https://file.aiquickdraw.com/mathbot/file/1729644876062002gmboo.jpg

The given expression in the image is:

\[
\frac{4}{3} + \frac{3}{7} \cdot 9 - \frac{2}{12} \times 5
\]

Let's solve this step by step:

1. **Calculate the multiplication and division first (order of operations):**
   - \( \frac{3}{7} \cdot 9 = \frac{27}{7} \)
   - \( \frac{2}{12} \times 5 = \frac{10}{12} = \frac{5}{6} \)

2. **Rewrite the expression:**
   \[
   \frac{4}{3} + \frac{27}{7} - \frac{5}{6}
   \]

3. **Find a common denominator for addition and subtraction:**
   - The least common multiple of 3, 7, and 6 is 42.

4. **Convert each fraction to have a denominator of 42:**
   - \( \frac{4}{3} = \frac{4 \times 14}{3 \times 14} = \frac{56}{42} \)
   - \( \frac{27}{7} = \frac{27 \times 6}{7 \times 6} = \frac{162}{42} \)
   - \( \frac{5}{6} = \frac{5 \times 7}{6 \times 7} = \frac{35}{42} \)

5. **Combine the fractions:**
   \[
   \frac{56}{42} + \frac{162}{42} - \frac{35}{42} = \frac{56 + 162 - 35}{42} = \frac{183}{42}
   \]

6. **Simplify the fraction:**
   - \( \frac{183}{42} = \frac{61}{14} \)

The final answer is:

\[
\frac{61}{14}
\]

Would you like more details on any step, or do you have any other questions?

Here are five related questions to expand your understanding:

1. How do you find the least common multiple of different denominators?
2. What are some tips for simplifying fractions more efficiently?
3. How would the solution change if the expression involved more complex numbers?
4. Can you explain the order of operations and why it’s important?
5. How can improper fractions be converted into mixed numbers?

**Tip:** When working with fractions, always try to simplify the fractions before performing any operations. This can often make calculations much easier.

Solve the expression shown in the image: 4/3 + 3/7 * 9 - 2/12 * 5.

This detailed solution walks through solving the fractional expression 4/3 + 3/7 * 9 - 2/12 * 5 using order of operations. Learn how to perform addition, multiplication, and subtraction of fractions, with a focus on finding the least common denominator (LCD).

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