Math Test

[jsharmon7]

Parentheses first. Then work the multiplication/division left to right.

The answer is 9.

WolframAlpha agrees:

6 ÷ 2 (2 + 1) = - Wolfram|Alpha

[ame]http://www.youtube.com/watch?v=fqs9DYisSsg[/ame]

 

[CathyInBlue]

It's called precedence. Addition and subtraction are of equal precedence. Multiplication and division are of equal precedence, which is a higher precedence than addition or subtraction. (Which is why the addition in the OP had to have its precedence raised by the use of a parenthetic subexpression.) When dealing with a string of operations from equal precedence operators, you always perform them in order from left to right. You would no more perform the following operation this way:

6-2+2*1 = 6-2+2 = 6-4 = 2

than you would do the OP's calculation and get an answer of 1. Division on the left happens before the multiplication on the right, just like the subtraction above happens before the addition above because of this same left-to-right order for operations of equal precedence.

Just for the hard of thinking, obviously, 6-2+2*1 = 6-2+2 = 4+2 = 6. Expressions like X + Y - Y are used to demonstrate cancelling of terms in algebra all the time. It's easier to recognize the "+ Y - Y" subexpressions and optimize them out of the calculations (they cancel each other out) rather than actually perform those calculations, getting no meaningful benefit for the effort expended.

 

[hornadylnl]

The correct answer is 1.
First, calculate what's inside parenthesis:
6 ÷ 2 (3) =
Second, calculate the multiplication (implied):
6 ÷ 6 = 1

Why? Because

6 ÷ 2 (2 + 1) =

is either
(A):

6
------------ = 1
2 (2 + 1)

OR
(B):

6
- X (2 + 1) = 9
2

A is correct. B is ridiculous. This is one reason why kids are failing in math.

Once the operation inside parentheses is completed, aren't the parentheses dropped?

 

[Bunnykid68]

Once the operation inside parentheses is completed, aren't the parentheses dropped?

Yes, you can drop the parentheses. Then you work from left to right.

 

[jtdet01]

Once the operation inside parentheses is completed, aren't the parentheses dropped?

The inclusion of the parenthesis implies multiplication of the value directly to the left, so this can not be ignored (so not immediately dropped). This multiplication occurs next.

This, a(b+c) shorthand implies: (a * (b+c))

Parentheses first. Then work the multiplication/division left to right.

The answer is 9.

WolframAlpha agrees:

6 ÷ 2 (2 + 1) = - Wolfram|Alpha

http://www.youtube.com/watch?v=fqs9DYisSsg

Cute Family Guy scene - love that seen - (so are you trying to imply something? When you imply something, it can't be ignored. No, I am not a jacka$$, just a geek).

WolframAlpha - garbage in / garbage out... the original equation is poorly written. To properly form the equation to represent the problem that OP is referring to, OP must include parenthesis to make it unambigous, such as:
(6 ÷ 2) (2 + 1) =

Sure, WolframAlpha agrees, and everything on the internet is 100% correct. They can't put anything on the internet that's not correct.

 

[steve666]

Bacon:

 

[Stschil]

I can't understand why any of you are arguing, the answer is obviously
Tax the rich

 

[CathyInBlue]

Better answer is to feed the homeless to the hungry.

 

[Double T]

The answer is actually one. The parenthesis are there also to multiply the 2 times the sum of the quotient contained therin.

6/2(2+1)
6/2(3)
6/6
1

Because...the equation can also be carried out like so:
6/2(2+1)
6/(4+2)
6/6
1

I think it is funny that people forget about that also. The answer can only be 1.

 

[cmj]

This is false. You would be correct if the equation was 6 + 2(2+1). Order of operations is law in mathematics. Every compiler, calculator and mathematician will tell you it is 9. There is a finite order in which mathematical operations occur, if this weren't the case math would become a Liberal Arts degree.

The answer is actually one. The parenthesis are there also to multiply the 2 times the sum of the quotient contained therin.

6/2(2+1)
6/2(3)
6/6
1

Because...the equation can also be carried out like so:
6/2(2+1)
6/(4+2)
6/6
1

I think it is funny that people forget about that also. The answer can only be 1.

 

[cmj]

Now seeing it your way, the notation just sucks.

