-2.5(1.4+3.1) + 6.9(-4.3)

These are the steps each student used.

Student P

Step 1: -3.5 + 7.75 + 6.9(-4.3)

Step 2: -3.5 + 7.75 - 29.67

Step 3: 7.75 - 3.5 - 29.6

Step 4: -25.42

Student Q

Step 1: -3.5 - 7.75 + 6.9(-4.3)

Step 2: -3.5 - 7.75 - 29.67

Step 3: -(3.5 - 7.75 - 29.67)

Step 4: -(-33.92)

Step 5: 33.92

Analyze the steps and describe any errors made by Student P and Student Q.

**Answer:**

Given expression:

-2.5(1.4+3.1) + 6.9(-4.3)

__Student P__

Step 1: -3.5 **+ 7.75** + 6.9(-4.3)

Step 2: -3.5 **+ 7.75** - 29.67

Step 3: **7.75** - 3.5 - 29.67

Step 4: **-25.42**

Student P made an error in step 1. When expanding the first part of the expression, they forgot the negative sign when multiplying -2.5 by 3.1.

So Step 1 should be: -3.5 **- 7.75** + 6.9(-4.3).

This error then impacted all following steps and gave an incorrect final solution.

__Student Q__

Step 1: -3.5 - 7.75 + 6.9(-4.3)

Step 2: -3.5 - 7.75 - 29.67

Step 3: **-(3.5 - 7.75 - 29.67)**

Step 4: **-(-33.92)**

Step 5: **33.92**

Student Q made an error in step 3. When placing the numbers in parentheses and placing a negative sign outside the parentheses, they should have changed the two negative signs inside the parentheses to positives.

So Step 3 should be: -(3.5 + 7.75 + 29.67).

This error then impacted all following steps and gave an incorrect final solution.

__Correct steps and solution__

Step 1: -3.5 - 7.75 + 6.9(-4.3)

Step 2: -3.5 - 7.75 - 29.67

Step 3: -(3.5 + 7.75 + 29.67)

Step 4: -(40.92)

Step 5: -40.92

Let's solve

Both did error in signs