Sure, let's go through the process of adding the fractions [tex]\(\frac{5}{14}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex] and then simplifying the result:
1. Identify the fractions to be added: [tex]\(\frac{5}{14}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex].
2. Common Denominator: Both fractions have the same denominator, which is 14.
3. Add the Numerators: Since the denominators are the same, we can simply add the numerators:
[tex]\[
\frac{5}{14} + \frac{3}{14} = \frac{5 + 3}{14} = \frac{8}{14}
\][/tex]
4. Simplify the Fraction: Now, we need to simplify [tex]\(\frac{8}{14}\)[/tex]. We do this by finding the greatest common divisor (GCD) of the numerator (8) and the denominator (14):
- The prime factorization of 8 is [tex]\(2^3\)[/tex].
- The prime factorization of 14 is [tex]\(2 \times 7\)[/tex].
- The common factor is 2.
So, the GCD of 8 and 14 is 2.
5. Divide the Numerator and Denominator by their GCD:
[tex]\[
\frac{8 \div 2}{14 \div 2} = \frac{4}{7}
\][/tex]
Therefore, the simplified form of [tex]\(\frac{8}{14}\)[/tex] is [tex]\(\frac{4}{7}\)[/tex].
So, the result of adding [tex]\(\frac{5}{14} + \frac{3}{14}\)[/tex] and simplifying the fraction is [tex]\(\boxed{\frac{4}{7}}\)[/tex].
