UpStudy Free Solution:

To solve \(\frac { 14} { 26} + \frac { 1} { 13} \), we first simplify each fraction and then find a common denominator to add them together.

Simplify \(\frac { 14} { 26} \):
\[\frac { 14} { 26} = \frac { 14 \div 2} { 26 \div 2} = \frac { 7} { 13} \]

The second fraction is already in its simplest form:
\[\frac { 1} { 13} \]

Since both fractions now have the same denominator, we can add them directly:
\[\frac { 7} { 13} + \frac { 1} { 13} = \frac { 7 + 1} { 13} = \frac { 8} { 13} \]
Thus, the answer in its lowest terms is:
\[\frac { 8} { 13} \]
 

Supplemental Knowledge

When adding fractions, the first step is to ensure they have a common denominator. If they don't, you need to find the least common multiple (LCM) of the denominators and convert each fraction accordingly.
For example, to add \(\frac { a} { b} \) and \(\frac { c} { d} \), you would:

Find the LCM of \(b\) and \(d\).

Convert both fractions to have this common denominator.

Add the numerators while keeping the common denominator.

Simplify the resulting fraction if possible.

Our platform provides step-by-step solutions to homework problems across all levels of mathematics, chemistry, physics and biology - no matter if they're complex equations or difficult word problems!