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What is the Answer to This Math Problem?

Rytex

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Location
Random house in Texas.
No, I am not trolling. I want to see how much discussion I can get over a very controversial math problem. So, that being said, what is the answer to this problem?

48÷2(9+3) = ?

Be sure to explain why your answer is 2 or 288.

EDIT: This also works with 6÷2(1+2)=? where the answers are 1 or 9.
 
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Nicole

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Location
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48/2(9+3)=?

Due to order of operations, the parentheses come first:

(9+3)=12

Bring down the rest of the problem:

48/2*12

Order of operations says to go left to right:

48/2=24

Bring the problem down:

24*12=288

I don't see the controversy. Unless I'm missing something, which is possible. :bleh:

The same process applies to the second problem:

6÷2(1+2)=?

(1+2)=3

6÷2*3

6÷2=3

3*3=9
 
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Ninten*

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48÷2(9+3)
Order of operations:
Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction
aka PEMDAS

9+3=12
48/2*12
24*12
288

I think I see the controversity. If you use the distributive property instead, it gives another answer
48/2(9+3)
Ignore the 48 for now.
(2*9=18)+(2*3=6)
6+18=24
48/24=2

I think that the distributive property should only be used if you don't know one of the numbers. Might make things easier.
 

zeldahuman

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48÷2(9+3) = ?

Using the Distributive Property on the Parentheses:
48÷(2*9)+(2*3) = ?
48÷18+6 = ?

Using PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, Subtraction), Division comes next:

2.6 + 3 = 5.6

***
48÷2(9+3) = ?

Using PEMDAS, everything in Parenthese goes first:
48÷2*12 = ?

Next comes Multiplication/Division, going left to right:

24*12 = 288

There are lots of ways to solve this.
 

Kybyrian

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Didn't I already answer this one?
Look at it one way, guys. First off, if you were using the distributive problem, it would come out like this:

48/2(9+3)
48/18+6

Now, stop right there. After distributing there are NO MORE PARENTHESES. This is true of the distributive property. Now, using the distributive property was wrong in the first place, but now I'm going to show you why it's even more erroneous with the possible answers we were provided. After distributing we get 18+6. The ORDER OF OPERATIONS STILL APPLIES.

48/18 = 2.67
2.67 + 6 = 8.67

Not only was it wrong to use the distributive property in the first place, but after distributing you did the problem completely wrong.

The correct answer is 288.
 
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Rytex

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Distributive property is incorrect in this case. When you do the distributive property, not only do you multiply the outside number by both inside numbers, it is still considered one quantity in parentheses. Therefore, 48/18+6 is incorrect. It would have to be 48/(18+6). Again, there are only two possible answers to this problem.

And I just had a flash of inspiration. I am going to the Math Department at my college today and presenting them with this problem. I want to see how huge a discussion I can get from Doctors of Mathematics over this.
 
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Actually I want to point out that the distributive property will work on both of these.

For the first one 48/2(9+3).
You realize that you have to multiply the quantity (9+3) by the quantity 48/2, or you would get 24(9+3)=24*9+24*3=216+72=288
Or you can even rewrite it as 48/2*(9+3)/1=48(9+3)/2=(48*9+48*3)/2=576/2=288

The same would work for the second problem.
 

Kybyrian

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Didn't I already answer this one?
Wait a minute, I did that wrong...

48÷2(9+3) = ?

24(9+3) = ?

216 + 72 = 288 :yes:

This also works if you do utilize the distributive property. It's still multiplication/division from left to right. Divide 48 by two first and then distribute, it's just multiplication.
 

Rytex

Resident Netizen
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Location
Random house in Texas.
You misunderstand. The Distributive property works, just not in the way you all were doing it. I'm taking College Algebra and they made a big deal about that, so I don't forget it.

Btw, the professors laughed when I presented it and said that a few others had decided they wanted to troll them with the same problems.
 

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