# How do you insert parentheses to make #4*2-2^2 ÷9+2=6# true?

##### 2 Answers

#(4*2-2)^2 -: 9 + 2 = 6#

or better:

#((4*2-2)^2 -: 9)+2 = 6#

#### Explanation:

PEMDAS is a mnemonic for the following conventions of order of operations:

PParentheses.

EExponents.

MDMultiplication and Division - evaluated left to right.

ASAddition and Subtraction - evaluated left to right.

Note that multiplication and division have the same priority and addition and subtraction have the same priority.

Using PEMDAS (or BODMAS, etc.) it is sufficient to add just one pair of parentheses:

#(4*2-2)^2 -: 9 + 2#

#= (8-2)^2 -: 9 + 2#

#= 6^2 -: 9 + 2#

#= 36 -: 9 + 2#

#= 4 + 2#

#=6#

**Further considerations**

PEMDAS (or BODMAS, etc) are intended to help clarify the meaning of expressions involving arithmetic operations, but sometimes lead to confusion instead.

For example, what is the intended meaning of the following expression?

#6-:2(1+2)#

PEMDAS says that the division (

#(6-:2)(1+2) = 9#

Those unfamiliar with PEMDAS or having slightly varied rules would probably interpret it more like:

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

It would be better to add more parentheses to the expression to make the intended meaning clear.

Since the current question does not specify PEMDAS, and does not specify that only one pair of parentheses are allowed, it is probably better to add a second pair of parentheses to make it clear that you want the division performed before adding

#((4*2-2)^2 -: 9) + 2 = 6#

Historically the obelus

#(4*2-2)^2-: (9 + 2) = 36/11#

#### Explanation:

To insert parenthesis appropriately so that following is always true.

Step 1. From PEMDAS we know that

Step 2. Inspection reveals that exponent operator will get precedence over the

Step 3. Use brute force to place left parenthesis before

Step 4. We have only two places to put the left parenthesis.

(a)

(b)

Final result