48÷2(9+3) = ????

[Spectrum]

Order of Operations

When expressions have more than one operation, we have to follow rules for the order of operations:

1. First do all operations that lie inside parentheses.
2. Next, do any work with exponents or radicals.
3. Working from left to right, do all multiplication and division.
4. Finally, working from left to right, do all addition and subtraction.

http://www.math.com/school/subject2/lessons/S2U1L2GL.html

48/2(9+3)
1. 9+3=12 48/2*12 read rule # 3 left to right
2. 48/2= 24
3. 24 *12 = 288

This has been stated over and over again. People just don´t understand the order of operations.

Here is another breakdown of it (from a math board).

The distributive property is simply multiplication in an expanded written form to, supposedly, allow for easier reading/understanding of what's going on. The reason you might incorrectly think that distribution holds a higher precedence in the order of operations is because it's only used by most people in algebra/geometry during high school and only taken to the extent of: 2x(4x + 7) + 8x^2(x -2) . As such, distribution for many may appear to be higher in the order of operations because 99% of the population only deals with it through adding/subtracting values that have been distributed (and multiplication is always performed before adding and subtracting). Distribution holds the same weight as multiplication in the order of operations because the distributive property is multiplication.

Also, whoever thinks there's something called an "implied parenthesis" is a fool. There's no such thing. There is an order of operations and there are parentheses.

The answer is 288.

 

[DarkVoid]

why would you get rid of the number in front of the () when it needs to be divided first according to the rules. The number in front of the () is actually 48/2.
If the problem says forty-eighty divided by two times the sum of 9 plus 3 why would you get rid of the 2 when its by multiplying when you just read that the problem ask for forty-eighty divided by twotimesthe sum of 9 plus 3

You are contradicting the problem

The Parentheses needs to go before anything else can be completed.


The End.

 

[praetor]

but as the equation is written 48 divided by 2(9+3). now 10/2(6+4) is not the same as 10÷2(6+4) which is not = (10/2)(6+4). Again the way the equation is written you will have 48÷2(12). 48÷2(12) is not (48/2)(12). 48÷2(12) is not 48/2 * 12.

take
x=9+3

y=48/2x
y=48/2(9+3)

the equation isnt 48/2 * x it is 48/2x. like it was stated earlier.

48÷2(12) reads 48 divided by 2 multiplied by 12.

following the order of operations, going from left to right, you would have to first start on the left and divide 48 by 2, which is 24 and then and only then you multiply by 12 which will give you 288.

 

[Rick Spanish]

why would you get rid of the number in front of the () when it needs to be divided first according to the rules. The number in front of the () is actually 48/2.
If the problem says forty-eighty divided by two times the sum of 9 plus 3 why would you get rid of the 2 when its by multiplying when you just read that the problem ask for forty-eighty divided by twotimesthe sum of 9 plus 3

You are contradicting the problem

No. Im simplifying the problem. If you're disputing the fact that you simplify when a number is naked in front of the Parentheses, there is nothing left to say. The problem is not valid until you simplify it. What you're doing is solving an invalid problem.

 

[Louis Koo]

This has been stated over and over again. People just don´t understand the order of operations.

Here is another breakdown of it (from a math board).

The distributive property is simply multiplication in an expanded written form to, supposedly, allow for easier reading/understanding of what's going on. The reason you might incorrectly think that distribution holds a higher precedence in the order of operations is because it's only used by most people in algebra/geometry during high school and only taken to the extent of: 2x(4x + 7) + 8x^2(x -2) . As such, distribution for many may appear to be higher in the order of operations because 99% of the population only deals with it through adding/subtracting values that have been distributed (and multiplication is always performed before adding and subtracting). Distribution holds the same weight as multiplication in the order of operations because the distributive property is multiplication.

Also, whoever thinks there's something called an "implied parenthesis" is a fool. There's no such thing. There is an order of operations and there are parentheses.

