To simplify the fraction [tex]\(\frac{6}{14}\)[/tex] to its lowest terms, we need to follow several steps:
1. Identify the Greatest Common Divisor (GCD):
- First, we need to find the greatest common divisor (GCD) of the numerator (6) and the denominator (14). The GCD is the largest number that divides both the numerator and the denominator without leaving a remainder.
- The GCD of 6 and 14 is 2.
2. Divide the Numerator and Denominator by the GCD:
- To simplify [tex]\(\frac{6}{14}\)[/tex], we divide both the numerator and the denominator by their GCD (2).
[tex]\[
\text{Simplified numerator} = \frac{6}{2} = 3
\][/tex]
[tex]\[
\text{Simplified denominator} = \frac{14}{2} = 7
\][/tex]
3. Write the Simplified Fraction:
- After dividing both the numerator and the denominator by their GCD, we get the simplified fraction.
[tex]\[
\frac{6}{14} = \frac{3}{7}
\][/tex]
Therefore, the fraction [tex]\(\frac{6}{14}\)[/tex] simplified to its lowest terms is [tex]\(\frac{3}{7}\)[/tex].
