- Perform the multiplication \(0.75 \times 8 = 6\) first, according to the order of operations.
- Add the terms \(4.5 + 0.25 + 2.5 = 7.25\) from left to right.
- Compare these results with Leticia's work and note that Step 1 incorrectly replaces the sum \(4.5 + 0.25\) with \(18\).
- The first mistake occurred in \(\boxed{\text{Step 1}}\).
Explanation
- Correct Evaluation of the Expression
We are tasked with evaluating the expression \(4.5 + 0.25 + 2.5 - 0.75 \times 8\) and identifying the first step where Leticia's simplification went wrong. To evaluate this expression correctly, we must follow the order of operations (PEMDAS/BODMAS), which dictates that multiplication is performed before addition and subtraction.
The original expression is:
\[4.5 + 0.25 + 2.5 - 0.75 \times 8\]
Applying the order of operations:
- First, perform the multiplication: \(0.75 \times 8 = 6\).
- The expression simplifies to: \(4.5 + 0.25 + 2.5 - 6\).
- Next, perform the addition and subtraction from left to right:
\(4.5 + 0.25 = 4.75\)
\(4.75 + 2.5 = 7.25\)
\(7.25 - 6 = 1.25\)
The correct value of the expression is \(1.25\).
- Identifying the Mistake
Now let's examine Leticia's steps:
- Initial expression: \(4.5 + 0.25 + 2.5 - 0.75 \times 8\)
- Step 1: \(18 + 2.5 - 0.75 \times 8\)
Leticia's Step 1 replaced \(4.5 + 0.25\) (or potentially a portion of the sum) with \(18\). However, we know that \(4.5 + 0.25 = 4.75\). Even if she added the entire initial part \(4.5 + 0.25 + 2.5\), the sum is \(7.25\), not \(18\). Therefore, the first step already contains an incorrect value, making it the first mistake.
Examples
Understanding the correct order of operations is crucial in everyday life, whether you are balancing a budget, calculating project costs, or even cooking! Imagine you are shopping for ingredients: you need to buy 3 packs of flour at \$\$4.50\$ each, 2 packs of sugar at \$\$0.25\$ each, and 1 jar of yeast at \$\$2.50\$, while you also have a store coupon that gives you \$\$0.75\$ off for each of the 8 items you bought. Applying the order of operations ensures you correctly calculate your total bill: \((3 \times 4.50) + (2 \times 0.25) + 2.50 - (8 \times 0.75)\). Following the rules of math prevents costly errors and ensures accuracy in your financial and daily planning.