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.