Final answer:
Leticia's first mistake was in Step 2 where she incorrectly combined '2 and one-half' with '0.75 times 8'. The accurate operation should have been to first multiply 0.75 by 8 and then add '2 and one-half' to the result along with the previous sum of 18.
Step-by-step explanation:
The expression Leticia simplified is 4.5 divided by one-fourth + 2 and one-half minus 0.75 times 8. Leticia made her first mistake at Step 2 where she incorrectly combined the terms 2 and one-half and 0.75 times 8. Let's review her steps:
- Step 1. 18 + 2 and one-half minus 0.75 times 8
(Here, she correctly converted 4.5 divided by one-fourth to 18). - Step 2. 18 + 1.75 times 8
(This is where the mistake occurred; she should have multiplied 0.75 by 8 first, before adding the 2 and one-half). - Step 3. 18 + 14
(Assuming her second step was correct, this step correctly multiplies 1.75 by 8). - Step 4. 32
(Again, assuming her previous steps were correct, this sums up to 32).
The mistake was the incorrect assumption that 2 and one-half minus 0.75 times 8 equals 1.75 times 8. She should have first performed the multiplication of 0.75 and 8 to correctly evaluate her expression.