https://file.aiquickdraw.com/mathbot/file/1725798655053fw62jz4j.jpg

Let's analyze the mathematical expression shown in the image:

1. The expression begins with two main parts on the left-hand side:
   \[
   -4 \times \frac{2}{15} + 4 \times \frac{2}{15}
   \]

2. This is simplified as:
   \[
   -\frac{8}{15} + \frac{8}{15} = 0
   \]
   
   So, the first part simplifies to \(0\).

3. Then, the next line seems to show another subtraction:
   \[
   -\frac{2 \times 9}{15}
   \]

4. Simplifying \(2 \times 9 = 18\), so:
   \[
   -\frac{18}{15} = -\frac{6}{5} = -1\frac{1}{5} 
   \]

5. The final step adds:
   \[
   1\frac{8}{15} - 1\frac{1}{5}
   \]

6. Converting \(1\frac{1}{5}\) to a fraction with the denominator 15:
   \[
   1\frac{1}{5} = 1\frac{3}{15}
   \]

7. Thus, the result is:
   \[
   1\frac{8}{15} - 1\frac{3}{15} = \frac{5}{15} = \frac{1}{3}
   \]

So, the final answer is \(\frac{1}{3}\).

Would you like further details or have any questions about this solution?

Here are five related questions for practice:

1. How do you simplify fractions with different denominators?
2. What is the process for multiplying fractions?
3. How can you convert an improper fraction to a mixed number?
4. What is the meaning of negative signs in fractions?
5. How do you add or subtract mixed numbers?

**Tip:** Always ensure the denominators are the same before adding or subtracting fractions!

Explore how to simplify a fractional expression involving negative numbers, multiplication, addition, and subtraction. This step-by-step solution shows how to handle fractions with different denominators. Suitable for middle school students in Grades 6-8.

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