2:
3 6 9 12
(i) , , , ,.........
3 1 3 2 3 3 3 4
, , , ,.........
Therefore, the next four rational numbers of this pattern would be
3 5, 3 6, 3 7, 3 8 = 15, 18, 21, 24
5 5 5 6 5 7 5 8 25 30 35 40
1 2 3
(ii) , , ,..........
1 1 1 2 1 3
, , ,..........
Therefore, the next four rational numbers of this pattern would be
1 4, 1 5, 1 6, 1 7 = 4, 5, 6, 7
4 4 4 5 4 6 4 7 16 20 24 28
1 2 3 4
(iii) , , , ,.........
6 12 18 24
1 1 1 2 1 3 1 4
, , , ,.........
6 1 6 2 6 3 6 4
Therefore, the next four rational numbers of this pattern would be
1 5 1 6 1 7 1 8 5 6 7 8
, , , = , , ,
6 5 6 6 6 7 6 8 30 36 42 48
2 2 4 6
(iv) , , , ,..........
3 3 6 9
2 1 2 1 2 2 2 3
, , , ,..........
3 1 3 1 3 2 3 3
Therefore, the next four rational numbers of this pattern would be
2 4 2 5 2 6 2 7 8 10 12 14
, , , = , , ,
3 4 3 5 3 6 3 7 12 15 18 21
Question 3:
Give four rational numbers equivalent to:
2 5 4
(i) (ii) (iii)
7 3 9
SOLUTION 3:
2
(i)
7
2 2 4 2 3 6 2 4 8 2 5 10
, , ,
7 2 14 7 3 21 7 4 28 7 5 35
4 6 8 10
Therefore, four equivalent rational numbers are , , , .
14 21 28 35
5
(ii)
3
5 2 10 5 3 15 5 4 20 5 5 25
, , ,
3 2 6 3 3 9 3 4 12 3 5 15
10 15 20 25
Therefore, four equivalent rational numbers are , , , .
6 9 12 15
(iii)
8 12 16 20
Therefore, four equivalent rational numbers are , , , .
18 27 36 45
Question 4:
Draw the number line and represent the following rational numbers on it:
3 5 7 7
(i) (ii) (iii) (iv)
4 8 4 8
SOLUTION 4:
(i)
(iv)
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.
Each part which is between the two numbers is divided into 3 parts.
Therefore, A = , P = , Q = and B =
Similarly T = 3, R = 4, S = 5 and U = 6
3 3 3 3
Thus, the rational numbers represented P, Q, R and S are 7 8, , 4 and 5
3 3 3 3 respectively.
Question 6:
Which of the following pairs represent the same rational numbers:
7 3
(i) and
21 9
16 20
(ii) and
20 25
2 2
(iii) and
3 3
3 12
(iv) and
5 20
8 24
(v) and
5 15
1 1
(vi) and
3
(vii) and
9 9
SOLUTION 6
(i)
(ii)
(iii)
(iv)
:
7 3
and
21 9
7 1 3 1
= and =
21 3 9 3
1 1
3 3
7 3
21 9
16 20
and
20 25
16 4 20 4 4
= and =
20 5 25 5 5
4 4
=
5 5
16 20
= 20 25
2 2
and
3 3
2 2 2 2
= and =
3 3 3 3
=
2 2
=
3 3
3 12
and
5 20
3 3 12 3 = and =
5 5 20 5
3 3
=
5 5
3 12
=
5 20
[Converting into lowest term]
[Converting into lowest term]
[Converting into lowest term]
[Converting into lowest term]
8 24
(v) and
5 15
8 8 24 8
= and = [Converting into lowest term]
5 5 15 5
8 8
= 5 5
8 24
=
5 15
1 1
(vi) and
3 9
1 1 1 1
= and = [Converting into lowest term]
3 3 9 9
1 1
3 9
1 1
3 9
5 5
(vii) and
9 9
5 5 5 5
= and = [Converting into lowest term]
9 9 9 9
5 5
9 9
5 5
9 9
Question 7:
Rewrite the following rational numbers in the simplest form:
8 25 44 8
(i) (ii) (iii) (iv)
6 45 72 10
SOLUTION 7:
8 8 2 4
(i) = = [H.C.F. of 8 and 6 is 2]
6 62 3
(ii) = [H.C.F. of 25 and 45 is 5]
44 44 4 11
72 724 18
(iv) 8 8 2 4
= = [H.C.F. of 8 and 10 is 2]
(iii) = = [H.C.F. of 44 and 72 is 4]
10 102 5
Question 8:
Fill in the boxes with the correct symbol out of <, > and =:
52 45 714 87
(i) (ii) (iii) (iv)
73 57 816 54
11 557
(v) (vi) (vii) 0
34 11116
SOLUTION 8:
5 2
(i) < Since, the positive number if greater than negative number.
