Natural Numbers, Integers, Rational Numbers Worksheet With Answers - Mathematics Secondary Course Page 11
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36MODULE -
1
Number Systems
Algebra
4
The point P represents
on the number line.
3
Notes
1.6 COMPARISON OF RATIONAL NUMBERS
In order to compare two rational numbers, we follow any of the following methods:
(i) If two rational numbers, to be compared, have the same denominator, compare their
numerators. The number having the greater numerator is the greater rational number.
5
9
and
Thus for the two rational numbers
, with the same positive denominator
17
17
9
5
>
>
17,
as
9
5
17
17
9
5
∴
>
17
17
(ii) If two rational numbers are having different denominators, make their denominators
equal by taking their equivalent form and then compare the numerators of the resulting
rational numbers. The number having a greater numerator is greater rational number.
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6
and
For example, to compare two rational numbers
, we first make their
7
11
denominators same in the following manner:
×
×
3
11
33
9
7
42
=
=
and
×
×
7
11
77
11
7
77
42
33
6
3
>
>
or
As 42 > 33,
77
77
11
7
(iii) By plotting two given rational numbers on the number line we see that the rational
number to the right of the other rational number is greater.
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and
For example, take
, we plot these numbers on the number line as below:
3
4
2
(
)
B
A
3
–2
–1
0
1
2
3
4
3
(
)
4
Mathematics Secondary Course
13
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