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Answer:
First method to find rational number between two numbers:
Since we have to find 5 rational numbers between 3/5 and 4/5, so we will mutiply the numerator and denominator of the given numbers by 5+1, i.e. equal to 6.
We get,
3
5
=
3
×
6
5
×
6
=
18
30
and
4
5
=
4
×
6
5
×
6
=
24
30
Now, we have to find 5 rational numbers between 18/30 and 24/30, which will come as
(
19
30
)
,
(
20
30
)
,
(
21
30
)
,
(
22
30
)
,
(
23
30
)
=
(
19
3
)
,
(
2
×
10
3
×
10
)
,
(
7
×
3
10
×
3
)
,
(
11
×
2
15
×
2
)
,
(
23
30
)
=
(
19
30
)
,
(
2
3
)
,
(
7
10
)
,
(
11
15
)
and
(
23
30
)
Thus, five rational numbers between 3/5 and 4/5 are
=
(
19
30
)
,
(
2
3
)
,
(
7
10
)
,
(
11
15
)
and
(
23
30
)
You can find as many rational numbers between given numbers using method given above.
Second method to find rational number between two numbers:
(1) One rational number between given numbers 3/5 and 4/5 will be the average between them.
Thus, average between 3/5 and 4/5 will be equal to
3
5
+
4
5
2
=
3
+
4
5
2
=
7
5
2
=
7
5
×
2
=
7
10
(2) Rational number between 3/5 and 7/10 will be the next rational number between 3/5 and 4/5, since 7/10 is a rational number between 3/5 and 4/5. Thus, next rational number between 3/5 and 7/10 can be found by calculating average between them. Calculation is as follows:
3
5
+
7
10
2
=
6
+
7
10
2
=
13
10
2
=
13
10
×
2
=
13
2