What is the simplified value of the expression below?
$8(9.75-3.25)+12 \times 4$
We need to simplify the mathematical expression \(8(9.75 - 3.25) + 12 \times 4\) by following the order of operations, often abbreviated as PEMDAS/BODMAS. This convention ensures that all calculations are performed in a consistent sequence: parentheses first, followed by exponents, multiplication and division (from left to right), and finally addition and subtraction (from left to right). Our goal is to calculate the value of the expression and match it to one of the given choices: 100, 152, 256, or 347.
The first step is to address the operation inside the parentheses. We have \(9.75 - 3.25\). Subtracting \(3.25\) from \(9.75\) gives us \(6.5\). Substituting this back into our expression, it now becomes \(8 \times 6.5 + 12 \times 4\).
Next, we perform the multiplication operations. First, we multiply \(8\) by \(6.5\). Since \(8 \times 6 = 48\) and \(8 \times 0.5 = 4\), their sum is \(48 + 4 = 52\). Second, we multiply \(12\) by \(4\), which equals \(48\). Now the expression is reduced to \(52 + 48\).
Finally, we perform the addition: \(52 + 48\). Adding these two values together results in \(100\). Comparing our final result with the provided options, we see that \(100\) is the correct choice.
Imagine you are purchasing art supplies for a classroom. You buy 8 sets of paints that are originally priced at \(R\$9.75\) but have a discount of \(R\$3.25\) per set, and you also buy 12 brushes priced at \(R\$4\) each. The total cost calculation, \(8(9.75 - 3.25) + 12 \times 4\), shows exactly how order of operations helps in calculating the total bill correctly: you first determine the net price of the paints, then multiply by quantity, add the total cost of brushes, and arrive at the final amount of \(R\$100\). Applying these rules ensures that budgets and shopping lists are accurate!