Step-by-step solution for adding fractions, demonstrating how to convert 9/5 to 63/35 to find a common denominator.

The image shows a math problem involving the addition of two fractions:

$$
\frac{9}{5} + \frac{14}{7}
$$

However, the solution shown in the image only partially solves the problem. Let's go through it step by step and correct any errors.

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Step 1: Simplify the fractions if possible

- $\frac{14}{7}$ can be simplified:
$$
\frac{14}{7} = 2
$$

So the expression becomes:
$$
\frac{9}{5} + 2
$$

Now we can write 2 as a fraction with denominator 5:
$$
2 = \frac{10}{5}
$$

So:
$$
\frac{9}{5} + \frac{10}{5} = \frac{19}{5}
$$

---

Step 2: Check the work in the image

The image shows:
$$
\frac{9}{5} \times \frac{7}{7} = \frac{63}{35}
$$

This is not adding the fractions — it's just converting $\frac{9}{5}$ to an equivalent fraction with denominator 35 (since $5 \times 7 = 35$). But it doesn't include the second fraction, $\frac{14}{7}$, which was not converted or added.

Also, the image incorrectly suggests that multiplying $\frac{9}{5}$ by $\frac{7}{7}$ gives $\frac{63}{35}$, which is correct:
$$
\frac{9}{5} \times \frac{7}{7} = \frac{63}{35}
$$

But this is only one part of the process.

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Step 3: Correct approach to add the fractions

We need to find a common denominator for $\frac{9}{5}$ and $\frac{14}{7}$.

- First, simplify $\frac{14}{7} = 2$, as shown above.
- Then convert 2 to $\frac{10}{5}$, so:
$$
\frac{9}{5} + \frac{10}{5} = \frac{19}{5}
$$

Alternatively, using the least common denominator (LCD) method:

- LCD of 5 and 7 is 35.
- Convert both fractions:
$$
\frac{9}{5} = \frac{9 \times 7}{5 \times 7} = \frac{63}{35}
$$
$$
\frac{14}{7} = 2 = \frac{2 \times 35}{35} = \frac{70}{35}
$$

Wait — actually, better:
$$
\frac{14}{7} = 2 = \frac{70}{35}? \quad \text{No! That’s wrong.}
$$

Let’s fix that.

Actually:
$$
2 = \frac{70}{35}? \quad \text{No, } \frac{70}{35} = 2 \text{ is correct, but let's double-check.}
$$

Yes:
$$
\frac{70}{35} = 2
$$

So:
$$
\frac{9}{5} = \frac{63}{35}, \quad \frac{14}{7} = 2 = \frac{70}{35}
$$

Now add:
$$
\frac{63}{35} + \frac{70}{35} = \frac{133}{35}
$$

Simplify:
$$
\frac{133}{35} = \frac{19}{5} \quad \text{(divide numerator and denominator by 7)}
$$

So final answer is:
$$
\boxed{\frac{19}{5}} \quad \text{or} \quad 3\frac{4}{5}
$$

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Summary

The image only shows the conversion of $\frac{9}{5}$ to $\frac{63}{35}$, but does not complete the addition.

✔ Correct solution:
$$
\frac{9}{5} + \frac{14}{7} = \frac{9}{5} + 2 = \frac{9}{5} + \frac{10}{5} = \frac{19}{5}
$$

Or:
$$
\frac{63}{35} + \frac{70}{35} = \frac{133}{35} = \frac{19}{5}
$$

✔ Final Answer: $\boxed{\frac{19}{5}}$ or $3\frac{4}{5}$

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💡 Note: The image from wikiHow may be illustrating a step in a process, but it's incomplete. Always make sure to include all parts of the problem.