The equation in the image is:

$\frac{6 \cdot \frac{2}{6} + 7}{\frac{4}{7}} + \frac{45}{3} \div \sqrt{\frac{25}{9}}$

Let's break this down step by step.

Step 1: Simplify the first fraction

The numerator of the first fraction is: $6 \cdot \frac{2}{6} + 7 = 2 + 7 = 9$

The denominator is: $\frac{4}{7}$

So the first term becomes: $\frac{9}{\frac{4}{7}} = 9 \cdot \frac{7}{4} = \frac{63}{4}$

Step 2: Simplify the second part

The second part is: $\frac{45}{3} \div \sqrt{\frac{25}{9}}$

First, simplify: $\frac{45}{3} = 15$

Next, simplify the square root: $\sqrt{\frac{25}{9}} = \frac{5}{3}$

So, we now have: $15 \div \frac{5}{3} = 15 \cdot \frac{3}{5} = 9$

Step 3: Add the two parts

Now, add the two results: $\frac{63}{4} + 9 = \frac{63}{4} + \frac{36}{4} = \frac{99}{4} = 24.75$

The correct answer is approximately 24.75, not 27.83.

Would you like more details on any part of the solution?

Related questions:

1. How do you simplify fractions with division and multiplication?
2. What is the method to rationalize square roots of fractions?
3. How can you convert a mixed fraction into an improper fraction?
4. Why is multiplying by the reciprocal used when dividing fractions?
5. How do you handle operations with decimals versus fractions?

Tip: Always simplify your square roots and fractions separately before performing further operations to avoid errors.