Questions: Leticia simplified an expression. Her work is shown below. 4.5-1/4+2 1/2-0.75 x 8 Step 1 18+2 1/2-0.75 x 8 Step 2 18+175 x 8 Step 3 18+14 32 Where did Leticia make her first mistake?

Leticia simplified an expression. Her work is shown below. 4.5-1/4+2 1/2-0.75 x 8 Step 1 18+2 1/2-0.75 x 8 Step 2 18+175 x 8 Step 3 18+14 32 Where did Leticia make her first mistake?
Transcript text: Leticia simplified an expression. Her work is shown below. \[ 4.5-\frac{1}{4}+2 \frac{1}{2}-0.75 \times 8 \] Step 1 \[ 18+2 \frac{1}{2}-0.75 \times 8 \] Step 2 \[ 18+175 \times 8 \] Step 3 \[ 18+14 \] 32 Where did Leticia make her first mistake?
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Solution

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Solution Steps

To determine where Leticia made her first mistake, we need to follow the order of operations (PEMDAS/BODMAS) and simplify the expression step by step. We will compare each step with Leticia's work to identify the error.

Step 1: Simplify the Original Expression

The original expression is: \[ 4.5 - \frac{1}{4} + 2.5 - 0.75 \times 8 \]

First, we handle the multiplication: \[ 0.75 \times 8 = 6 \]

So the expression becomes: \[ 4.5 - \frac{1}{4} + 2.5 - 6 \]

Step 2: Convert Fractions to Decimals

Next, we convert \(\frac{1}{4}\) to its decimal form: \[ \frac{1}{4} = 0.25 \]

So the expression now is: \[ 4.5 - 0.25 + 2.5 - 6 \]

Step 3: Perform Addition and Subtraction

Now, we perform the addition and subtraction from left to right: \[ 4.5 - 0.25 = 4.25 \] \[ 4.25 + 2.5 = 6.75 \] \[ 6.75 - 6 = 0.75 \]

Final Answer

\[ \boxed{0.75} \]

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