Gian S.

asked • 08/25/16

60÷5(7-5)= 6 or not dont undwrstand

People say it 24 but I say six and try to see what is the correct way.

Tito E.

Order of operations = disorder of implied operations
Here is what i go by
60)5(2)=24
60/5(2)=6
60)5x2=24
60/5x2=24
 
 
You will see people argue about this all day. I can see why it is both. Of course I cannot concede that this 24 and not 6 but i can also understand why it is 24 and not six. The reason i think it is six is because of the way it was specifically written. O well that is why people hate math lol 
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09/07/17

Dfgh D.

use G-E-M-A
 
Grouping(so anything in parentheses brackets or absolute value
Exponents
Multiplication or division whichever come first from left to right 
Addition or subtraction whichever comes first from left to right
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10/25/17

3 Answers By Expert Tutors

By:

David W. answered • 08/25/16

Tutor
4.7 (90)

Experienced Prof

Noelle S.

This answer is not correct! You are taking the acronym PEMDAS too literally. Just because in the acronym PEMDAS or PPMDAS the M for multiplication comes before the D for division it does not mean multiplication should be done first. An acronym is just a guide to help you remember. The rules for PEMDAS are that when you complete the parentheses/exponents step multiplication and division step should be done from left to right in the order they appear in the equation, the same goes for addition and subtraction. 
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08/27/16

Eric P.

Kim is absolutely correct.  The parens have meaning and for sure change the way you need to solve the expression.  I had one guy try to tell me the parens are only there to make it easier to read.  Hoo boy.  This is what? 5 grade stuff at best.  Shocking to see how many people don't get it.  Even Google has it wrong!  Now if I could only figure out why I waste my time on stuff like this, I might have something...
 
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08/29/16

Mika E.

I say it's 6. 
 
It doesn't say that there's a multiplication sign in the middle of 5 and (7-2). Adding a sign there would make the equation different. It would be regrouped into:
 
60 ÷ 5 × ( 7 - 5 ) = ( 60 ÷ 5 ) ( 7 - 5 )
 
Which is different from the original equation.
 
But if no multiplication sign was added, it would be purely '60 divided by the product of 5 and 7 minus 2' which is 6.
 
60 ÷ 5 ( 7 - 2 )
60 ÷ 5 ( 2 )
60 ÷ 10
6
 
If you don't believe me, check the calculator. Look at the difference. Don't Google the answer. Google isn't always correct. 
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08/30/17

Brian N.

Just so you all are aware (just as stated in the first answer) a(b) is the exact same as a*b even if you were to look at it as "do parenthesis first" you are simply getting a product out of the two numbers which means multiplication. For the comment of put it into a calculator and get the answer please do because I have and 24 was the answer I got. My friend used a different calculator and got 6. As far as everyone should have been taught a number surrounded by parenthesis next to another number means you multiply them together. PEMDAS states multiplication and division are done as they appear from left to right in the equation.
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09/01/17

Mitchell B.

This question shows 3 groups of people.
Group 1: Remember PEMDAS as literal and multiply before dividing which gives an answer of 6 (which is the correct value but the wrong way to find it)
Group 2: Remember multiplication and division are inverse operations and work from left to right. This leads to an answer of 24, which is wrong however Iit is
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09/02/17

Mitchell B.

The right way to apply MD AS.   
Now we get the third group that remember that the term 5(7-5) is a monomial term that has been simplified from (35-25) and that you need to DISTRIBUTE the 5 back into the brackets to solve the brackets. (Yes you can use multiplication or addition to distribute however that is done in the Parenthesis step)
The common mis-step that people do is to put a 'hidden multiplier' inbetween the number and brackets then assume that it is ok to do so.
Most calculators will do the same
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09/02/17

David W.

Sorry, Mitchell, the steps to process 5(7-5) are 5(2), then 5*2;  they are not 5(7-5) to (35-25).
 
The scanner program step recognizes numbers (constants), variables, and operations [in a legal expression].  It puts the expression into a tree like this:
 
                         *
                      /   \
                    5     -
                         /   \
                        7    5
Then, the Reverse Polish notation is constructed by traversing the tree recursively [left subtree; right subtree; node].  For the expression 5(7-5), this is 5<paren>*. then 5 7 5 - *.
 
The evaluation of a Reverse Polish expression is unambiguous:
       Using a left-to-right scan
         If number, then Push it onto stack [use value for a variable]
         If operator, then pop last value(s), perform operation, push result back onto stack
       Continuer left-to-right scan
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09/02/17

Julie E.

The answer 6 is incorrect. Leaving the 2 in parentheses (2) doesn't make it a problem to be solved within parentheses. A number by itself isn't a problem to be solved. Since the 5 isn't within parenthesis with the two, the order of operations is to finish this problem from left to right. Multiplication and division are on equal standing. Addition and subtraction are also on equal standing in PEMDAS. 
60÷5(7-5)=60÷5×(7-5)
60÷5(2)=60÷5×2
After solving the problem within parentheses for this problem solve the rest from left to right. Rember multiplication and division are on equal standing which is why the rest of the problem is solved left to right. Solving first, the 5×2 or 5(2) before 60÷5 causes the answer to be incorrect. Left to right after solving the problem within parentheses is correct for PEMDAS.
12(2)=12×2
24
 
60÷5(7-5)
60÷5×2
12×2
24
 
P -      Parentheses
E -      Exponents
M,D - Multiplication, Division 
A,S -  Addition, Subtraction
 
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09/04/17

Jack M.

60÷5(7-5) = a÷b(c-b) = a÷(bc-b2)

Simple math. Brackets first means you have to redistribute the 5 into the brackets because there is no multiplier so the equation is not a÷b*1(c-b)

Therefor, 6 is the only acceptable answer.
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09/27/17

David W.

The rule named "Distributive Property of Multiplication over Addition" is a(b+c) = ab + ac.
 
When you say "distribute the 5" you are saying multiply the 5 by the 7 and then multiply the 5 by the -5.  This uses the word "multiply" twice, because that is what you do.  How can you say, "there is no multiplier????"
 
This is why "÷" is not usually used when expressions are on one line; the "/" is preferred.
 
And,  parentheses always make the order of operations unambiguous.
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09/27/17

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