Question

Grace was given the description “three less than the quotient of a number squared and nine, increased by eight” and was asked to evaluate it when n = 6. Her work is shown below.

Step 1: 3 minus StartFraction n squared Over 9 EndFraction + 8
Step 2: 3 minus StartFraction 6 squared Over 9 EndFraction + 8
Step 3: 3 minus StartFraction 36 Over 9 EndFraction + 8
Step 4: 3 minus 4 + 8
Step 5: 7

In which step did she make an error?
step 1
step 2
step 4
step 5

Answer 1

Let's analyze Grace's work step by step to find where she made an error.

1. The description states “three less than the quotient of a number squared and nine, increased by eight.” This means we should start with the expression:
\[
\frac{n^2}{9} - 3 + 8
\]
which should actually be written as:
\[
\frac{n^2}{9} - 3 + 8
\]
or simplified to:
\[
\frac{n^2}{9} + 5
\]

2. Grace's Step 1:
\[
3 - \frac{n^2}{9} + 8
\]
Should have been:
\[
\frac{n^2}{9} - 3 + 8
\]
Grace correctly noted that it should be “three less than the quotient” indicating it should subtract 3, but she put the 3 in front of the fraction which is incorrect.

3. Let's go through her steps:
- Step 1: Incorrect expression.
- Step 2:
\[
3 - \frac{6^2}{9} + 8 \quad \text{(using the incorrect expression)}
\]
- Step 3:
\[
3 - \frac{36}{9} + 8 = 3 - 4 + 8
\]
- Step 4:
\[
3 - 4 + 8 = 7
\]

Given that her entire expression is built on an incorrect basis (Step 1), we can conclude that the error began there.

Thus, the correct answer is **step 1** where the error was made.