Add the fractions [tex]\frac{5}{14} + \frac{3}{14}[/tex]. Simplify your answer.

A. [tex]\frac{8}{14}[/tex]
B. [tex]\frac{1}{7}[/tex]
C. [tex]\frac{15}{196}[/tex]
D. [tex]\frac{4}{7}[/tex]



Answer :

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].