Simplify this fraction.
6/5
The Correct Answer and Explanation is :
The fraction ( \frac{6}{5} ) is already in its simplest form, as both 6 and 5 share no common factors other than 1.
To explain further, let’s break down the process of simplifying fractions and understanding their structure:
Understanding Fractions
A fraction consists of two parts: the numerator (the top number) and the denominator (the bottom number). In the fraction ( \frac{6}{5} ), 6 is the numerator, and 5 is the denominator. The fraction represents the division of the numerator by the denominator, which, in this case, can also be interpreted as 6 divided by 5.
Simplifying Fractions
The process of simplifying fractions involves reducing them to their lowest terms, which means finding the greatest common divisor (GCD) of the numerator and the denominator and dividing both by that number. Here’s how you can do this step-by-step:
- Identify the GCD: The GCD of 6 and 5 is 1, as they have no common factors other than 1.
- Divide Both Numerator and Denominator: Since the GCD is 1, we divide the numerator and the denominator by 1:
- Numerator: ( \frac{6}{1} = 6 )
- Denominator: ( \frac{5}{1} = 5 )
This gives us back ( \frac{6}{5} ), confirming it is in its simplest form.
Mixed Numbers
If desired, we can also express ( \frac{6}{5} ) as a mixed number. A mixed number combines a whole number and a proper fraction. In this case, ( \frac{6}{5} ) can be converted as follows:
- Divide the Numerator by the Denominator: ( 6 \div 5 = 1) with a remainder of ( 1).
- Write as a Mixed Number: This means ( \frac{6}{5} = 1 \frac{1}{5} ).
Conclusion
Ultimately, the fraction ( \frac{6}{5} ) remains the same in its simplest form. Understanding fractions and how to simplify them is essential in mathematics, ensuring clarity in representation and calculations.