Let's solve the expression step by step:

Given expression:

\[
15 \cdot \frac{3\left(12 - 7\right)}{3}
\]

1. **Simplify inside the parentheses**:
   \[
   12 - 7 = 5
   \]

   Now the expression becomes:
   \[
   15 \cdot \frac{3 \times 5}{3}
   \]

2. **Multiply 3 by 5**:
   \[
   3 \times 5 = 15
   \]

   Now the expression is:
   \[
   15 \cdot \frac{15}{3}
   \]

3. **Simplify the fraction**:
   \[
   \frac{15}{3} = 5
   \]

   Now the expression becomes:
   \[
   15 \times 5
   \]

4. **Finally, multiply**:
   \[
   15 \times 5 = 75
   \]

So, the value of the expression is:

\[
\boxed{75}
\]

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

Here are some related questions:
1. How would you solve the expression \(\frac{20 \cdot (10 - 3)}{5}\)?
2. What happens if you change the division by 3 to division by 5 in the original problem?
3. Can you simplify the expression \(\frac{4 \cdot (8 + 2)}{2}\)?
4. How do you evaluate \(10 \times \frac{6(9 - 3)}{2}\)?
5. What is the result of \(18 \cdot \frac{2(10 - 4)}{6}\)?

**Tip:** Always simplify inside parentheses first according to the order of operations (PEMDAS).

Learn how to solve the arithmetic expression 15 times the quantity of 3 times the quantity of 12 minus 7 divided by 3 step by step. This problem covers arithmetic operations and order of operations (PEMDAS). Suitable for students in Grades 6-8.

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