Find the Error  A student is finding a 6.5% commission on $525.08 worth of sales. Find the student's mistake and correct it. Let x represent the amount of commission.

 

x525.08=65100
 

 

x525.08 = 0.65
 

 

x = 341.30
 

 

The student wrote the percent as 
 out of 100.

It should be 
 out of 100.

The commission should be $
.

Let's go through the steps the student used to find the 6.5% commission on $525.08:

1. **The student's equation**: 
   \[
   \frac{x}{525.08} = \frac{65}{100}
   \]
   This equation is incorrect because the student wrote **6.5%** as **65 out of 100** instead of **6.5 out of 100**. The correct equation should be:
   \[
   \frac{x}{525.08} = \frac{6.5}{100}
   \]

2. **Step 2**: 
   The student seems to have incorrectly simplified the percentage to **0.65** instead of **0.065**. 
   
   The correct form would be:
   \[
   x = 525.08 \times 0.065
   \]

3. **Step 3**: 
   Let's calculate the correct commission:

   \[
   x = 525.08 \times 0.065 = 34.1302
   \]

   Rounding to two decimal places, the correct commission is:
   \[
   x = 34.13
   \]

### The student's mistake:
- They wrote 6.5% as 65/100 instead of 6.5/100.
- They mistakenly multiplied by **0.65** instead of **0.065**.

### Correct Commission:
The correct commission should be **$34.13**.

---

Do you need further details or have any questions?

Here are some related questions:

1. How do you convert percentages to decimals correctly?
2. Why is 6.5% represented as 0.065 in decimal form?
3. Can you show how to convert other percentages (like 15%) into decimals?
4. What is the difference between percent and percentage points?
5. How would the calculation change if the percentage was 7% instead of 6.5%?

**Tip**: Always double-check your percentage conversion when solving commission or percentage-based problems!

Find the Error: A student is finding a 6.5% commission on $525.08 worth of sales. Find the student's mistake and correct it. Let x represent the amount of commission. The student wrote the percent as 65 out of 100 instead of 6.5 out of 100.

Learn how to correct a student's mistake when calculating a 6.5% commission on $525.08 worth of sales. This problem demonstrates how to properly convert percentages to decimals and find commission amounts. Suitable for Grades 6-8.

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