Examples of Comparing Rational Numbers

Example 1. Which is greater, -1/2 or – 1/5 of the two rational numbers?

Solution:

Given rational numbers are -1/2 and – 1/5

Taking the LCM of denominators, which are 2 and 5

LCM comes out to be 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.

Example 2. Of the two rational numbers, which is greater, 2/5, or -3/4 is greater?

Solution:

To compare ⅖ and -¾

We know that between a positive rational number and a negative rational number, a positive rational number is always greater.

Therefore, 2/5 is greater than -3/4.

Example 3. Of the two rational numbers, which is greater, 2/3 or 5/7?

Solution:

To Compare the Rational Numbers ⅔ and 5/7

Taking the LCM of the denominators 3 and 7, which comes out to be 21

Rational numbers with the same denominator using the LCM obtained, 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.

Comparison of Rational Numbers: Rational numbers are crucial for problem-solving across various disciplines. They help us solve equations, analyze data, make predictions, and model real-world scenarios in science, engineering, economics, and finance. Comparing rational numbers is similar to comparing fractions and integers.

These numbers are compared using the numerators and denominators. It is compared using either the decimal or the same denominator method.

The article will detail the rational numbers and the methods to compare them with examples.