Matt and Karen both attempted to solve the same math problem, but they arrived at different answers. Let's examine their work step-by-step to identify any errors and determine who, if either, is correct.
**Matt's Work:**
1. \(6 - 4(3 - 5)^2 + 30 \div 5\)
2. \(6 - 4(-2)^2 + 30 \div 5\)
3. \(6 - 4(4) + 30 \div 5\)
4. \(6 - 16 + 30 \div 5\)
5. \(-10 + 30 \div 5\)
6. \(20 \div 5\)
7. Result: \(4\)
**Karen's Work:**
1. \(6 - 4(3 - 5)^2 + 30 \div 5\)
2. \(6 - 4(-2)^2 + 30 \div 5\)
3. \(6 - 4(-4) + 30 \div 5\)
4. \(6 + 16 + 30 \div 5\)
5. \(6 + 16 + 6\)
6. \(22 + 6\)
7. Result: \(28\)
**Analysis:**
- Both Matt and Karen initially rewrite the expression correctly, substituting \( (3 - 5) \) with \(-2\).
- In step 3, Matt calculates \((-2)^2\) as \(4\), which is correct. However, Karen incorrectly calculates \((-2)^2\) as \(-4\).
- Matt proceeds with his calculation correctly by multiplying and following the order of operations, but Karen's incorrect calculation in step 3 leads to an incorrect result.
**Correct Solution:**
1. Start with \(6 - 4(3 - 5)^2 + 30 \div 5\).
2. Substitute \(3 - 5\) with \(-2\): \(6 - 4(-2)^2 + 30 \div 5\).
3. Calculate \((-2)^2\) as \(4\): \(6 - 4(4) + 30 \div 5\).
4. Multiply: \(6 - 16 + 30 \div 5\).
5. Perform division: \(-10 + 6\).
6. Add to find the result: \(4\).
Matt is correct, and the correct answer is \(4\). Karen made an error by calculating \((-2)^2\) incorrectly.
Answer (3)
so in matt's equation, he made a mistake in the a transision from line 2 to line 3 in line 2: -4(-2)2 in line 3: -4(4) the mistake is that -2 times 2 is not equal +4 it is equal to -4 also from lines 5 to 6 he made a mistake in order of opperations (mulit division then addition and subtract) line 5: -10+30/5 line 6: 20/5
so he first subtracted 10 then divided, he should have divided then subtracted so the equation should have equaled
Karen used the correct (-) times (+) property and the order of operations so Karen is correct and Matt is wrong.
Karen is correct. (-2)2 is -4, not 4 in Matt's answer. Also, Karens, order of operations on the 4th line is correct. She does her division first, and Matt completes his subtraction first. PEMDAS, parenthesis, exponents, multiplication, division, addition, subtraction.
Matt is correct; his final answer is 4 after correctly following the order of operations. Karen made an error by incorrectly calculating ( − 2 ) 2 as − 4 instead of 4 , leading to her incorrect answer of 28 . The correct answer to the math problem is 4 .
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