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Let's work through the problems visible in the image you uploaded.

### 1. Mathematical Operations:
**a) \( \frac{5}{4} + \frac{9}{8} - \frac{19}{8} \):**
   - First, find a common denominator for \( \frac{5}{4} \) and the other two fractions. The common denominator for 4 and 8 is 8.
   - Convert \( \frac{5}{4} \) to \( \frac{10}{8} \).
   - Now the expression becomes \( \frac{10}{8} + \frac{9}{8} - \frac{19}{8} \).
   - Combine the fractions: \( \frac{10+9-19}{8} = \frac{0}{8} = 0 \).

**Answer: 0**

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**b) \( 5 + 2 - 20 + 4 + 10 \):**
   - Perform the additions and subtractions in order: \( 5 + 2 = 7 \), \( 7 - 20 = -13 \), \( -13 + 4 = -9 \), and \( -9 + 10 = 1 \).

**Answer: 1**

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**c) \( 2 + \frac{3}{4} = \frac{11}{4} \):**
   - Convert 2 into a fraction: \( 2 = \frac{8}{4} \).
   - Add \( \frac{8}{4} + \frac{3}{4} = \frac{11}{4} \).

**Answer: \( \frac{11}{4} \)**

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**d) \( (3) - (4) \times (5) \):**
   - Apply the order of operations (PEMDAS—parentheses, exponents, multiplication and division, addition and subtraction).
   - First, multiply \( 4 \times 5 = 20 \), then subtract: \( 3 - 20 = -17 \).

**Answer: -17**

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### 2. Conceptual Questions:

**a) Explica en tus propias palabras el concepto de *frecuencia absoluta*:**
   - La *frecuencia absoluta* es el número de veces que ocurre un evento o dato en un conjunto de datos. Es simplemente el conteo de la aparición de un valor específico en una lista o serie de observaciones.

**b) Explica en tus propias palabras el concepto de *frecuencia relativa*:**
   - La *frecuencia relativa* es la proporción o porcentaje que representa la frecuencia absoluta respecto al total de datos. Se calcula dividiendo la frecuencia absoluta de un valor por el número total de observaciones.

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Would you like any further details or explanations on these topics?

Here are 5 related questions for expanding this topic:
1. How do you convert mixed numbers to improper fractions in operations?
2. Can you explain the concept of least common denominators when adding fractions?
3. What is the difference between absolute and relative frequency in statistical data?
4. How does the order of operations (PEMDAS) affect more complex calculations?
5. How would you apply frequency concepts to real-life data analysis?

**Tip:** Always remember to convert whole numbers into fractions when adding them to fractional values to make calculations easier.

Solve the following operations and answer the conceptual questions about absolute and relative frequency.

This lesson covers basic arithmetic operations, including adding and subtracting fractions, multiplication, and understanding absolute and relative frequency. Step-by-step solutions are provided for problems suitable for Grades 6-8.

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