7 3
5 7 7 5 35 35 5 7
7 2 14 1 14 14 7 14
(ii) 4 75 5 28 < 25 4 < 5
82 16 1 16 16 8 16
8 4 7 5 32 35 8 7
(iii) = =
(iv) > >
5 44 5 20 20 5 4
11 1 1
(v) <
34 3 4
55 5 5
11 11
7 11 11
(vi) =
(vii) 0 > Since, 0 is greater than every negative number. 6
Question 9:
Which is greater in each of the following:
2 5 5 4 3 2 1 1
(i) , (ii) , (iii) , (iv) ,
3 2 6 3 4 3 4 4
2 4
(v) 3 , 3
7 5
SOLUTION 9:
(i) and
4 15 2 5
Since < Therefore
6 6 3 2
5 1 5 4 2 8
(ii) and 6 1 6 3 2 6
Since 5 > 8 Therefore 5 > 4
6 6 6 3
3 3 9 2 4 8
(iii) and
4 3 12 3 4 12
Since 9 < 8 Therefore 3 2
12 12 4 3
1 1
(iv) < Since positive number is always greater than negative
4 4 number.
(v) 32 23 23 5 115 and 34 19 19 7 133
7 7 7 5 35 5 5 5 7 35
Since 115 > 133 Therefore 3 2 > 3 4
35 35 7 5
Question 10:
Write the following rational numbers in ascending order:
(i) 3, 2, 1
1 2 4
(ii)
(iii) 3, 3, 3
7 2 4
SOLUTION 10:
3 2 1
(i) , ,
5 5 5
3 2 1
5 5 5
1 2 4 3 2 12
(ii) , , , , [Converting into same denominator]
3 9 3 9 9 9
12 2 3 4 2 1 Now
9 9 9 3 9 3
3 3 3
(iii) , ,
7 2 4
3 3 3
2 4 7
Exercise 9.2
Question 1:
Find the sum:
5 11 5 3
(i) 4 4 (ii) 3 5
9 22 3 5
(iii) (iv)
10 15 11 9
8 2 2
(v) (vi) 0
19 57 3
1 3
(vii) 2 4
3 5
SOLUTION 1:
5 11 5 11 6 3
(i) 4 = 4 = 4 2 4
5 3 25 9
(ii) = [L.C.M. of 3 and 5 is 15]
3 5 15 15
259 34 4
= 2
15 15 15
9 22 9 3 22 2 27 44
(iii) = = [L.C.M. of 10 and 15 is 30]
10 15 10 3 15 2 30 30
27 44 17
=
30 30
3 5 3 9 5 11 27 55
(iv) = = [L.C.M. of 11 and 9 is 99]
11 9 11 9 9 11 99 99
2755 82
=
99 99
8 2 8 3 2 1 24 2
(v) = = [L.C.M. of 19 and 57 is 57]
19 57 19 3 57 1 57 57
24 2 26
= =
57 57
2 2
(vi) 0
3 3
1
(vii) 21 43 = 7 23 = 7 5 23 3 = 35 69 [L.C.M. of 3 and 5 is 15]
3 5 3 5 3 5 5 3 15 15
34 4
= = 2
15 15
Question 2:
(i) 7 17
24 36 (ii) 5 6
21
63
(iii) 6 7
15
13 (iv) 3 7
8 11
Find:
(v) 2 6
SOLUTION 2:
7 1721 34
(i) = = [L.C.M. of 24 and 36 is 72]
24 3672 72
21 34 13
= =
72 72
5 6 5 1 6 3 5 18
(ii) 63 21 = 63 1 21 3 = 63 63 [L.C.M. of 63 and 21 is 63]
5 18 5 18 23
= =
63 63 63
6 7 6 15 7 13 90 91
(iii) 13 15 = 13 15 15 13 = 195 195 [L.C.M. of 13 and 15 is 195]
90 91 90 91 1
195 195 195
3 7 3 11 7 8 33 56 (iv) = =
8 11 8 11 11 8 88 88
33 56 89 1
= = 1
88 88 88 [L.C.M. of 8 and 11 is 88]
1
(v) 2 6 = 19 6 = 19 1 6 9
9 9 1 9 1 1 9
19 54 19 54 73 1 [L.C.M. of 9 and 1 is 9]
= =
= = = 8
9 9 9 9 9
2
Question 3:
Find the product:
9 7
(i) 4
2
6 9
(iii)
5 11
3 2
(v)
11 5
SOLUTION 3:
9 7 9 7 63 7
(i) 2 4 = 2 4 = 8 7 8
3 3 9
(ii) 9 272 7
10 10 10 10
6 9 6 9 54
(iii)
5 11 5 11 55
3 2 3 2 6 (iv) 5 7 5 35
7
3 2 3 2 6 (v)
11 5 11 5 55
3 5 3 5
(vi) 5 3 1
5 3
Question 4:
Find the value of:
(i) 4
4
(iii) 3
5
2 1
(v)
13 7
3 4
(vii)
13 65
(ii)
(iv)
(vi)
(ii)
(iv)
(vi) 9
3 2
5
7
3 5
5 3
3
2
5
1 3
8 4
7 2
13
12
SOLUTION 4:
(i) 4 = 4 2 3 6
3 3 1 3 1
(ii) 2 = 3
5 5 2 5 2 10
4 4 1 4 1 4 (iii) 3 = 5 5 3 5 3 15
1 3 1 4 1 1 1 (iv) = =
8 4 8 3 2 3 6
2 1 2 7 2 7 14 1
(v) = 1
13 7 13 1 13 1 13 13
7 2 7 13 7 13 91 19
(vi) 13 = 12 2 = 12 2 24 324
12
3 4 3 65 3 5 15 3
(vii) 65 = 134 1 4 4 34 13
No comments:
Post a Comment