If + means +, x means -, ÷ means + and the following: means, then simplifyFind the value of - 720+ [16 × 15 × 3(9 × (7 × 1)))].

The given problem involves some operator substitutions, where:

- \( + \) means addition (which remains unchanged),
- \( \times \) (multiplication) means subtraction,
- \( \div \) (division) means addition.

We need to simplify the expression under these substitutions:

\[
-720 + [16 \times 15 \times 3(9 \times (7 \times 1))]
\]

We will apply the substitutions and solve accordingly.

1. The innermost operation is \( 7 \times 1 \). Since \( \times \) means subtraction, this becomes:

\[
7 \times 1 = 7 - 1 = 6
\]

2. Next, substitute \( 9 \times (7 \times 1) \) or \( 9 \times 6 \). Since \( \times \) means subtraction:

\[
9 \times 6 = 9 - 6 = 3
\]

3. Now, simplify \( 16 \times 15 \times 3(9 \times (7 \times 1)) \). Substituting values, this becomes \( 16 \times 15 \times 3(3) \):

- \( 16 \times 15 = 16 - 15 = 1 \) (since \( \times \) means subtraction).
- \( 1 \times 3 = 1 - 3 = -2 \).

Thus, the entire expression simplifies to:

\[
-720 + [-2]
\]

Finally:

\[
-720 + (-2) = -720 - 2 = -722
\]

Thus, the value of the expression is \( \boxed{-722} \).

Would you like a detailed breakdown of any specific part? Here are five related questions to deepen your understanding:

1. How does changing the operations affect the result in similar expressions?
2. What would happen if we swapped the addition and subtraction symbols instead?
3. Can we apply the same substitutions to larger equations?
4. How do parentheses impact the order of operations in modified expressions?
5. How does operator substitution change if combined with exponents?

**Tip:** Always work through the innermost parentheses first when dealing with complex expressions!

If + means +, x means -, ÷ means + and the following: means, then simplify Find the value of - 720+ [16 × 15 × 3(9 × (7 × 1)))]

Explore how to simplify an expression using operator substitution. In this problem, multiplication means subtraction and division means addition. The problem requires applying the order of operations and basic arithmetic rules. Suitable for students in Grades 6-8.

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