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The problem states:

> **"El cuádruple de la tercera parte de un número, aumentado en su novena parte es igual a 13. Indica el triple de dicho número."**

Let's define the unknown number as \( x \).

### Breaking down the problem:
1. **"El cuádruple de la tercera parte de un número"**: This is \( 4 \times \left(\frac{x}{3}\right) = \frac{4x}{3} \).
2. **"Aumentado en su novena parte"**: This adds the ninth part of the number to the expression, so we have \( \frac{4x}{3} + \frac{x}{9} \).
3. **"Es igual a 13"**: This gives us the equation:
   \[
   \frac{4x}{3} + \frac{x}{9} = 13
   \]

### Solving the equation:
To solve this, we first find a common denominator. The least common denominator between 3 and 9 is 9. Rewriting the equation:
\[
\frac{12x}{9} + \frac{x}{9} = 13
\]

Now, combine the terms on the left side:
\[
\frac{12x + x}{9} = 13
\]

Simplifying further:
\[
\frac{13x}{9} = 13
\]

Multiply both sides by 9:
\[
13x = 117
\]

Finally, divide by 13:
\[
x = 9
\]

### Finding the triple of the number:
The problem asks for the triple of the number, so \( 3 \times 9 = 27 \).

### Conclusion:
The triple of the number is **27**.

---

Would you like further clarification? Here are some related questions:

1. How can you verify that the solution \( x = 9 \) satisfies the original equation?
2. What other types of problems involve fractions and algebraic expressions?
3. How can you manipulate an equation when fractions are involved?
4. What are other applications of this type of algebra in real-world problems?
5. How does finding a common denominator help in solving equations with fractions?

**Tip:** When dealing with fractions in equations, always try to simplify the equation by finding a common denominator before proceeding with solving.

El cuádruple de la tercera parte de un número, aumentado en su novena parte es igual a 13. Indica el triple de dicho número.

Learn how to solve an algebraic equation involving fractions: the quadruple of a number's third part, increased by its ninth part, equals 13. Find the triple of this number, perfect for students in Grades 7-9.

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