What is the simplified value of the expression below?
$8.2+4.1(6.3-4)$
We need to simplify the arithmetic expression \(8.2 + 4.1 \times (6.3 - 4)\). Following the order of operations (PEMDAS/BODMAS), we must handle the operations in a specific sequence: parentheses first, then multiplication, and finally addition. The values are simple decimals, so we will perform each step carefully.
First, we compute the value inside the parentheses:
\[6.3 - 4 = 2.3\]
Next, we perform the multiplication step by multiplying \(4.1\) by the result:
\[4.1 \times 2.3 = 9.43\]
Finally, we add this product to the initial value:
\[8.2 + 9.43 = 17.63\]
The simplified value of the expression is \(17.63\). Comparing this result to the given options, we identify it as the second option.
In everyday life, this type of calculation is common when managing a budget or shopping. For instance, if you buy 8.2 units of an item as a base charge and then decide to add 4.1 units of a service that costs 2.3 dollars more than a reference price of 4 dollars (represented by 6.3 - 4), you are essentially applying the distributive property of multiplication. Mastering these operations ensures you can accurately track costs and manage your finances effectively.