Let's solve the expression step-by-step:

Given expression:
\[ \frac{7}{5 \times 2 - \left(\frac{6}{3}\right)} \]

1. First, simplify the term inside the parentheses:
\[ \frac{6}{3} = 2 \]

2. Substitute this back into the expression:
\[ \frac{7}{5 \times 2 - 2} \]

3. Next, perform the multiplication:
\[ 5 \times 2 = 10 \]

4. Substitute this result back into the expression:
\[ \frac{7}{10 - 2} \]

5. Finally, perform the subtraction:
\[ 10 - 2 = 8 \]

So, the simplified expression is:
\[ \frac{7}{8} \]

Therefore, the value of the expression is:
\[ \frac{7}{8} \]

Would you like further details or have any questions?

Here are some related questions to expand your understanding:

1. How do you simplify fractions?
2. What are the steps for evaluating expressions with parentheses?
3. How do you handle operations inside parentheses first?
4. What is the order of operations (PEMDAS/BODMAS)?
5. How can you multiply and divide fractions?
6. What are common mistakes to avoid in fraction simplification?
7. How do you convert a fraction to a decimal?
8. How do you solve more complex expressions with multiple layers of parentheses?

**Tip:** Always perform operations inside parentheses first and follow the order of operations to avoid mistakes in calculations.

Learn how to simplify the expression 7 divided by the quantity 5 times 2 minus the fraction 6 divided by 3. Follow a detailed step-by-step solution including arithmetic operations, fractions, and the order of operations (PEMDAS/BODMAS). Suitable for students in Grades 6-8.

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