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12÷2(6-7+4)x2=

What is the correct answer for:

12÷2(6-7+4)x2=

Comments

Wow. I am surprised by the number of people who did not get this problem correct; the answer is 36. Here is how you do the problem.

12 ÷2(6-7+4) x2=?

Remember to use the sentence, "Please Excuse My Dear Aunt Sally".

P= Parenthesis (6-7+4). When you do what is in the parenthesis first you are left with 3.

12÷2(3)x2.

The next part is Excuse which is exponents. We do not have any to worry about so we move on to "My" which is for Multiplication.

Multiplication includes division. We move from left to right. 12÷2

6(3)x2

18 x 2 =

36

--------
So the entire process looks like the following:
12 ÷ 2 (6 - 7 +4) x2
12 ÷ 2 (3) x 2
6(3) x 2
18 x 2
36

Hope that helps someone.

why would it not be:
 
12 ÷ 2 (6-7+4) x2
12 ÷ 2 ( 3) *2
12÷ 2 * 6
12 ÷ 12
1
 
I was always taught multiplication is done FIRST????\
 
Thanks!
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3 Answers

Emily S. is right on the money.  For students new to this concept (order of operations) we teach the sentence, "Please excuse my dear aunt Sally."  Each word representing an operation to be used left to right.  THe only reason this is done is so we can all get the same answer.

In the phrase "Please Excuse My Dear Aunt Sally" each first letter stands for an operation like this "Parenthesis Exponents Multiplication OR Division Addition OR Subtraction".

So, in a problem, you look first for parenthesis -- 12÷2(6-7+4)x2 -- then you solve what is inside of the inner most set of parenthesis. Here, we only have one set of parenthesis, so we solve that. Because there are two operations inside of the parenthesis, and both of them are addition OR subtraction, we just solve it working left to right.

(6-7+4) ==> (-1+4) ==> (3)

If inside the parenthesis, there was an addition/subtraction first and then a multiplication/division, you would still solve the multiplication/division first, as in the order of operations (e.g. (100-25x3) ==> (100-75) ==> (25) )

Next, we look for exponents -- 12÷2(3)x2 -- because there are no exponents here, we move to the next step. 

Looking at the equation, all that's left to do is either multiplication OR division so we work the problem from left to right. 

12÷2(3)x2 ==> 6(3)x2 ==> 18x2 ==> 36

If there was adition or subtraction afterwords, you would finish solving the equation from left to right based on what shows up first. 

 

 

TL;DR -- In the phrase "Please Excuse My Dear Aunt Sally" each first letter stands for an operation like this "Parenthesis Exponents Multiplication OR Division Addition OR Subtraction". Do them in that order. 

Just Math:

12÷2(6-7+4)x2 ==> 12÷2(-1+4)x2 ==> 12÷2(3)x2 ==> 6(3)x2 ==> 18x2 ==> 36

 

When answering this question, keep in mind using the correct order of operations (parenthesis, exponents, multiply/divide left to right, add/subtract left to right).  Begin with the parenthesis:  6-7+4 = -1+4 = 3.  Then you have 12÷2(3)X2.  12÷2 = 6, so now you have 6(3)X2.  Multiply 6 by 3 and you have 18X2.  So the final answer is 36.

Comments

Here is what NO ONE seems to understand about this problem....


12 divided by 2 IS NOT what this problem is asking.  It is asking for 12 divided by THE PRODUCT of 2 (times what is in the parentheses)... you must FIRST use the distributive property. Which means you must not only compute (6-7+4), you then have to distribute the 2 over that product.  If there was a x between the 2 and the () then PMDAS would be the correct next step.  But there is no x sign.  So, you must distribute the 2 to the (3), which gives you 6.


What you are left with is 12 divided by 6... then times 2.

 

Answer is 4.

Well Google says you are WRONG Monica. And because there isn't a second set of parentheses it IS in fact 12 divided by 2 = 6, multiplied by 3 = 18, multiplied by 2 = 36. Plug it in to a Scientific calculator and it will tell you the same.