Question

Clarence tried to evaluate an expression. Here is his work:
9+(73–19+4)2÷3
=
9+(21–19+4)2÷3 Step 1
=
9+(2+4)2÷3 Step 2
=
9+62÷3 Step 3
=
9+36÷3 Step 4
=
9+12 Step 5
=
21 Step 6
Is Clarence's work correct?




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Answer 1

Let's go through Clarence's work step by step and check for any mistakes.

Given expression:
\[ 9 + (73 - 19 + 4) \cdot 2 \div 3 \]

**Step 1:**
\[ 9 + (73 - 19 + 4) \cdot 2 \div 3 \]
This is correct as it is the original expression.

**Step 2:**
Clarence wrote:
\[ 9 + (21 - 19 + 4) \cdot 2 \div 3 \]
This step is incorrect. The calculation \(73 - 19\) should yield \(54\), not \(21\). The correct calculation is:
\[ 73 - 19 = 54\]
So this should be:
\[ 9 + (54 + 4) \cdot 2 \div 3 \]

**Step 3:**
He then simplified \(21 - 19 + 4\) to \(2 + 4\) which is, as shown, incorrect. He should have continued with:
\[ 54 + 4 = 58\]
Then it should be:
\[ 9 + (58) \cdot 2 \div 3 \]

**Step 4 & 5:**
Continuing his incorrect method, he wrote:
\[ 9 + 6^2 \div 3 \]
But this is based on incorrect inputs and calculations. It should have eventually gone to:
\[ 9 + (58 \cdot 2) \div 3 \]
Calculating \(58 \cdot 2\):
\[ 116 \div 3 = \frac{116}{3} \]

**Final Step:**
After calculating \(116 \div 3\), we would find \(9 + \frac{116}{3} = 9 + 38.67\), which is not \(21\).

**Conclusion:**
Clarence's work is incorrect. The calculated final answer should have been around \(47.67\) if followed correctly, rather than \(21\).