Insert a rational number between the following pairs of numbers.
a.4and5
b.3/5and4/5
c.5/6and9/10
d.0.5and0.51
Answers
Step-by-step explanation:
Number System
Exercise 1.1 Part 2
Question 3: Find five rational numbers between 3/5 and 4/5.
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
20
(3) Similarly, rational number between 4/5 and 7/10 will be the another rational number between 3/5 and 4/5. This another rational number between 3/5 and 4/5 can be found by calculating average between 4/5 and 7/10, calculation is as follows:
4
5
+
7
10
2
=
8
+
7
10
2
=
15
10
2
=
15
10
×
2
=
3
4
(4) Similarly, rational number between 3/5 and 13/20 will be the another rational number between 3/5 and 4/5, which can be found by calculating average between 3/5 and 13/20, calculation is as follows:
3
5
+
13
20
2
=
12
+
13
20
2
=
25
20
2
=
25
20
×
2
=
5
8
(5) Similarly, rational number between 3/5 and 5/8 will be the another rational number between 3/5 and 4/5, which can be found by calculating average between 3/5 and 5/8, calculation is as follows:
3
5
+
5
8
2
=
24
+
25
40
2
=
49
40
×
2
=
49
80
Thus, five rational numbers between 3/5 and 4/5 are 7/10, 13/20, 3/4, 5/8 and 49/80
You can find more rational numbers between the given two numbers 3/5 and 4/5 using above method.
Answer:
a) 4 1/2
b) 7/10
c) 52/60
d) 0.501