Write the fraction in the simplest form 6/8
The Correct Answer and Explanation is:
To simplify the fraction ( \frac{6}{8} ), we need to reduce it to its simplest form by finding the greatest common divisor (GCD) of 6 and 8. The simplest form of a fraction is achieved when the numerator and the denominator are divided by their GCD.
Step 1: Find the GCD of 6 and 8.
To find the GCD, we first list the factors of each number:
- The factors of 6 are: 1, 2, 3, and 6.
- The factors of 8 are: 1, 2, 4, and 8.
The greatest common factor (or GCD) is the largest number that appears in both lists of factors. Here, the GCD of 6 and 8 is 2.
Step 2: Divide both the numerator and denominator by the GCD.
To simplify the fraction, divide both the numerator (6) and the denominator (8) by their GCD (2):
[
\frac{6}{8} = \frac{6 \div 2}{8 \div 2} = \frac{3}{4}.
]
Step 3: Confirm the result.
Now, the fraction ( \frac{6}{8} ) has been simplified to ( \frac{3}{4} ), which is in its simplest form because 3 and 4 have no common factors other than 1. The numerator 3 is a prime number, and the denominator 4 has factors of 1, 2, and 4. Since 3 and 4 share no common factors, ( \frac{3}{4} ) is the simplest form of the fraction.
Conclusion:
The simplest form of ( \frac{6}{8} ) is ( \frac{3}{4} ).
Simplifying fractions is an essential skill in mathematics. It ensures that fractions are presented in the most efficient form, making them easier to work with in calculations, comparisons, and problem-solving. Reducing fractions to their simplest form involves identifying the greatest common divisor and dividing both the numerator and the denominator by this number.