Certainly! To add the fractions [tex]\(\frac{1}{7}\)[/tex] and [tex]\(\frac{3}{14}\)[/tex], we need to follow these steps:
1. Find a common denominator: The denominators of the given fractions are 7 and 14. The least common denominator (LCD) is the least common multiple (LCM) of these two numbers. The least common multiple of 7 and 14 is 14.
2. Convert the fractions to have the same denominator:
- For the fraction [tex]\(\frac{1}{7}\)[/tex], we need to convert it to a fraction with a denominator of 14.
- To do this, we multiply both the numerator and the denominator by [tex]\(2\)[/tex] (since [tex]\(14 \div 7 = 2\)[/tex]):
[tex]\[
\frac{1 \times 2}{7 \times 2} = \frac{2}{14}
\][/tex]
- For the fraction [tex]\(\frac{3}{14}\)[/tex], it already has the denominator of 14, so we don't need to change it.
[tex]\[
\frac{3}{14}
\][/tex]
3. Add the fractions:
- Now that both fractions have the same denominator, we can add their numerators directly:
[tex]\[
\frac{2}{14} + \frac{3}{14} = \frac{2 + 3}{14} = \frac{5}{14}
\][/tex]
4. Reduce the fraction (if possible):
- To check if the fraction can be reduced, we find the greatest common divisor (GCD) of the numerator and denominator. The GCD of 5 and 14 is 1, as 5 is a prime number and does not share any common factors with 14 other than 1. Thus, [tex]\(\frac{5}{14}\)[/tex] is already in its simplest form.
In summary:
[tex]\[
\begin{array}{r}
\frac{1}{7}=\frac{2}{14} \\
+\frac{3}{14} \\
\hline
\frac{5}{14}
\end{array}
\][/tex]
