Solving Mathematical Expressions

Understanding the order of operations is crucial when solving mathematical expressions like $(-6)[40 \div \{7 - (-3)\}]$. We follow the BODMAS or PEMDAS rule, which dictates the sequence for performing operations:

• Brackets (or Parentheses)
• Orders (exponents, roots, etc.) (or Exponents)
• Division and Multiplication (from left to right)
• Addition and Subtraction (from left to right)

Let's break down the given expression step by step:

The expression is: $(-6)[40 \div \{7 - (-3)\}]$

Step 1: Solve the innermost brackets/braces.

We have $\{7 - (-3)\}$ inside the braces. Subtracting a negative number is the same as adding its positive counterpart.

\(7 - (-3) = 7 + 3 = 10\)

Now the expression becomes: $(-6)[40 \div 10]$

Step 2: Solve the operation inside the square brackets.

We have $40 \div 10$ inside the square brackets.

\(40 \div 10 = 4\)

Now the expression becomes: $(-6)[4]$ or simply $(-6) \times 4$

Step 3: Perform the multiplication.

Finally, multiply $(-6)$ by $4$. When multiplying a negative number by a positive number, the result is negative.

\((-6) \times 4 = -24\)

So, the value of the expression $(-6)[40 \div \{7 - (-3)\}]$ is $-24$.

Checking the Options

Let's compare our result with the given options:

The calculated value, $-24$, matches option 4.

Revision Table: Order of Operations

Additional Information: Integer Operations

When solving mathematical expressions involving integers, remember these rules for basic operations:

• Addition:
  • Same signs: Add the absolute values and keep the sign. \(3 + 5 = 8\), \((-3) + (-5) = -8\)
  • Different signs: Subtract the smaller absolute value from the larger one and take the sign of the number with the larger absolute value. \(5 + (-3) = 2\), \((-5) + 3 = -2\)
• Subtraction:
  • Subtracting a number is the same as adding its opposite. \(7 - (-3) = 7 + 3 = 10\), \(3 - 5 = 3 + (-5) = -2\)
• Multiplication and Division:
  • Same signs: Result is positive. \(3 \times 5 = 15\), \((-3) \times (-5) = 15\), \(10 \div 2 = 5\), \((-10) \div (-2) = 5\)
  • Different signs: Result is negative. \(3 \times (-5) = -15\), \((-3) \times 5 = -15\), \(10 \div (-2) = -5\), \((-10) \div 2 = -5\)