The answer is 288.

zactly.

i'm the resident dual ivy league Asian guy on this board. how dare anyone contradict what i say, especially about math?

 

[followup]

I did already
48/2(9+3)

=

48/2(9) + 48/2(3)
= 432/2 +144/2
=216+72
=288

another fatal mistake....I'll show you why (you were not goo at fractions, right?):
48/2(9+3) = 48/2 * 1/(9+3) = 48/(9+3) * 1/2
Remember when multiplying 2 fractions, your new numerator is numerator * numerator, and your new denominator is denominator * denominator
The way you have typed it above does not equal what you typed on the following line.

While distributing the 2, you are doing multiplication. The order of operations state that multiplication and division must be done in order from left to right. You can not multiply by 2 without first dividing 48 by 2.

if 9+3 = x

then
48÷2*x

equals
24*x = 288

not 24/x

Absolutely false...2*x is the same as 2x. You can not pick and choose which one divides 48. You must divide 48 by both of them--they are both in the denominator...

Exactly, I do not understand the logic that is being applied where people are ignoring the 2(9+3) portion. The distributive property necessitates that you multiply (9+3) by 2.

Any counterpoints?

Exactly. The distributive property supercedes all other rules because it applies to PARENTHESES it is not the same as multiplication of 2 numbers...

SO is there a difference between
48÷2*x
and
48÷2(x)

Like -2^2 = -4
and (-2)^2= 4

you are comparing apples & dominos. In the first example, there is no difference. In the second example you are comparing squaring a number and then multiplying it by -1 with squaring a negative number by itself.

the 2(9+3) portion is not being ignored. Putting 2 next to (9+3) simply means that you multiply 2 times the sum when it is time for the multiplication to take place according to the order of operations. Since 48/ 2 is to the left of 2*12, 48 / 2 must be done first. The () only serve to tell you to add 9 to 3 before you start multiplying and dividing.

wrong again. Putting the 2 in front of the parentheses means that you multiply whatever FUNCTION is inside of the parentheses by the number 2..... (9+3) is a FUNCTION that needs to be multiplied by 2 before you proceed with anything else

 

[tre2k4]

The Parentheses needs to go before anything else can be completed.


The End.

Whats in the parenthesis is solved already

 

[Rick Spanish]

The Parentheses needs to go before anything else can be completed.


The End.

As well as a naked number thats in front of it.

 

[Rick Spanish]

Whats in the parenthesis is solved already

No. It. Is. Not.

 

[followup]

The Parentheses needs to go before anything else can be completed.


The End.

you got it....you can not mmove forward until everything involving those parentheses gets dealt with...

 

[NightMare Paint]

It reiterates what Im saying that you solve the Parentheses first, then multiply by the number in front of it, then solve the equation. If you see something different you're seeing the world through cum colored glasses homes.

That was Mutual of Omaha Wild Homo

 

[Spectrum]

wrong again. Putting the 2 in front of the parentheses means that you multiply whatever FUNCTION is inside of the parentheses by the number 2..... (9+3) is a FUNCTION that needs to be multiplied by 2 before you proceed with anything else

Distribution holds the same weight as multiplication in the order of operations because the distributive property is multiplication.

 

[Rick Spanish]

you got it....you can not mmove forward until everything involving those parentheses gets dealt with...

Especially any numbers directly in front of it...

 

[tre2k4]

No. Im simplifying the problem. If you're disputing the fact that you simplify when a number is naked in front of the Parentheses, there is nothing left to say. The problem is not valid until you simplify it. What you're doing is solving an invalid problem.

Its still the same

1/2(5) is One divided over two times five
which is 2.5

48/2(12) is forty-eighty divided by two times 12
which is 288

Unless you are telling me 48/2(12) is not the same as 48÷2(9+3)

 

[followup]

This has been stated over and over again. People just don´t understand the order of operations.

