6/2*(1+2)=?

~~[MERIT]~~ · 04-29-2011, 01:53 PM

Quote:

Originally Posted by storymilo

You were correct until the bolded part. Just as division is the inverse of multiplication, multiplication is the inverse of division. It works both ways. Neither should be dealt with before other, unless they come first in the equation.

Regardless of left-to-right, Multiplication always takes precedence over Division, as Addition always does over Subtraction. You must simplify it into the most basic terms before performing the "left-to-right" mathematics. The correct order is as follows:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Applying that to the equation: 6/2*(1+2) will yield:

Parenthesis: 6/2*(1+2) = 6/2*(3)
Exponents: 6/2*(3)
Multiplication: 6/2*(3) = 6/6
Division: 6/6 = 1
Addition: 1 = 1
Subtraction: 1 = 1

THE ANSWER IS 1

Guybrush · 04-29-2011, 01:54 PM

To me, it looks like an expression simplifiable (is that a word?) to 3*3, so I'd say 9.

Burning Down · 04-29-2011, 01:55 PM

There aren't any exponents in the equation, though.

storymilo · 04-29-2011, 01:56 PM

Quote:

Originally Posted by oojay

Regardless of left-to-right, Multiplication always takes precedence over Division, as Addition always does over Subtraction. You must simplify it into the most basic terms before performing the "left-to-right" mathematics. The correct order is as follows:

Parenthesis
Exponents
Multiplication
Division
Addition
Subtraction

Applying that to the equation: 6/2*(1+2) will yield:

Parenthesis: 6/2*(1+2) = 6/2*(3)
Exponents: 6/2*(3)
Multiplication: 6/2*(3) = 6/6
Division: 6/6 = 1
Addition: 1 = 1
Subtraction: 1 = 1

THE ANSWER IS 1

Well I guess I'm not eloquent enough to simply convince you, so perhaps this will help?

Order of Operations

edit: check example three

Guybrush · 04-29-2011, 01:57 PM

This was pointed out earlier, but when I put it into google, I also get 9.

Burning Down · 04-29-2011, 01:57 PM

Quote:

Originally Posted by storymilo

Well I guess I'm not eloquent enough to simply convince you, so perhaps this will help?

Order of Operations

omgsh, there's even exercises on that page! Time to practice math!

storymilo · 04-29-2011, 01:59 PM

Quote:

Originally Posted by Burning Down

omgsh, there's even exercises on that page! Time to practice math!

Ha it's just the first google result when you search "order of operations." It's not meant to be demeaning.

~~[MERIT]~~ · 04-29-2011, 02:00 PM

Quote:

Originally Posted by storymilo

Yeah... oojay's fatal flaw is his conviction that multiplication is always done before division.

It is not a fatal flaw, it is a fact:

Quote:

The order of operations is a convention that tells us how to evaluate mathematical expressions (these could be purely numerical). The problem arises because expressions consist of operators applied to variables or values (or other expressions) that each demand individual evaluation, yet the order in which these individual evaluations are done leads to different outcomes.

A conventional order of operations solves this. One could technically do without memorizing this convention, but the only alternative is to use parentheses to group every single term of an expression and evaluate the innermost operations first.

For example, in the expression ab+c , how do we know whether to apply multiplication or addition first? We could interpret even this simple expression two drastically different ways:

Add b and c ,
Multiply the sum from (1) with a .
or

Multiply a and b ,
Add to the product in (1) the value of c .
One can see the different outcomes for the two cases by selecting some different values for a , b , and c . The issue is resolved by convention in order of operations: the correct evaluation would be the second one.

The nearly universal mathematical convention dictates the following order of operations (in order of which operators should be evaluated first):

Factorial.
Exponentiation.
Multiplication.
Division.
Addition.
Any parenthesized expressions are automatically higher ``priority'' than anything on the above list.
There is also the problem of what order to evaluate repeated operators of the same type, as in:

abcd
The solution in this problem is typically to assume the left-to-right interpretation. For the above, this would lead to the following evaluation:

(((ab)c)d)
In other words,

Evaluate ab .
Evaluate (1)/c .
Evaluate (2)/d .
Note that this isn't a problem for associative operators such as multiplication or addition in the reals. One must still proceed with caution, however, as associativity is a notion bound up with the concept of groups rather than just operators. Hence, context is extremely important.

Exponentiation is an exception to the left-to-right assumption, as it is evaluated right-to-left. That is, a ^b ^c is computed as

Evaluate b ^c .
Evaluate a ^(1).
Of course, this could also have been written as abc , and in this form can be thought of as evaluated ``highest to lowest''.

For more obscure operations than the ones listed above, parentheses should be used to remove ambiguity. Completely new operations are typically assumed to have the highest priority, but the definition of the operation should be accompanied by some sort of explanation of how it is evaluated in relation to itself. For example, Conway's chained arrow notation explicitly defines what order repeated applications of itself should be evaluated in (it is right-to-left rather than left-to-right)!

PlanetMath: order of operations

So once again:

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

THE ANSWER IS STILL 1

~~[MERIT]~~ · 04-29-2011, 02:04 PM

There seems to be disagreement with everyone's internet sources, and our own personal mathematical teachings. Whether this varies by country or textbook, I'm not sure. The order of operations is clearly different in each of our sources. Hmmm, what to do...

storymilo · 04-29-2011, 02:07 PM

I guess I'll stick to my way and you to yours? I've always been taught that multiplication does not take precedence over division. In fact I'm still being taught that. That link of yours is the only source I've ever seen that says otherwise, but maybe things are just different in other places.

edit: Nine is also the answer that comes up when I put the equation into my calculator.

04-29-2011, 01:54 PM	#22 (permalink)
Guybrush Juicious Maximus III Join Date: Nov 2008 Location: Scabb Island Posts: 6,525	To me, it looks like an expression simplifiable (is that a word?) to 33, so I'd say 9. __________________ Something Completely Different*

04-29-2011, 01:57 PM	#25 (permalink)
Guybrush Juicious Maximus III Join Date: Nov 2008 Location: Scabb Island Posts: 6,525	This was pointed out earlier, but when I put it into google, I also get 9. __________________ Something Completely Different

04-29-2011, 01:55 PM	#23 (permalink)
Burning Down The Music Guru. Join Date: Jun 2009 Location: Beyond the Wall Posts: 4,858	There aren't any exponents in the equation, though.

04-29-2011, 02:04 PM	#29 (permalink)
~~[MERIT]~~ Account Disabled Join Date: Nov 2004 Location: Missouri, USA Posts: 4,814	There seems to be disagreement with everyone's internet sources, and our own personal mathematical teachings. Whether this varies by country or textbook, I'm not sure. The order of operations is clearly different in each of our sources. Hmmm, what to do...

04-29-2011, 02:07 PM	#30 (permalink)
storymilo Music Addict Join Date: Jun 2009 Posts: 1,845	I guess I'll stick to my way and you to yours? I've always been taught that multiplication does not take precedence over division. In fact I'm still being taught that. That link of yours is the only source I've ever seen that says otherwise, but maybe things are just different in other places. edit: Nine is also the answer that comes up when I put the equation into my calculator.