What is the simplified value of the expression below?
$24-12 \div 2 \times 3.2$
The problem requires evaluating the expression \(24 - 12 \div 2 \times 3.2\) by following the standard order of operations, often referred to as PEMDAS or BODMAS. This rule dictates that multiplication and division have higher priority than addition and subtraction, and when multiple operations of the same priority appear, they are performed from left to right. Here, we identify a division, a multiplication, and a subtraction. The division and multiplication are evaluated first, working from left to right.
We first address the division: \(12 \div 2\). This calculation results in \(6\). The expression now becomes \(24 - 6 \times 3.2\). Next, we perform the multiplication: \(6 \times 3.2\). Calculating \(6 \times 3.2\), we get \(19.2\). Finally, we perform the subtraction: \(24 - 19.2\). Subtracting \(19.2\) from \(24\) yields \(4.8\).
Following the established order of operations, we successfully computed the value of the expression \(24 - 12 \div 2 \times 3.2\), which is \(4.8\). This corresponds to the first option provided in the problem. Thus, the simplified value is \(\boxed{4.8}\).
The order of operations is essential in everyday life, especially in fields like finance and engineering. For example, if you are calculating the final price of an item that has a base price of \(\$24\), and you need to subtract a discount of \(\$12\) divided by \(2\) units of a product, then multiplied by a tax rate factor of \(3.2\), applying the order of operations ensures you correctly arrive at the actual total amount. Without these rules, calculations could lead to inconsistent and incorrect results in billing, budgeting, or scientific measurements.