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When adding fractions, the first step is to ensure that they have the same denominator. A denominator is the bottom number of a fraction that tells you into how many equal parts the whole is divided. For instance, the fraction \( \frac{4}{15} \) has 15 as its denominator. In this specific problem, both fractions already share the same denominator of 15:
\[ \frac{4}{15} + \frac{7}{15} \]
This makes our job a lot easier because we do not need to adjust or change anything about the denominators. It's important to remember that when the denominators match, we can directly proceed to the next steps in fraction addition.

Once you confirm that the two fractions have the same denominator, you can add the numerators. The numerator is the top part of the fraction that indicates how many parts are being considered. In the problem above, we have the numerators 4 and 7. To add them, follow these simple steps:

• Write down the numerators of both fractions: 4 and 7.
• Add these numerators together: \(4 + 7 = 11\).

So, the fraction addition process becomes:\[ \frac{4}{15} + \frac{7}{15} = \frac{11}{15} \]
The new numerator (11 in this case) is placed over the shared denominator, giving us the fraction \( \frac{11}{15} \).

Sometimes, the last step in working with fractions is simplification. This involves reducing a fraction to its simplest form. A fraction is simplified when the numerator and the denominator are as small as possible and still represent the same value. Simplification is done by finding the greatest common divisor (GCD) of the numerator and denominator and dividing both by this number. However, in our example, \( \frac{11}{15} \) is already in its simplest form.

Since 11 and 15 have no common factors other than 1, there's no need to simplify further. This is a critical check as it ensures your answer is as clear and concise as possible. Knowing how to simplify fractions allows you to effectively communicate your answers, making them understandable and easy to verify.