What is the simplified value of the expression below?
$4.2+0.6 \div 3-5(0.9-0.5)$
To solve the expression \(4.2 + 0.6 \div 3 - 5(0.9 - 0.5)\), we follow the Order of Operations (often remembered by the acronym PEMDAS or BODMAS), which dictates the sequence of operations:
The first step is to evaluate the expression inside the parentheses:
\[0.9 - 0.5 = 0.4\]
Substituting this result back into our expression, we get:
\[4.2 + 0.6 \div 3 - 5(0.4)\]
Next, we perform the multiplication and division from left to right:
First, the division:
\[0.6 \div 3 = 0.2\]
Then, the multiplication:
\[5 \times 0.4 = 2.0\]
Now, substitute these back into the expression:
\[4.2 + 0.2 - 2.0\]
Finally, we perform the addition and subtraction from left to right:
\[4.2 + 0.2 = 4.4\]
\[4.4 - 2.0 = 2.4\]
The simplified value of the expression is \(2.4\).
Understanding the order of operations is crucial in everyday life, such as when calculating the total cost of a project. For instance, if you buy 3 packs of pens for R\$4.20 each and you are given a discount on a bundle, you must calculate the subtractions and additions in the correct order to ensure you pay the right amount. By strictly following the rules of arithmetic, you avoid costly mistakes and ensure your personal budgeting is accurate and reliable.