\begin{tabular}{l} Add. \ $$ \qquad \frac{4}{5}+\frac{3}{7} $$ \ Write your answer as a fraction in simplest form. \ $$ \square $$ \ \hline$$ \frac{\square}{\square} \square \frac{\square}{\square} $$ \ \hline\end{tabular}

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UpStudy AI · Accepted Answer

To add the fractions $$ \frac{4}{5} $$ and $$ \frac{3}{7} $$, we need to follow these steps:

1. **Find a common denominator**: The denominators are 5 and 7. The least common multiple (LCM) of 5 and 7 is 35.

2. **Convert each fraction to have the common denominator**:
   - For $$ \frac{4}{5} $$:
     $$
     \frac{4}{5} = \frac{4 \times 7}{5 \times 7} = \frac{28}{35}
     $$
   - For $$ \frac{3}{7} $$:
     $$
     \frac{3}{7} = \frac{3 \times 5}{7 \times 5} = \frac{15}{35}
     $$

3. **Add the fractions**:
   $$
   \frac{28}{35} + \frac{15}{35} = \frac{28 + 15}{35} = \frac{43}{35}
   $$

4. **Simplify the result**: The fraction $$ \frac{43}{35} $$ is already in simplest form since 43 is a prime number and does not share any factors with 35.

Thus, the final answer is:
$$
\frac{43}{35}
$$

In the provided format, it can be written as:
$$
\frac{43}{35} \text{ (in simplest form)}
$$
$$ \frac{43}{35} $$

\begin{tabular}{l} Add. \\ \( \qquad \frac{4}{5}+\frac{3}{7} \) \\ Write your answer as a fraction in simplest form. \\ \( \square \) \\ \hline\( \frac{\square}{\square} \square \frac{\square}{\square} \) \\ \hline\end{tabular}

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