Comparison of Rational Numbers
Comparison of Rational Numbers
We know how to compare two integers or two fractions and tell which is smaller or which is greater among them. We know that every positive integer is greater than zero and every negative integer is less than zero. Also every positive integer is greater than every negative integer. Let us now see how we can compare two rational numbers.
Comparison of Rational Numbers:
Similar to the comparison of integers, we have the following facts about how to compare the rational numbers.
(i) Every positive rational number is greater than 0.
(ii) Every negative rational number is less than 0.
(iii) Every positive rational number is greater than every negative rational number.
(iv) Every rational number represented by a point on the number line is greater than every rational number represented by points on its left.
(v) Every rational number represented by a point on the number line is less than every rational number represented by points on its right.
How to Compare the Two Rational Numbers?
1. Comparison Using Number line: Two rational numbers can be compared by using a number line. For example to compare two negative rational numbers and
using number line. We know that the integer which was on the right side of the other integer, was the greater integer.For example, 5 is to the right of 2 on the number line and
. The integer
is on the right of
on the number line and
. Similarly we will mark the given rational numbers on the number line and then the number on the right side will be greater than the other number.
2. Comparison using the method of Fractions: Two positive rational numbers, like and
can be compared as studied earlier in the case of fractions. In order to compare any two rational numbers, we can use the following steps:
Illustration: Which of the given rational numbers is greater?
Solution: To find the greater rational number we will follow the steps:
First we write each of the given numbers with positive denominator.
Next step find the LCM
.L.C.M. of 4 and 6 = 12
Therefore,
Now we will compare the numerators, so we get -9 > -10
Hence
Arrange the following numbers in descending order: | |||
| Right Option : C | |||
| View Explanation | |||
Arrange the following numbers in descending order: | |||
| Right Option : B | |||
| View Explanation | |||
Which is the correct sequence of numbers in ascending order while arranging | |||
| Right Option : D | |||
| View Explanation | |||
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