We are all familiar with the concept of comparing two integers or two fractions and determining which is smaller or greater. Let us go a step ahead and compare Two Rational Numbers . We know fact that every positive integer is greater than 0, and a negative integer is less than 0. By knowing this fundamental rule we can infer some facts about how to compare rational numbers. They are listed below
- Every Positive Rational Number is Greater than Zero.
- Every Negative Rational Number is Less than Zero.
- Comparison of Positive and Negative Rational Number is quite obvious i.e. Positive Rational Number is greater than a negative rational number.
- Every Rational Number represented on a number line is greater than every other rational number represented present to its left.
- Every Rational Number represented on a number line is less than every other rational number represented present to its right.
How to Compare Rational Numbers?
In order to compare any two rational numbers, you can go through the below-mentioned steps. They are as under
Step 1: Check the given rational numbers
Step 2: Write down the given rational numbers in a way that they have their denominators the same.
Step 3: Determine the Least Common Multiple of the Positive Denominators you obtained in the earlier step.
Step 4: Express rational numbers obtained in the second step using the LCM obtained as Common Denominator.
Step 5: Compare the numerators of rational numbers obtained and declare the one having a greater numerator as a greater rational number.
Solved Examples
1. Of the two rational numbers which is greater 2/3 or 5/7?
Solution:
Given Rational Numbers are 2/3, 5/7
LCM of 3, 7 is 21
Expressing the rational numbers with the same denominator using the LCM obtained we get
Therefore, we get 2/3 = (2*7)/(3*7) = 14/21
5/7 = (5*3)/(7*3) = 15/21
See the numerators of both the rational numbers obtained i.e. 14/21, 15/21
Since 15 is greater the rational number 5/7 is greater.
Therefore, of the two rational numbers, 2/3 and 5/7, 5/7 is greater.
2. Which of the two rational numbers 2/5 and -3/4 is greater?
Solution:
Given Rational Numbers are 2/5 and -3/4
We clearly know between a positive rational number and a negative rational number positive rational number is always greater.
Therefore, 2/5 is greater than -3/4.
3. Which is greater among -1/2 and – 1/5?
Solution:
Given rational numbers are -1/2 and -1/5
LCM of 2, 5 is 10
Expressing the rational numbers with the same denominator using the LCM obtained.
-1/2 = (-1*5)/(2*5)= -5/10
-1/5 = (-1*2)/(5*2) = -2/10
-2 > -5
Therefore, – 1/5 is greater than -1/2.
4. Which of the numbers 3/4 and -3/4 are greater?
Solution:
We know that every positive rational number is greater than a negative rational number. Therefore, 3/4 is greater than -3/4.
