Question

Leticia simplified an expression. Her work is shown below. 4.5 divided by one-fourth + 2 and one-half minus 0.75 times 8

Step 1 18 + 2 and one-half minus 0.75 times 8
Step 2 18 + 1.75 times 8
Step 3 18 + 14
Step 4 32
Where did Leticia make her first mistake?

A. 1
B. 2
C. 3
D. 4

Answer 1

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.