Question

Two of your friends, Matt and Karen, both run to you to settle a dispute. They were working on a math problem, and got different answers. Wisely, you decide to look at their work to see if you can spot the source of confusion.
Matt

6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(4) + 30 ÷ 5
6 – 16 + 30 ÷ 5
−10 + 30 ÷ 5
20 ÷ 5
4
Karen

6 – 4(3 – 5)2 + 30 ÷ 5
6 – 4(–2)2 + 30 ÷ 5
6 – 4(−4) + 30 ÷ 5
6 + 16 + 30 ÷ 5
6 + 16 + 6
22 + 6
28 Explain to Matt and Karen who, if either, is correct, and identify errors that you find. Provide the correct manner to fix those solutions, and identify the correct answer. Use complete sentences.

Answer 1

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.

Answer 2

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.