The image shows a math exercise focusing on dividing fractions and converting mixed fractions into improper fractions. Here’s a step-by-step breakdown of how to approach this problem:

Problem Setup:

• You are asked to divide the fractions shown by converting mixed fractions into improper fractions first, and then proceeding with the division.

1. First Conversion (Mixed Fraction to Improper Fraction):

   • Mixed fractions should be converted to improper fractions.
   • The mixed fractions given are $1 \frac{5}{14}$ and $2 \frac{3}{7}$.
   • To convert a mixed fraction to an improper fraction, use the formula:
     $\text{Improper fraction} = \left( \text{Whole number} \times \text{Denominator} \right) + \text{Numerator}$

   For $1 \frac{5}{14}$: $\text{Improper fraction} = (1 \times 14) + 5 = 14 + 5 = \frac{19}{14}$

   For $2 \frac{3}{7}$: $\text{Improper fraction} = (2 \times 7) + 3 = 14 + 3 = \frac{17}{7}$

2. Division of Fractions:

   • Dividing fractions involves multiplying by the reciprocal of the divisor. This means that: $\frac{19}{14} \div \frac{17}{7} = \frac{19}{14} \times \frac{7}{17}$

3. Multiplication of Fractions:

   • Multiply the numerators together and the denominators together: $\frac{19}{14} \times \frac{7}{17} = \frac{19 \times 7}{14 \times 17} = \frac{133}{238}$

This is the simplified fraction that results from the division.

Would you like further details or have any questions? Here are 5 related questions:

1. How do you simplify fractions after multiplying?
2. What is the process for inverting a divisor in a division problem involving fractions?
3. Can mixed fractions always be converted to improper fractions before solving?
4. How can you check your solution after dividing fractions?
5. What strategies can help in multiplying fractions quickly?

Tip: Always remember to simplify your fractions if possible to get the simplest form of your answer.