Order of Operation problem

Question

There are 89 comments about this math problem on FB. 

 

20/2(5+5)=

 

the answers include 0, 1, and 100

 

no wonder many of our kids have trouble 

with math when the adults in their lives can't get the correct answer. 

 

At the time of this edit there are four answers. And once again they split 2 for 100, and 2 for something else. One person providing a questionable/wrong answer 

 

is a PhD candidate. Hopefully not in anything dealing with basic math. 

 

The problem presented is the problem. The task was to explain this problem. You do not have the luxury of moving or adding parentheses for that will in most cases change the problem, with the exception being grouping for clarity 20/2(5+5)=(20/2)•(5+5)

20/(2•10) does not equal the above problems nor does it equal 20/(2•5)+5

Changing the grouping and the order you perform the math operations creates a different problem with the same digits involved.

 

Answer 1

As given, the answer is 100. 

 

It can be better visualized by including some symbols that are normally implied, and adjusting the way the faction is viewed.

 

20/2 (5+5) = 20 * (5+5) = 20 * (10) = 200 = 100

                    ------------         -------          -----

                           2                   2                2

  

 

If the question is instead given as 20/(2*(5+5)), then the answer would be 1.

Answer 2

Use PEMDAS.

 

Parenthesis

Exponents

Multiply or divide from left to right

Add or subtract from left to right.

 

 

First, we deal with the parenthesis.

 

20 / 2(10) =

 

 

Then we divide.

 

10(10)

 

 

The final result is then 100.

Answer 3

it's not the kids and it's not the parents, it's the person who wrote the problem

the problem is ambiguous

whoever wrote the problem did not write it properly; the person left out a set of parentheses or some other grouping symbol

it should have been written in one of two ways:

(20/2)(5+5) or 20/[2(5+5)]

order of operations

1 grouping symbols (parentheses, brackets, braces, or the fraction bar)

2 exponentiation (raise to a power)

3 multiplication and division in order from left to right whichever occurs first

4 addition and subtraction in order from left to right whichever occurs first

(20/2)(5+5)=(10)(10)=100

20/[2(5+5)]=20/[2(10)]=20/[20]=1

the answer could be 100 or it could be 1, depending on where you put the parentheses

 

 

 

Answer 4

That depends on how the question is written originally. 

PEMDAS Please Excuse My Dear Aunt Sally is a neuemonic that describes the order of operation. It's stands for Parentheses Exponent Multiply Divid Add Subtract. This is the order you must follow. If the (5+5) was intended to be in the numerator (top) then

(20/2)*(5+5)=(20/2)*10=10*10=100. If the (5+5) is in the denominator then 20/(2*(5+5))= 20/(2*10)=20/20=1. If the equation is in a line as you wrote, I would assume that the (5+5) was in the numerator (the top of the fraction).