Question
Chase tried to evaluate an expression. Here is his work:
2(12÷2)2–14+6
=
262–14+6 Step 1
=
236–14+6 Step 2
=
72–14+6 Step 3
=
72–20 Step 4
=
52 Step 5
Is Chase's work correct? if not why
2(12÷2)2–14+6
=
262–14+6 Step 1
=
236–14+6 Step 2
=
72–14+6 Step 3
=
72–20 Step 4
=
52 Step 5
Is Chase's work correct? if not why
Answers
Answered by
GPT-4o mini
Let's go through Chase's calculations step-by-step to verify if his work is correct.
1. **Original Expression**: \(2(12 \div 2)2 - 14 + 6\)
2. **Step 1**:
- He computed \(12 \div 2\), which equals 6.
- The expression now is \(2(6)2 - 14 + 6\).
- However, Chase seems to have rewritten this incorrectly. It should have been understood as \(2 \times 6 \times 2\).
- Properly, it would be \(2 \times 6 \times 2 = 24\), not 262.
3. **Step 2**:
- He writes \(236\), but this value does not match our expectation. Instead, it should have been \(24 - 14 + 6\).
4. **From Step 3 to Step 5**:
- Following from the incorrect value in Step 2, his calculations thereafter are misinformed.
- The steps he took, starting from \(236\) to \(72\) and beyond, are not valid because the previous step was incorrect.
The correct evaluation of the original expression is as follows:
\[ 2(12 \div 2) \times 2 - 14 + 6 \]
Calculating this:
1. First calculate \(12 \div 2 = 6\).
2. Then we have \(2 \times 6 \times 2 = 24\).
3. Now, substitute it back:
\[ 24 - 14 + 6 \]
4. Simplify:
- \(24 - 14 = 10\)
- \(10 + 6 = 16\)
So, the correct answer is \(16\).
**Conclusion**: Chase's work is incorrect due to errors in the handling of the expression, particularly in interpreting multiplication and order of operations. The correct final answer is \(16\).
1. **Original Expression**: \(2(12 \div 2)2 - 14 + 6\)
2. **Step 1**:
- He computed \(12 \div 2\), which equals 6.
- The expression now is \(2(6)2 - 14 + 6\).
- However, Chase seems to have rewritten this incorrectly. It should have been understood as \(2 \times 6 \times 2\).
- Properly, it would be \(2 \times 6 \times 2 = 24\), not 262.
3. **Step 2**:
- He writes \(236\), but this value does not match our expectation. Instead, it should have been \(24 - 14 + 6\).
4. **From Step 3 to Step 5**:
- Following from the incorrect value in Step 2, his calculations thereafter are misinformed.
- The steps he took, starting from \(236\) to \(72\) and beyond, are not valid because the previous step was incorrect.
The correct evaluation of the original expression is as follows:
\[ 2(12 \div 2) \times 2 - 14 + 6 \]
Calculating this:
1. First calculate \(12 \div 2 = 6\).
2. Then we have \(2 \times 6 \times 2 = 24\).
3. Now, substitute it back:
\[ 24 - 14 + 6 \]
4. Simplify:
- \(24 - 14 = 10\)
- \(10 + 6 = 16\)
So, the correct answer is \(16\).
**Conclusion**: Chase's work is incorrect due to errors in the handling of the expression, particularly in interpreting multiplication and order of operations. The correct final answer is \(16\).