Finding a rational number between 0.75 and 1.2

To find a rational number lying between two given numbers, we need to follow the following steps:

Step 1: Find the common denominator of the two numbers.

Step 2: Convert the given numbers into fractions with the common denominator.

Step 3: Find the average of the two fractions.

Step 4: Simplify the fraction obtained in step 3.

Step 5: Check if the simplified fraction lies between the given numbers.

Let's apply these steps to find a rational number between 0.75 and 1.2.

Step 1: Find the common denominator of 0.75 and 1.2.

The decimal form of 0.75 is equivalent to the fraction 75/100 or 3/4, while the decimal form of 1.2 is equivalent to the fraction 12/10 or 6/5. The common denominator of 3/4 and 6/5 is 20.

Step 2: Convert the given numbers into fractions with the common denominator.

0.75 can be written as 15/20, and 1.2 can be written as 12/20.

Step 3: Find the average of the two fractions.

The average of 15/20 and 12/20 is (15/20 + 12/20) / 2 = 27/40.

Step 4: Simplify the fraction obtained in step 3.

27/40 can be simplified by dividing both the numerator and denominator by their greatest common factor, which is 3. So, 27/40 simplifies to 9/13.

Step 5: Check if the simplified fraction lies between the given numbers.

9/13 is a rational number lying between 0.75 and 1.2.

Conclusion

By following the above steps, we have found a rational number lying between 0.75 and 1.2, which is 9/13.

0.975