Verified Answer :

  • Follow the order of operations by performing multiplication and division first.
  • Solve \(6 \cdot 4 = 24\) and \(10 \div 2 = 5\).
  • Simplify the resulting expression to \(8 - 24 + 5\).
  • Calculate from left to right to reach the final answer of \(\boxed{-11}\).

Explanation

  1. Understanding the Order of Operations

To evaluate the expression \(8 - 6 \cdot 4 + 10 \div 2\), we must follow the standard order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right). This ensures that mathematical expressions are computed consistently. Our goal is to break the problem into smaller, manageable parts based on these rules.

  1. Performing Multiplication and Division

First, we address multiplication and division, moving from left to right.
The expression contains one multiplication and one division:

  • The multiplication is \(6 \cdot 4 = 24\).
  • The division is \(10 \div 2 = 5\).

Replacing these values back into our original expression, we get:
\(8 - 24 + 5\).

  1. Completing the Addition and Subtraction

Now, we perform the remaining addition and subtraction, again working strictly from left to right:

  • First, the subtraction: \(8 - 24 = -16\).
  • Then, the addition: \(-16 + 5 = -11\).

Thus, the final numerical value of the expression is \(-11\).

Examples

Arithmetic order of operations is essential in daily tasks such as calculating a total budget, managing bank accounts, or adjusting recipes. For example, if you have \$8 in your wallet, you then make 6 purchases of \$4 each, but receive a refund split equally between 2 items (\(10 \div 2 = 5\)), calculating your final balance would follow the same steps we just used: \(8 - (6 \times 4) + 5\). Mastering this ensures you accurately track your finances and handle real-world quantitative problems.

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