Here is another breakdown of it (from a math board).

The distributive property is simply multiplication in an expanded written form to, supposedly, allow for easier reading/understanding of what's going on. The reason you might incorrectly think that distribution holds a higher precedence in the order of operations is because it's only used by most people in algebra/geometry during high school and only taken to the extent of: 2x(4x + 7) + 8x^2(x -2) . As such, distribution for many may appear to be higher in the order of operations because 99% of the population only deals with it through adding/subtracting values that have been distributed (and multiplication is always performed before adding and subtracting). Distribution holds the same weight as multiplication in the order of operations because the distributive property is multiplication.

Also, whoever thinks there's something called an "implied parenthesis" is a fool. There's no such thing. There is an order of operations and there are parentheses.

The answer is 288.

I'll only use this part of your example [2x(4x + 7)] because YOU definitely will not understand the 2nd part:
2x(4x + 7) = (8x^2) + (14x)...
2(9+3)=????
2(9) + 2(3) or 2(12)
(18+6)
24

 

[tre2k4]

you got it....you can not mmove forward until everything involving those parentheses gets dealt with...

INSIDE...INSIDE the()

Nothing says anything about the outside

 

[followup]

Distribution holds the same weight as multiplication in the order of operations because the distributive property is multiplication.

absolutely NOT. a parenthetical equation ALWAYS takes priority.
Another example:
2*3+4 vs 2(3+4)
Answers are 10 and 14, respectively. HUGE difference.....

 

[tre2k4]

I'll only use this part of your example [2x(4x + 7)] because YOU definitely will not understand the 2nd part:
2x(4x + 7) = (8x^2) + (14x)...
2(9+3)=????
2(9) + 2(3) or 2(12)
(18+6)
24

its simpler to just do 2(9+3)=2(12)

 

[followup]

INSIDE...INSIDE the()

Nothing says anything about the outside

absolutely NOT. a parenthetical equation ALWAYS takes priority.
Another example:
2*3+4 vs 2(3+4)
Answers are 10 and 14, respectively. HUGE difference.....

get it? a factor of a parenthetical equation is still a parenthetical equation and takes priority...

 

[Dragonfly Jones]

Especially any numbers directly in front of it...

lol stop adding that new rule you just made up. Nowhere in the order of operations does it say that. It says inside the parentheses only. Then from left to right multiplication and division. If you follow the rules you get 288. If you make your own rule/ law you get 2. 2(9+3) by it self is 24 but when you have 48/2(9+3) it's 48/2*12. If the problem was this 48/(2(9+3)) then the answer is two and everything you have been saying is correct. The only parentheses in this problem is (9+3) That is the only math that has to be done first. Stop multiplying the 2 with it. The 2 is not inside the parentheses.

 

[followup]

its simpler to just do 2(9+3)=2(12)

LOL!!! and what does that equal????????

*holding my breath*

 

[spider705]

man even babies is arguing over this shit................

 

[praetor]

another fatal mistake....I'll show you why (you were not goo at fractions, right?):
48/2(9+3) = 48/2 * 1/(9+3) = 48/(9+3) * 1/2
Remember when multiplying 2 fractions, your new numerator is numerator * numerator, and your new denominator is denominator * denominator
The way you have typed it above does not equal what you typed on the following line.

Absolutely false...2*x is the same as 2x. You can not pick and choose which one divides 48. You must divide 48 by both of them--they are both in the denominator...

Exactly. The distributive property supercedes all other rules because it applies to PARENTHESES it is not the same as multiplication of 2 numbers...

you are comparing apples & dominos. In the first example, there is no difference. In the second example you are comparing squaring a number and then multiplying it by -1 with squaring a negative number by itself.

wrong again. Putting the 2 in front of the parentheses means that you multiply whatever FUNCTION is inside of the parentheses by the number 2..... (9+3) is a FUNCTION that needs to be multiplied by 2 before you proceed with anything else

the only function that needs to be processed is what's INSIDE the parentheses. That's what the parentheses are for. Writing a number next to a parenthesis, a variable, or anything else is just short hand for multiplication. And just like every other part of the equation, multiplication and division must be done from left to right.

