What is the simplified value of the expression below?
$\frac{4.5-5.9}{0.2 \times 3-0.2}$
To simplify the expression \(\frac{4.5 - 5.9}{0.2 \times 3 - 0.2}\), we identify the components: a numerator and a denominator. We must follow the order of operations, simplifying each part independently before performing the final division. The numerator is a subtraction of two decimal numbers, and the denominator involves a multiplication followed by a subtraction.
First, we calculate the value of the numerator:
\[4.5 - 5.9 = -1.4\]
This represents the top part of our fraction.
Next, we calculate the value of the denominator. According to the order of operations, we perform the multiplication first:
\[0.2 \times 3 = 0.6\]
Then, we subtract the final term from this result:
\[0.6 - 0.2 = 0.4\]
Thus, the denominator simplifies to \(0.4\).
Now, we substitute the simplified numerator and denominator back into the original expression:
\[\frac{-1.4}{0.4} = - \frac{14}{4} = -3.5\]
Comparing this result with the given options, we find that the value corresponds to -3.5. Therefore, the simplified value is \(\boxed{-3.5}\).
Understanding how to simplify expressions using the order of operations is essential in everyday life, such as when calculating final costs with discounts and taxes. For example, if you are buying a series of items and applying a discount rate across specific subsets of those items, the order in which you group and calculate the operations ensures you arrive at the correct final amount to pay. Mastering these basic arithmetic skills prevents common calculation errors in financial management and shopping.