Okay Math Geniusues... What's 48÷2(9+3) ?

[MyTrixie143]

Originally Posted by Ellie May

Okay, if M and D are equal, then it makes sense why it would be done left to right , but:

48/2(9+3)
48/2(12)
We still haven't gotten rid of the parentheses. So we can just pull 12 out and make it read 48/2x12 and ignore that the 12 is still in the ()?

Technically you got rid of the parentheses by adding and getting 12. It is now only there to show that you need to multiply the 2 and the 12.

[JeanieK]

Originally Posted by Ellie May

Okay, if M and D are equal, then it makes sense why it would be done left to right , but:

48/2(9+3)
48/2(12)
We still haven't gotten rid of the parentheses. So we can just pull 12 out and make it read 48/2x12 and ignore that the 12 is still in the ()?

Yes, you do the math that is in the ( ). Once thfat is done there is not longer fa nee for the parentheses. The order would be different if there were no ( )

48/2*9+3 Would give you a different answer because you would do the multiplication and division first and the addition last

48/2*9+3
48/2=24
24*9=288
216+3=219

See why the parentheses are important?

[JeanieK]

Originally Posted by MyTrixie143

Technically you got rid of the parentheses by adding and getting 12. It is now only there to show that you need to multiply the 2 and the 12.

yes, you could, at this point, replace the parentheses with * or x

[JeanieK]

Originally Posted by MyTrixie143

Ah by why did you multiply the 2x12 first? After the parentheses in this equation you work left to right. The parentheses around the 12 just means multiply that is the only reason it is still there, to tell you to multiply. Technically you got rid of the parentheses by adding the 9+3. So the equation technically looks like this: 48/2x12. Working from left to right you divide before you multiply hence coming up with 288.

And that is why it is important to work left to right, if you don't you get the wrong answer.

if we knew where the numbers came from the order would be more obvious.

[107barney]

48÷2(9+3)

I am solving the problem by first dealing w/ the parentheses
1) 9+3 = 12

Then I am treating multiplication and division as on equal footing but going from left to right to solve the equation

2) 48÷2 = 24

3) 12 x 24 = 288

Therefore 48÷2(9+3) = 288

[kjc]

Originally Posted by Ellie May

Okay, if M and D are equal, then it makes sense why it would be done left to right , but:

48/2(9+3)
48/2(12)
We still haven't gotten rid of the parentheses. So we can just pull 12 out and make it read 48/2x12 and ignore that the 12 is still in the ()?

Exactly... no bc the number outside the () has to be applied to the number inside the () before moving forward. The () is like glue, all operations must happen to it first before going on. You see 2(12) then you can read it as 2 x 12, but you perform the function and make it 24, then put it back into the problem 48/24. which =2.

If that were allowed, you could also do it like 48/2x9(+3) or 48/2x9+3 or ...

[kjc]

Originally Posted by 107barney

48÷2(9+3)

I am solving the problem by first dealing w/ the parentheses
1) 9+3 = 12

Then I am treating multiplication and division as on equal footing but going from left to right to solve the equation

2) 48÷2 = 24

3) 12 x 24 = 288

Therefore 48÷2(9+3) = 288

You skipped a step, and added a step. You used the 2 twice, X 12 then 48/2... you can only use it once, and it's a multiplier of the number inside the ().

[Ellie May]

So if we can just get rid of the () after adding:

48/2(12)=
48/2x12

Then that means that the quadratic equation:
x=-b+or- the square root of b^-4(a)(c)/2(a)

Then why don't we divide everything by 2 in this case and then multiply by a? In this case we could remove the a from the () and write 2 x a, but it still has to be done separately from the rest of the problem.

[107barney]

Originally Posted by kjc

You skipped a step, and added a step. You used the 2 twice, X 12 then 48/2... you can only use it once, and it's a multiplier of the number inside the ().

Huh?

I'll rephrase --

48÷2(9+3)

Answer:
I added 9 + 3 to get 12 to lose the parenthesis giving me
48÷2 x 12 and you have to work from L to R.

48 divided by 2 = 24 and 24 x 12 = 288

Not sure what you mean about using the two twice.

[107barney]

Originally Posted by Ellie May

So if we can just get rid of the () after adding:

48/2(12)=
48/2x12

Then that means that the quadratic equation:
x=-b+or- the square root of b^-4(a)(c)/2(a)

Then why don't we divide everything by 2 in this case and then multiply by a? In this case we could remove the a from the () and write 2 x a, but it still has to be done separately from the rest of the problem. So how can we be sure that the (9+3) is not part of the denominator if written on one line?

Here is the equation for the answer 2:

48/[2(9+3)]

This makes the denominator 24 so when you do this above equation, you would get two. BUT...the question posted did not have the brackets, you guys can't make them up.

[roseylovestosho]

I am watching this thread closely because I hope you guys will arrive at the answer because quite frankly Algebra perplexes me! I do love calculus though!

[JMuedog]

Originally Posted by fasteddie

That's what I thought too, but there seems to be fierce debate about the order of which goes first and whatnot...

I won't spoil it yet...

I'm beginning to see the debate

[107barney]

Originally Posted by Ellie May

So if we can just get rid of the () after adding:

48/2(12)=
48/2x12

Then that means that the quadratic equation:
x=-b+or- the square root of b^-4(a)(c)/2(a)

Then why don't we divide everything by 2 in this case and then multiply by a? In this case we could remove the a from the () and write 2 x a, but it still has to be done separately from the rest of the problem.

If the real answer to the question is 288 then your writing of the quadratic equation is incorrect, you would have actually written this --

x = -b + or - the square root of b squared -4ac --> all that divided by 2

Multiplied by a over 1 meaning a/1

Otherwise, if the answer is 2, then you have correctly wrote out the quadratic equation.

I believe the quadratic equation has 2a as the entire denominator, which would give me the 288 answer to the question posted.

[kjc]

Originally Posted by 107barney

Huh?

I'll rephrase --

48÷2(9+3)

Answer:
I added 9 + 3 to get 12 to lose the parenthesis giving me
48÷2 x 12 and you have to work from L to R.

48 divided by 2 = 24 and 24 x 12 = 288

Not sure what you mean about using the two twice.

Oh gotcha... but...

48÷2(9+3) The 2(means 2 X what is in the () and they cannot be removed until the contents of the () are multiplied by the number in front of the (). That is a rule. Really. It can be done this way 2(12) or the Rule of Distribution which would be 2x9 + 2x3, or 18 + 6 = 24.

[107barney]

Originally Posted by kjc

Oh gotcha... but...

48÷2(9+3) The 2(means 2 X what is in the () and they cannot be removed until the contents of the () are multiplied by the number in front of the (). That is a rule. Really. It can be done this way 2(12) or the Rule of Distribution which would be 2x9 + 2x3, or 18 + 6 = 24.

It only matters what is INSIDE the parentheses....Once you solve what is inside, you can change the parenthesis to an asterisk and go from L to R to get 288.

x/y(4-2) is the same as x/y*2 NOT x/(y*2)