Why has no one provided proof that a number in front of parentheses must be multiplied before anything else can be done????????

 

[Louis Koo]

Especially any numbers directly in front of it...

 

[Dragonfly Jones]

get it? a factor of a parenthetical equation is still a parenthetical equation and takes priority...

correct now with that same problem put a 10/ in front and what do you come up with? left to right.

 

[Rick Spanish]

lol stop adding that new rule you just made up. Nowhere in the order of operations does it say that. It says inside the parentheses only. Then from left to right multiplication and division. If you follow the rules you get 288. If you make your own rule/ law you get 2. 2(9+3) by it self is 24 but when you have 48/2(9+3) it's 48/2*12. If the problem was this 48/(2(9+3)) then the answer is two and everything you have been saying is correct. The only parentheses in this problem is (9+3) That is the only math that has to be done first. Stop multiplying the 2 with it. The 2 is not inside the parentheses.

I made it up when I just posted an example from a Math site doing the exact same thing? You're delusional homes.


The 2 is simplified with the Parentheses. The resulting answer of the equation is 2. End Story.

 

[followup]

zactly.

i'm the resident dual ivy league Asian guy on this board. how dare anyone contradict what i say, especially about math?

worst math I've ever seen by an Asian LOL....you definitely did not earn degrees in anything scientific or mathematical Sorry.

 

[Dota]

yes I'm serious. If so then (12) = 12.

So 48÷2(9+3) = 48÷2(12) = 48÷2*12

after that is is LEFT TO RIGHT for multiplication OR division.

Seriously is there anywhere on the internet where you can place bets on this?

 

[Spectrum]

I'll only use this part of your example [2x(4x + 7)] because YOU definitely will not understand the 2nd part:
2x(4x + 7) = (8x^2) + (14x)...
2(9+3)=????
2(9) + 2(3) or 2(12)
(18+6)
24

Listen followup.

Take a deep breath and re-read what was posted. Furthermore, I´ve been here long enough to have earned a reputation in terms of comprehension...especially in regards to technical problems. So you can swallow that talk.

You don´t even need to argue against me. Make your statement against the rule: order of operations.

 

[Rick Spanish]

Wow. You hard headed niggas are hilarious...

 

[Louis Koo]

worst math I've ever seen by an Asian LOL....you definitely did not earn degrees in anything scientific or mathematical Sorry.

nope. just undergrad dual major in finance and stats, and then a masters in accounting with a tax minor.

 

[Louis Koo]

This thread will top the the "Is a house an asset?" thread for all time ignorance

 

[tre2k4]

lol the answer 2
Its 2 if its true that 2 times (9+3) outranks division

Im done

 

[followup]

correct now with that same problem put a 10/ in front and what do you come up with? left to right.

K. I'll make it EXTRA clear for you what the difference is? When you get it let me know
The 2 different equations: 2*3+4 vs 2(3+4)

First: 10/2*3+4 = 5*3+4= 15+4 = 19 (multiplication and division are equal and both take priority over addition. there are no parentheses in this equation. In short, you can perform the function from left to right)

Second: 10/2(3+4) = 10/[2(3+4)] = 10/[2(7)] = 10/14 = 5/7 (parentheses take priority over EVERYTHING. you must get rid of the complete function before you do anything else)

Now, let's replace the (3+4) with an x to simplify things:
10/2(x) = 10/2x = 5/x
If x=(3+4) then 5/x = 5/(3+4) = 5/7.

 

[Rick Spanish]

nope. just undergrad dual major in finance and stats, and then a masters in accounting with a tax minor.

And you cant process simple math? Sound like some bullshit you just made up homes...