Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 24
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36MODULE -
1
Number Systems
Algebra
+
⎛
⎞
1
15
24
39
=
=
⎜
⎟
⎝
⎠
2
20
40
×
Notes
3
3
10
30
=
=
Now
×
4
4
10
40
×
6
6
8
48
=
=
and
×
5
5
8
40
30
39
48
<
<
Obviously
40
40
40
39
3
6
and
i.e.
is a rational number between the rational numbers
.
40
4
5
3
39
6
=
=
=
0.75,
0.975
and
1.2
Note:
4
40
5
∴
<
<
. 0
75
. 0
975
1
2 .
3
39
6
<
<
or
4
40
5
∴ This can be done by either way:
(i) reducing each of the given rational number with a common base and then taking
their average
or (ii) by finding the decimal expansions of the two given rational numbers and then
taking their average.
The question now arises, “How many rationals can be found between two given rationals?
Consider the following examples.
1
3
and
Example 1.18:
Find 3 rational numbers between
.
2
4
×
1
1
8
8
=
=
Solution:
×
2
2
8
16
×
3
3
4
12
=
=
and
×
4
4
4
16
8
9
10
11
12
<
<
<
<
As
16
16
16
16
16
26
Mathematics Secondary Course
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