write two rational numbers that lie between the two given numbers 6/21 , 12/36
Answers
Answer:
Answer
Making the same denominator of the rational numbers
5
4
and
3
2
.
5
4
=
5×3
4×3
=
15
12
3
2
=
3×5
2×5
=
15
10
The rational numbers between
15
12
and
15
10
is,
2
15
12
+
15
10
=
30
22
So,
15
10
<
30
22
<
15
12
The rational number between
15
10
and
30
22
is,
2
15
10
+
30
22
=
30×2
42
=
30
21
The rational number between
15
12
and
30
22
is,
2
15
12
+
30
22
=
30×2
46
=
30
23
Thus,
15
10
<
30
21
<
30
22
<
30
23
<
15
12
.
Therefore the three rational numbers are
30
21
,
30
22
,
30
23
.
ANSWER:
(i)
5
36
+
6
42
At first, we will calculate the LCM of 36 and 42. The prime factorisation is 36 and 42 is,
36 = 2 × 2 × 3 × 3
42 = 2 × 3 × 7
Now, LCM of 36 and 42 = 2 × 2 × 3 × 3 × 7 = 252
5
36
+
6
42
=
5×7
36×7
+
6×6
42×6
=
35
252
+
36
252
=
35+36
252
=
71
252
(ii) 1
2
3
+2
4
5
=
1×3+2
3
+
2×5+4
5
=
5
3
+
14
5
Now, LCM of 3 and 5 is 15.
5
3
+
14
5
=
5×5
3×5
+
14×3
5×3
=
25
15
+
42
15
=
67
15
=4
7
15
(iii)
11
17
+
13
19
Now, LCM of 17 and 19 is 323.
11
17
+
13
19
=
11×19
17×19
+
13×17
19×17
=
209
323
+
221
323
=
430
323
(iv) 2
3
11
+1
3
77
=
2×11+3
11
+
1×77+3
77
=
25
11
+
80
77
Now, LCM of 11 and 77 is 77.
25
11
+
80
77
=
25×7
11×7
+
80×1
77×1
=
175
77
+
80
77
=
255
77
=3
24
77