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 any, is correct and identify errors that you find. Provide the correct manner to fix those solutions and identify correct answer

Answer 1

Why is karen wrong?

Answer 2

The first difference is the line
Matt: 6 – 4(4) + 30 ÷ 5
Karen: 6 – 4(−4) + 30 ÷ 5

matt is multiplying the (-2)2 and getting 4
karen is multiplying the (-2)2 and getting -4

Answer 3

the next problem is the order of operations -
matt does brackets, multiplications, subtracting, adding then dividing
karen does brackets, multiplication, division, then adding (she does not have and subtracting to do)

only one of those is the right way

Answer 4

Matt is wrong because after the second step he puts 4 in the brackets instead of negative 4 which alters his whole equation. When you multiply 2 by -2 you get -4, not 4. Matt also messes up after fourth step when he divides instead of subtracts first, and we know that you are supposed to divide first following the rule of P.E.D.M.A.S (Parenthesis, Exponents, Division, Multiplication, Addition, Subtraction.) Matt's mistake was subtracting before dividing, and putting product as positive when it should be a negative. We know that Karen is wrong because she follows the rules of P.E.D.M.A.S to the very end of her equation. She goes Parenthesis, then division because there's no exponents, then addition because there is no multiplication and no subtraction afterwards.

Answer 5

This was my original answer, but my teacher told me that Karen is also wrong and asked me to identify where she went wrong and what is the correct answer?

Answer 6

@kantalope

Answer 7

I can't see any mistake Karen did... Perhaps your teacher made a mistake? Of course I am probably the one in error here.

Answer 8

I think she made a mistake too, but I honestly don't know and I don't
want to get her mad

Answer 9

6 – 4(−4) + 30 ÷ 5--->third line of karen's answer
(-2)^2= POSITIVE 4

Answer 10

Where does it say -2 squared?

Answer 11

That is one more thing. Did you write your equations with the correct format? Sometimes when you copy and paste those with mathematical format it comes out wrong when you paste it.

Answer 12

I'm checking the website now. One second ...

Answer 13

is it \[6 – 4(3 – 5)2 + 30 ÷ 5?\]
I assume that the two is exponent because it is placed after the bracket...

Answer 14

You are so right. When I copied and pasted it onto word pad from the website it changed to a regular two. Only God knows why.

Answer 15

oh ok, there you go.. karen's mistake is only squaring a negative number

Answer 16

yeah..(^_^)

Answer 17

I think Matt's mistake is not doing the division first before addition/subtraction.

Answer 18

Thank you SO MUCH for helping me to realize that. The correct answer would be -4?

Answer 19

Division and multiplication have to be done before addition and subtraction while any of each pair can be done first among them.