Semi-urgent math question -- we think the answer book is wrong

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The question is:

-22 - (-2)3

-22 - (-2)3

= 4 - (-8)

= 4+8

= 12

-22 - (-2)3

= -4 -(-8)

= -4 + 8

= 4

Who is right? And if ds is wrong, why?

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Ok - the answer book is right. It's because the first -2 is not in parens. You could also write it as ...

(-1)(2^2) - (-2)^3

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-22 - (-2)3

=-(22 )- (-2)3

=-4 - (-8)

=-4+8

=4

The first part is negative (two squared). So it is -(2*2), not (-2*-2)

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The question is:

-22 - (-2)3

-22 - (-2)3

= 4 - (-8)

= 4+8

= 12

-22 - (-2)3

= -4 -(-8)

= -4 + 8

= 4

Who is right? And if ds is wrong, why?

-(2^2) - [(-2)^3]

= -(4) - [-8]

= 4

Think of it as:

0 - 22 - (-2)3

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Answer book is right. It's because the negative square of 2 is -4. If -2 was in parens, the square of a negative 2 is positive. Clear as mud?

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Thank you for your responses and explanations. That made it clearer. Somewhere along the way, we both forgot the issue of parentheses. Ds is now very sad that he missed that. But... at least we've learned something! So, it's all good.

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Audrey,

I did the problem without scrolling down to the book answer, and I got what your son got. Now I have to try to figure out why my (our) answer is wrong.

I agree, this is befuddling.

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-22 - (-2)3

=-(22 )- (-2)3

=-4 - (-8)

=-4+8

=4

The first part is negative (two squared). So it is -(2*2), not (-2*-2)

-2(squared) is not equal to (-2)squared? No wonder Algebra was a blur for me. Is there hope to ever understand it? Oldest is now in 2nd grade... :sad:

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Oh, and also another reason -- with the order of operations, exponents are done first.

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-2(squared) is not equal to (-2)squared? No wonder Algebra was a blur for me. Is there hope to ever understand it? Oldest is now in 2nd grade... :sad:

The exponent acts first unless parentheses are present.

-22 = -(22) = - (2 x 2) = -4 OR -22 = (-1) x (22) = (-1) x (2 x 2) = (-1) x (4) = -4

(-2)2 = (-2) x (-2) = 4

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-2(squared) is not equal to (-2)squared? No wonder Algebra was a blur for me. Is there hope to ever understand it? Oldest is now in 2nd grade... :sad:

Yup. I missed it too. I think I missed the day on order of operations. :lol: I guess it's a good thing our oldest's are in 2nd. We have time to self educate math! ;)

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The exponent acts first unless parentheses are present.

-22 = -(22) = - (2 x 2) = -4 OR -22 = (-1) x (22) = (-1) x (2 x 2) = (-1) x (4) = -4

(-2)2 = (-2) x (-2) = 4

Ah, I remember now: The Dreaded PEMDAS and the Exponents of Death.

Thanks, nmoira! ;)

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Yup. I missed it too. I think I missed the day on order of operations. :lol: I guess it's a good thing our oldest's are in 2nd. We have time to self educate math! ;)

I must have been out that day, too. ;)

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I remind my kids that the exponent only applies to whatever it "touches": If it touches parentheses, then it squares (or cubes or whatever) everything within the parentheses. But if it's touching a number or a variable, it only applies to that number/variable.

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