$4.2 + 15 \times (8.6 - 5)$
The goal is to calculate the value of the numerical expression \(4.2 + 15 \times (8.6 - 5)\). To solve this correctly, we must adhere to the 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). Our expression contains parentheses, a multiplication, and an addition, so we will process these operations in the specified order.
First, we address the operation inside the parentheses: \(8.6 - 5\). By subtracting 5 from 8.6, we obtain:
\[8.6 - 5 = 3.6.\]
Now, substituting this result back into our expression, we get:
\[4.2 + 15 \times 3.6.\]
Next, we perform the multiplication according to the order of operations: \(15 \times 3.6\). Calculating this product, we find:
\[15 \times 3.6 = 54.0.\]
Now, our expression simplifies to the final addition:
\[4.2 + 54.0.\]
Finally, we add the remaining terms:
\[4.2 + 54.0 = 58.2.\]
The numerical value of the given expression is therefore \(\boxed{58.2}\).
Order of operations is essential in everyday life, for example, when calculating a total bill. Imagine you are buying 15 notebooks at a discounted price. The original price of a notebook is \$8.60, but you have a \$5.00 discount coupon that applies to each notebook. You also have a \$4.20 flat shipping fee. Your total cost can be represented as \(4.2 + 15 \times (8.6 - 5)\). Following the correct order of operations ensures you calculate your total expense accurately, which in this case is \(\$58.20\).