CAT Finding numbers between two rational numbers - Practice Questions & MCQ

Definition of Rational Numbers:

Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers, and q is not equal to zero.Finding Numbers between two Rational Numbers:

To find numbers between two given rational numbers, we can follow the following steps: 

1. Write down the two given rational numbers. 

2. Convert the rational numbers to a common denominator if necessary. 

3. Observe the difference between the numerators and denominators. 

4. Use this difference to find rational numbers between the given numbers.

Example:

Let's take an example to understand this concept better. Consider the numbers 1/3 and 2/3. We need to find the numbers between these two rational numbers.

Solution: 

Step 1: Write down the two given rational numbers - 1/3 and 2/3. 

Step 2: The denominators are already the same. 

Step 3: The difference between the numerators is 2 - 1 = 1. 

Step 4: Use this difference to find rational numbers between the given numbers. Here, we can add 1/6 to 1/3 to get 1/2, which is a rational number between 1/3 and 2/3.

Tips and Tricks:

1. When the given rational numbers have the same denominator, finding numbers between them is simpler. Just calculate the difference between the numerators and use it to find the number of fractional parts to be divided. 

2. When the denominators of the given rational numbers are different, convert them to a common denominator before finding numbers between them. 

3. While finding numbers between two rational numbers, always consider the numerically smaller number as the starting point and the numerically larger number as the endpoint.

Solved Example:

Let's solve a question related to finding numbers between two rational numbers.

Question: Find all the rational numbers between 1/5 and 3/5. 

Solution: 

Step 1: Write down the two given rational numbers - 1/5 and 3/5. 

Step 2: The denominators are already the same. 

Step 3: The difference between the numerators is 3 - 1 = 2. 

Step 4: Use this difference to find rational numbers between the given numbers. Adding 2/5 to 1/5, we get 3/5, which gives us the number between 1/5 and 3/5. Therefore, the rational numbers between 1/5 and 3/5 are 2/5.

In conclusion, the concept of finding numbers between two rational numbers is an essential topic in the Classification of Numbers section of the Number System chapter. It is crucial to understand the steps involved and practise various questions to master this concept.