math help please!

[Disney Addicted]

My son just finished some Grade 9 math homework. I double-check his answers and make him re-do any questions he answered incorrectly. Thanks to the text book examples (and answers in the back that he doesn't seem to have figured out yet), so far I can refresh my own memory and explain what he did wrong/how the equation works if he cannot come up with the correct formula/answer.

This one question has me stumped however. The book says the answer is 24. He and I are coming up with a different answer.

Substitute the given values into each expression. Then, evaluate the expression.

x = -6 for this question

x^2 - 2x - 24

This is what we get:
-6^2 - (2 x -6) - 24
-(6x6) - (2 x -6) - 24
-36 - (-12) - 24
-24 - 24
0

What are we doing wrong?

 

[R&RsMom]

I think I can help:
-6 squared = -6 x -6 = +36 (minus X minus =+)
-(2 x -6) = - (-12) = +12
So: +36 +12 - 24 = 24

 

[deedubb]

It's 36 - (-12) -24 which is 48 - 24 = 24

 

[G719]

-6^2 Is -6 x -6 = 36

So 36 -2x-6 -24 = 36 + 12 - 24 = 48-24= 24

 

[AngelDisney]

I am math teacher. When substituting, it’s better to put brackets around the substituted value. It’s (-6)^2 not -6^2 which is negative of 6^2. (-6)^2 is -6 x -6 whereas -6^2 is -(6^2) if we follow BEDMAS to simplify 6^2 before multiplying by the negative.
Then 36 + 12 - 24 is 24.

Also -24-24 is -48 not 0 because you have a total of 48 negatives when combining the two numerical terms. Starting at -24 going to the left 24 further to -48 on the number line.

 

[Disney Addicted]

Well, hell. (wry grin) Thanks everyone! That's originally what I was insisting on. A negative number x a negative number comes out a positive number.

But his darn text book shows an example that is the opposite. So we were following that example and kept coming up with a negative 36

His text book shows this example:
-3^4 = -(3 x 3 x 3 x 3) = -81

Where as I wanted to say it should be -3 x -3 x - 3 x -3 = 81 positive.

 

[AngelDisney]

Well, hell. (wry grin) Thanks everyone! That's originally what I was insisting on. A negative number x a negative number comes out a positive number.

But his darn text book shows an example that is the opposite. So we were following that example and kept coming up with a negative 36

His text book shows this example:
-3^4 = -(3 x 3 x 3 x 3) = -81

Where as I wanted to say it should be -3 x -3 x - 3 x -3 = 81 positive.

The example is correct. Your substitution process was incorrect.
x^2 = (-6)^2 =-6 x -6 = 36
It’s not -6^2.
-6^2 = -(6 x 6) = -36 by BEDMAS

 

[Disney Addicted]

I am math teacher. When substituting, it’s better to put brackets around the substituted value. It’s (-6)^2 not -6^2 which is negative of 6^2. (-6)^2 is -6 x -6 whereas -6^2 is -(6^2) if we follow BEDMAS to simplify 6^2 before multiplying by the negative.
Then 36 + 12 - 24 is 24.

Also -24-24 is -48 not 0 because you have a total of 48 negatives when combining the two numerical terms. Starting at -24 going to the left 24 further to -48 on the number line.

Thanks for replying. I'm confused as to why the textbook is showing us a different example though (see above post). Is it incorrect? Or is it showing us something else entirely different?

I was taking the final part of the equation to mean "minus a positive 24" so negative 24 minus positive 24 = 0. Because it was not written as -24 but had a space like this - 24.

 

[Disney Addicted]

I just saw your reply. Thank you.

 

[AngelDisney]

Thanks for replying. I'm confused as to why the textbook is showing us a different example though (see above post). Is it incorrect? Or is it showing us something else entirely different?

I was taking the final part of the equation to mean "minus a positive 24" so negative 24 minus positive 24 = 0. Because it was not written as -24 but had a space like this - 24.

