Let's break down the expression step by step:

Expression:

$716 - \left\{ \left(\frac{1950}{5} \times 3\right) - \left(4 + \frac{217}{7}\right) \right\}$

1. Start with the division and multiplication:

   • $\frac{1950}{5} = 390$
   • $390 \times 3 = 1170$

   So, $\frac{1950}{5} \times 3 = 1170$.

2. Next, simplify the other part inside the brackets:

   • $\frac{217}{7} = 31$
   • $4 + 31 = 35$

3. Now subtract inside the brackets: $1170 - 35 = 1135$

4. Finally, subtract from 716: $716 - 1135 = -419$

So, the final result is $-419$.

Would you like a detailed explanation or further assistance?

Related Questions:

1. How do you apply the order of operations to more complex expressions?
2. What is the meaning of "of" in mathematical terms?
3. How can dividing by a number affect the outcome of an expression?
4. Why do we need parentheses in expressions like these?
5. How do mixed operations (division, multiplication, addition) interact in an equation?

Tip:

Always perform operations inside parentheses first, then follow the order of operations (PEMDAS).