 

[jsharmon7]

Cute Family Guy scene - love that seen - (so are you trying to imply something? When you imply something, it can't be ignored. No, I am not a jacka$$, just a geek).

WolframAlpha - garbage in / garbage out... the original equation is poorly written. To properly form the equation to represent the problem that OP is referring to, OP must include parenthesis to make it unambigous, such as:
(6 ÷ 2) (2 + 1) =

Sure, WolframAlpha agrees, and everything on the internet is 100% correct. They can't put anything on the internet that's not correct.

That wasn't directed at you, or I would have quoted your post. It was directed at the disagreement these questions generate. Also, as far as garbage in/garbage out, it was solving (as was I) the equation as written. Whether the equation is written poorly or not is of no consequence. People are solving it as written, not as it should have been written. Relax, it's just the internet.

 

[Ted]

This entire thread, as well as the lack of ability to perform math in this country, is Bush's fault.

Bush Derangement Syndrome - Wikipedia, the free encyclopedia

 

[Double T]

There is a finite order, but please explani why one cannot perform the second equation.

This is false. You would be correct if the equation was 6 + 2(2+1). Order of operations is law in mathematics. Every compiler, calculator and mathematician will tell you it is 9. There is a finite order in which mathematical operations occur, if this weren't the case math would become a Liberal Arts degree.[/QUOTE

 

[kyotekilr]

division is not an algebraic operation. It fails the commutative property. When you see division it really means to multiply by the reciprocal. Therefore, you should write it as a rational number.

6/2(2+1) were 6 is the numerator and 2(2+1) is in the denominator.

The answer is 1
I am a math teacher I am sure I am correct

 

[cmj]

There is a finite order, but please explani why one cannot perform the second equation.

This is false. You would be correct if the equation was 6 + 2(2+1). Order of operations is law in mathematics. Every compiler, calculator and mathematician will tell you it is 9. There is a finite order in which mathematical operations occur, if this weren't the case math would become a Liberal Arts degree.

I see how you are thinking, and it doesn't help that the stated problem is ambiguously notated.

2(2+2) can be done (2+2) * 2 = 8, or using distribution as you prefer.. It's the same answer. The problem lies when you add multiple problems in one equation. You should ALWAYS follow the order of operations.

1. Parenthesis 2. Exponents 3. Multiplication/Division (left to right) 4. Addition/Subtraction (left to right).

Distribution is most commonly used when the data inside the parenthesis is coupled with a variable (since you can't add unlike terms). There are no variables in the equation so you would follow order.

 

[cmj]

division is not an algebraic operation. It fails the commutative property. When you see division it really means to multiply by the reciprocal. Therefore, you should write it as a rational number.

6/2(2+1) were 6 is the numerator and 2(2+1) is in the denominator.

The answer is 1
I am a math teacher I am sure I am correct

This would only be the case if the equation were notated 6/(2(2+1))

It's really a case of ****ty notation as stated before. Following procedure literally (which you should ALWAYS do) the answer is 9

 

[GodFearinGunTotin]

No subject is ever too frivolous to generate pages and pages of debate on INGO

 

[Phil502]

Don't you need extra parenthisis on the second half to get 1 as an answer, otherwise it's written poorly.


( 6 / 2 ) * ( 1 + 2 ) =

or

6 / [ 2 ( 1 + 2 ) ] =

Using the standardized order of operations...
6 / 2 ( 1 + 2 )
6 / 2 ( 3 ) or 6 / 2 * 3
Answer = 9

Using parenthetical implications via multiplication by juxtaposition and the distributive property...
6 / 2 ( 1 + 2 )
6 / [ ( 2 * 1 ) + ( 2 * 2 ) ]
6 / 6
Answer = 1

 

[kyotekilr]

This would only be the case if the equation were notated 6/(2(2+1))

It's really a case of ****ty notation as stated before. Following procedure literally (which you should ALWAYS do) the answer is 9

No you are wrong. sorry

First it is not an equation, it is an expression
second division fails the commutative property

Think about it does 1 divided by 3 = 3 divided by 1. of course not.

However does 3 * 1/3 = 1/3* 3 yes

working from left to right is not mandatory. Often it is not the easiest route.

in this case left to right does not even matter since it should be written as a quotient i.e rational number


When you see division you multiply by the reciprocal.