Negative 24 minus 24
Think about your bank is overdraft by 24 dollars then you withdraw another 24 dollar. How much money is in your account? You owe 48 dollar. It’s -48.

 

[Disney Addicted]

Negative 24 minus 24
Think about your bank is overdraft by 24 dollars then you withdraw another 24 dollar. How much money is in your account? You owe 48 dollar. It’s -48.

Yes, I realize.

What I meant was in my original post we were coming up with 0 because

-6^2 - (2 x -6) - 24 (<-- I took the final part as minus a positive 24)
-(6x6) - (2 x -6) - 24
-36 - (-12) - 24
-24 - 24 (<-- so a negative 24 minus a positive 24 = 0)
0

ARgh.. never mind. Man, I feel so stupid tonight. I see, I see (yes, I see it's -48). OMG.

Thank you for replying! I didn't realize we were doing the subsitution process incorrectly. Now if I can just get my son to believe me when I explain what we were doing wrong and how to do it correctly. He's so stubborn.

 

[AngelDisney]

Yes, I realize.

What I meant was in my original post we were coming up with 0 because

-6^2 - (2 x -6) - 24 (<-- I took the final part as minus a positive 24)
-(6x6) - (2 x -6) - 24
-36 - (-12) - 24
-24 - 24 (<-- so a negative 24 minus a positive 24 = 0)
0

ARgh.. never mind. Man, I feel so stupid tonight. I see, I see. OMG.

Thank you for replying! I didn't realize we were doing the subsitution process incorrectly. Now if I can just get my son to believe me when I explain what we were doing wrong and how to do it correctly. He's so stubborn.

I am trying to explain that -24 - 24 is not 0. It’s -48.

 

[Disney Addicted]

lol - I know, I know. I saw and edited my answer. Like I said, feeling particularly slow tonight. It's time for bed. I appreciate your help!!

 

[damo]

The example is correct. Your substitution process was incorrect.
x^2 = (-6)^2 =-6 x -6 = 36
It’s not -6^2.
-6^2 = -(6 x 6) = -36 by BEDMAS

What AngelDisney has posted is a REALLY important concept for your son to understand. I'm also a high school math teacher and I can guarantee that a bunch of kids will struggle with this, so make sure you have him do lots of questions like this to drill it in.

 

[Disney Addicted]

What AngelDisney has posted is a REALLY important concept for your son to understand. I'm also a high school math teacher and I can guarantee that a bunch of kids will struggle with this, so make sure you have him do lots of questions like this to drill it in.

Yes, that was a hard concept and it makes a huge difference. What I am understanding from this is we follow the text book example as long as it's specifically giving a base number (ie, 2^5 or the -3^4 example). But anytime an equation calls for a substitution, we need to put brackets around it and follow AngelDisney's example.

I am grasping this correctly now AngelDisney, Damo?

 

[AngelDisney]

Yes, that was a hard concept and it makes a huge difference. What I am understanding from this is we follow the text book example as long as it's specifically giving a base number (ie, 2^5 or the -3^4 example). But anytime an equation calls for a substitution, we need to put brackets around it and follow AngelDisney's example.

I am grasping this correctly now AngelDisney, Damo?

You got it!

 

[AngelDisney]

What AngelDisney has posted is a REALLY important concept for your son to understand. I'm also a high school math teacher and I can guarantee that a bunch of kids will struggle with this, so make sure you have him do lots of questions like this to drill it in.

Totally agree with you here!

 

[hdrolfe]

What grade math is this? Just so I'm prepared

 

[AngelDisney]

What grade math is this? Just so I'm prepared

DisneyAddicted mentioned Grade 9 in OP.

 

[mort1331]

Now if we can only get everyone to understand Disney math. How they calculate bridging (or not), how to add on a day or two. How and when the pricing goes up, and when to buy. So many variables not enough letters.
Good luck all.