Solving Mathematical Expressions with Order of Operations

To solve the given mathematical expression, we need to follow the order of operations, often remembered by acronyms like BODMAS or PEMDAS.

• B/P: Brackets or Parentheses (including curly braces)
• O/E: Orders or Exponents
• D/M: Division or Multiplication (from left to right)
• A/S: Addition or Subtraction (from left to right)

The given expression is: \(7 \times \{4 + (-2) \times (-3)\}\)

Let's solve it step-by-step:

1. First, we evaluate the expression inside the curly braces. Within the curly braces, we have addition and multiplication. According to the order of operations, multiplication is done before addition.
2. Calculate the multiplication inside the braces: \((-2) \times (-3)\). The product of two negative numbers is a positive number.
3. So, \((-2) \times (-3) = 6\).
4. Now substitute this value back into the expression inside the curly braces: \(4 + 6\).
5. Perform the addition inside the braces: \(4 + 6 = 10\).
6. Now the expression simplifies to: \(7 \times \{10\}\) or \(7 \times 10\).
7. Finally, perform the multiplication outside the braces: \(7 \times 10\).
8. \(7 \times 10 = 70\).

Thus, the value of the expression \(7 \times \{4 + (-2) \times (-3)\}\) is 70.

Step-by-Step Calculation

Given expression: \(7 \times \{4 + (-2) \times (-3)\}\)

Step 1: Evaluate the multiplication inside the braces.

\((-2) \times (-3) = 6\)

Step 2: Substitute the result back into the expression inside the braces.

\(\{4 + 6\}\)

Step 3: Evaluate the addition inside the braces.

\(\{4 + 6\} = 10\)

Step 4: Substitute the result back into the original expression.

\(7 \times 10\)

Step 5: Perform the final multiplication.

\(7 \times 10 = 70\)

Revision Table: Order of Operations & Integers

Additional Information: Mastering Integer Operations

Understanding how to perform operations with positive and negative integers is crucial for solving expressions like the one in this problem. Let's look at some key points:

• Multiplication of Signs: Remember the simple rule: like signs give a positive product, unlike signs give a negative product. This is why \((-2) \times (-3)\) results in a positive 6.
• Addition and Subtraction with Signs: When adding or subtracting integers, think of it in terms of movements on a number line or combining debts and credits. \(4 + (-2)\) is like starting at 4 and moving 2 units to the left, ending at 2. \(-2 + 4\) is like starting at -2 and moving 4 units to the right, ending at 2.
• Parentheses and Brackets: These group parts of an expression, indicating that the calculation inside must be done first. Curly braces \(\{\}\), square brackets \([]\), and standard parentheses \(()\) all serve this purpose.
• Applying BODMAS/PEMDAS consistently: Always work from the innermost grouping symbol outwards. Within each level, follow the DM (Division/Multiplication) then AS (Addition/Subtraction) sequence from left to right.

By carefully applying the order of operations and the rules for integer arithmetic, solving such expressions becomes straightforward.