https://file.aiquickdraw.com/mathbot/file/17264338118162lzb640e.jpg

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.

Solve the following equation: (6 * (2/6) + 7) / (4/7) + 45/3 ÷ √(25/9)

This problem involves simplifying a complex algebraic expression with fractions and square roots. It requires knowledge of fraction operations and the square root of fractions. Suitable for students in Grades 8-10, the problem walks through simplification steps leading to the correct solution.

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