Question
Kimi tried to evaluate an expression. Here is her work:
18–321–(9–5)2+8
=
18–321–42+8 Step 1
=
18–3[21–16]+8 Step 2
=
18–35+8 Step 3
=
155+8 Step 4
=
75+8 Step 5
=
83 Step 6
Is Kimi's work correct?
Questions And where did she make the mistake like step
18–321–(9–5)2+8
=
18–321–42+8 Step 1
=
18–3[21–16]+8 Step 2
=
18–35+8 Step 3
=
155+8 Step 4
=
75+8 Step 5
=
83 Step 6
Is Kimi's work correct?
Questions And where did she make the mistake like step
Answers
GPT-4o mini
Let's evaluate Kimi's expression step by step and see where she made a mistake.
The original expression is:
\[ 18 - 321 - (9 - 5)^2 + 8 \]
### Step 1: Evaluate \((9 - 5)^2\)
\[
(9 - 5) = 4
\]
\[
(9 - 5)^2 = 4^2 = 16
\]
So we rewrite the expression:
\[
18 - 321 - 16 + 8
\]
### Step 2: Perform the operations from left to right
Now let's perform the operations in order:
1. Start with \(18 - 321\):
\[
18 - 321 = -303
\]
2. Then, subtract \(16\):
\[
-303 - 16 = -319
\]
3. Finally, add \(8\):
\[
-319 + 8 = -311
\]
### Final Result
The correct result is:
\[
-311
\]
### Where Did Kimi Go Wrong?
Kimi's mistakes occurred primarily in the following steps:
- **Step 1 to Step 2**: She incorrectly tried to break down the expression incorrectly and also incorrectly evaluated \((9 - 5)^2\) as \(4^2\) but made errors in transitions.
- **Step 3**: The evaluation of \(321\) itself was incorrect, which contributed to further mistakes down the line.
Thus, Kimi's final calculation was incorrect, and her final answer of \(83\) is not correct. The correct final result of evaluating the expression is \(-311\).
The original expression is:
\[ 18 - 321 - (9 - 5)^2 + 8 \]
### Step 1: Evaluate \((9 - 5)^2\)
\[
(9 - 5) = 4
\]
\[
(9 - 5)^2 = 4^2 = 16
\]
So we rewrite the expression:
\[
18 - 321 - 16 + 8
\]
### Step 2: Perform the operations from left to right
Now let's perform the operations in order:
1. Start with \(18 - 321\):
\[
18 - 321 = -303
\]
2. Then, subtract \(16\):
\[
-303 - 16 = -319
\]
3. Finally, add \(8\):
\[
-319 + 8 = -311
\]
### Final Result
The correct result is:
\[
-311
\]
### Where Did Kimi Go Wrong?
Kimi's mistakes occurred primarily in the following steps:
- **Step 1 to Step 2**: She incorrectly tried to break down the expression incorrectly and also incorrectly evaluated \((9 - 5)^2\) as \(4^2\) but made errors in transitions.
- **Step 3**: The evaluation of \(321\) itself was incorrect, which contributed to further mistakes down the line.
Thus, Kimi's final calculation was incorrect, and her final answer of \(83\) is not correct. The correct final result of evaluating the expression is \(-311\).